The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 6.00 s, at which time it is turning at 5.00 rev/s. At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub smoothly slows to rest in 13.0 s. Through how many revolutions does the tub turn while it is in motion?

Answers

Answer 1

Answer:

16.035 revolutions

Explanation:

Part 1:

t = 6 s, f0 = 0 , f = 5 rps,

Let the number of revolutions be n1.

Use first equation of motion for rotational motion

w = w0 + α t

2 x 3.14 x 5 = 0 + α x 6

α = 5.233 rad/s^2

Let θ1 be the angle turned.

Use second equation of motion for rotational motion

θ1 = w0 t + 12 x α x t^2

θ1 = 0 + 0.5 x 5.233 x 6 x 6 = 94.194 rad

n1 = θ1 / 2π = 94.194 / 2 x 3.14 = 15 revolutions

Part 2:

f0 = 5 rps, f = 0, t = 13 s

Let the number of revolutions be n2.

Use first equation of motion for rotational motion

w = w0 + α t

0 = 2 x 3.14 x 5 + α x 13

α = - 2.415 rad/s^2

Let θ2 be the angle turned.

Use third equation of motion for rotational motion

w^2 = w0^2 + 2 x α x θ2

0 = 2 x 3.14 x 5 - 2 x 2.415 x θ2

θ2 = 6.5 rad  

n2 = θ2 / 2π = 6.5 / 2 x 3.14 = 1.035 revolutions

total revolutions n = n1 + n2 = 15 + 1.035 = 16.035 revolutions


Related Questions

Suppose a 20-foot ladder is leaning against a building, reaching to the bottom of a second-floor window 15 feet above the ground. What angle, in radians, does the ladder make with the ground Round your answer to two decimal places

Answers

Final answer:

To find the angle, in radians, that the ladder makes with the ground, we can use trigonometry. The length of the ladder can be found using the Pythagorean theorem, and the angle can be calculated as the arcsine of the ratio of the height of the building to the length of the ladder. The angle is approximately 0.6435 radians.

Explanation:

To find the angle, in radians, that the ladder makes with the ground, we can use trigonometry. The ladder, the ground, and the building form a right triangle. The ratio of the opposite side (the height of the building) to the hypotenuse (the length of the ladder) is equal to the sine of the angle. Using this information, we can calculate the angle in radians.

First, we need to find the length of the ladder using the Pythagorean theorem: l^2 = 20^2 + 15^2 = 625. Taking the square root of both sides, we find that the length of the ladder is 25 feet.

The sine of the angle can be calculated as the ratio of the height of the building to the length of the ladder: sin(angle) = 15/25 = 0.6. Taking the arcsine (inverse sine) of 0.6, we find that the angle in radians is 0.6435 (rounded to two decimal places).

Learn more about Trigonometry here:

https://brainly.com/question/11016599

#SPJ3

It is desiredto FDM 30voice channels (each with a bandwidth of 4.5KHz) along with a guard band of 0.8KHz. Ignoring a guard band before the first channel and the one after the last channel, what is the total bandwidth, in KHz,required for such a system.

Answers

Answer:

Total bandwidth required  = 158.2 KHz

Explanation:

given data:

number of channel 30

bandwidth of each channel is 4.5 KHz

bandwidth of guard band 0.8 KHz

According to the given information, first guard band and the guard band after last channel should be ignored, therefore we have total number of  29 guard band.

As per data, we can calculate total bandwidth  required

total bandwidth = 30*4.5 + 29*0.8

total bandwidth required  = 158.2 KHz

Two long, straight wires are parallel and are separated by a distance of d = 0.210 m. The top wire in the sketch carries current I1 = 4.00 A , toward the right, and the bottom wire carries current I2 = 5.90 A , also to the right. At point P, midway between the two wires, what are the magnitude and direction of the net magnetic field produced by the two wires?

Answers

Answer:

[tex]1.88\cdot 10^{-5} T[/tex], inside the plane

Explanation:

We need to calculate the magnitude and direction of the magnetic field produced by each wire first, using the formula

[tex]B=\frac{\mu_0 I}{2\pi r}[/tex]

where

[tex]\mu_0[/tex] is the vacuum permeability

I is the current

r is the distance from the wire

For the top wire,

I = 4.00 A

r = d/2 = 0.105 m (since we are evaluating the field half-way between the two wires)

so

[tex]B_1 = \frac{(4\pi\cdot 10^{-7})(4.00)}{2\pi(0.105)}=7.6\cdot 10^{-6}T[/tex]

And using the right-hand rule (thumb in the same direction as the current (to the right), other fingers wrapped around the thumb indicating the direction of the magnetic field lines), we find that the direction of the field lines at point P is inside the plane

For the bottom wire,

I = 5.90 A

r = 0.105 m

so

[tex]B_2 = \frac{(4\pi\cdot 10^{-7})(5.90)}{2\pi(0.105)}=1.12\cdot 10^{-5}T[/tex]

And using the right-hand rule (thumb in the same direction as the current (to the left), other fingers wrapped around the thumb indicating the direction of the magnetic field lines), we find that the direction of the field lines at point P is also inside the plane

So both field add together at point P, and the magnitude of the resultant field is:

[tex]B=B_1+B_2 = 7.6\cdot 10^{-6} T+1.12\cdot 10^{-5}T=1.88\cdot 10^{-5} T[/tex]

And the direction is inside the plane.

The magnitude and direction of the net magnetic field generated by the two wires will be [tex]1.55\times 10^{-8}[/tex].

What is magnetic field strength?

The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as induced magnetic field strength .it is denoted by B.

[tex]B = \frac{u_00I}{2\pi r}[/tex]

(I) is the current

r is the distance from the probe

B is the induced magnetic field

r denotes the distance between the wire and the object.

[tex]u_0[/tex] is the permeability to vacuum

For magnetic field in the top wire

Given

0.105 m = r = d/2

[tex]B_1= \frac{4\pi\times10^{-7}\times4.00}{2\pi \times 0.105}[/tex]

[tex]\rm{B_1=7.6\times 10^{-6}}[/tex] T

As the current to the left other fingers wrapped around the thumb showing the direction of the magnetic field lines.

Given data for bottom wire

I= 5.90 A

r = 0.105 m r = 0.105 m r = 0.105 m

[tex]B_2= \frac{4\pi\times10^{-7}\times5.90}{2\pi \times 0.105}[/tex]

[tex]\rm{B_2=1.12 \times 10^-5[/tex] T

As the current to the left other fingers wrapped around the thumb showing the direction of the magnetic field lines. The field lines direction at point P is also inside the plane.

The megnitude of the resultant magnetic field be the sum of both the field

[tex]\rm{B=B_1+B_2}[/tex]

[tex]\rm{B=7.6\times 10^{-6}+ 1.12\times 10^{-5}}[/tex]

[tex]B = 1.88\times 10^{-5}[/tex] T

Hence The megnitude of the resultant magnetic field be the sum of both the fields  [tex]1.88\times 10^{-5}[/tex]T.

To learn more about the strength of induced magnetic field refer to the link;

https://brainly.com/question/2248956

By how much will the length of a chicago concrete walkway that is 18 m long contract when the equipment drops from 24 degrees celcius in July to (-16 degrees celcius) in Janruary?

Answers

Answer:

Contraction of Chicago concrete walkway = 8.64 x 10⁻³ m

Explanation:

Thermal expansion or compression is given by ΔL = LαΔT

Here Length of Chicago concrete walkway, L = 18 m

         Change in temperature, ΔT = (-16 - 24) = -40 °C

         Coefficient of thermal expansion for concrete, α = 12 x 10⁻⁶ °C⁻¹

Substituting

    ΔL = LαΔT = 18 x 12 x 10⁻⁶ x (-40) = -8.64 x 10⁻³ m

Contraction of Chicago concrete walkway = 8.64 x 10⁻³ m

The steady-state diffusion flux through a metal plate is 7.8 × 10-8 kg/m2-s at a temperature of 1220˚C ( 1493 K) and when the concentration gradient is -500 kg/m4. Calculate the diffusion flux at 1000˚C ( 1273 K) for the same concentration gradient and assuming an activation energy for diffusion of 145,000 J/mol.

Answers

Final answer:

To calculate the diffusion flux at 1000˚C for the same concentration gradient, use the Arrhenius equation.

J ≈ 2.4 × 10-12 kg/m2-s

Explanation:

To calculate the diffusion flux at 1000˚C (1273 K) for the same concentration gradient, we can use the Arrhenius equation:

J = J0 * exp(-Q/RT)

Where J is the diffusion flux, J0 is the pre-exponential factor, Q is the activation energy for diffusion, R is the gas constant, and T is the absolute temperature.

Given that the diffusion flux at 1220˚C (1493 K) is 7.8 × 10-8 kg/m2-s and the activation energy for diffusion is 145,000 J/mol, we can calculate the diffusion flux at 1000˚C as:

J = (7.8 × 10-8) * exp(-145000/(8.314*1273))

J ≈ 2.4 × 10-12 kg/m2-s

Learn more about Diffusion here:

https://brainly.com/question/33319237

#SPJ12

Final answer:

To calculate the steady-state diffusion flux at a different temperature, use the Arrhenius equation to find the diffusion coefficients at the two temperatures, and find the ratio based on the fact that the diffusion flux is proportional to the diffusion coefficient when the concentration gradient is constant. Input the known values into the equation to solve for the unknown diffusion flux.

Explanation:

The steady-state diffusion through a metal plate can be calculated using the Arrhenius equation, which relates the diffusion coefficient (D) to temperature. The equation is D = D0e^-(Q/RT), where D0 is the pre-exponential factor, Q is the activation energy for diffusion, R is the gas constant and T is the temperature in K.

Given that the diffusion flux (J) is defined as J = -D×(dc/dx), where dc/dx is the concentration gradient. We can find that when the concentration gradient remains the same, the ratio of the two diffusion fluxes at different temperatures can be represented as J1/J2 = D1/D2.

Substitute the Arrhenius equation into the ratio, we get J1/J2 = e^(Q/R)×(1/T1-1/T2). Then you can use the given values, namely Q = 145,000 J/mol, R = 8.314 J/(mol×K), and temperatures T1 = 1493K , T2 = 1273K, as well as the known J1, to calculate J2.

Learn more about Steady-state Diffusion here:

https://brainly.com/question/9128896

#SPJ11

A solenoid has a radius Rs = 14.0 cm, length L = 3.50 m, and Ns = 6500 turns. The current in the solenoid decreases at the rate of 79.0 A/s. A circular coil with a single turn and radius rc = 20.0 cm encircles the solenoid with its plane perpendicular to the axis of the solenoid. Determine the magnitude of the average induced electric field in the coil.

Answers

Final answer:

The magnitude of the average induced electric field in the coil, encircling a solenoid with given dimensions and a decreasing current of 79.0 A/s, is approximately [tex]\(1.80 \times 10^{-4}\)[/tex]volts per meter.

Explanation:

The induced electric field in the coil is determined by Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a closed loop is equal to the negative rate of change of magnetic flux through the loop. In this scenario, the solenoid serves as the primary coil, and the circular coil is the secondary coil.

The magnetic flux through a single turn of the circular coil is given by[tex]\(\Phi = B \cdot A\)[/tex], where is the magnetic field strength and  is the area of the coil. The magnetic field inside a solenoid is given by[tex]\(B = \mu_0 \cdot N_s \cdot I\)[/tex].

Substituting these expressions into the formula for magnetic flux, we get [tex]\(\Phi = \mu_0 \cdot N_s \cdot I \cdot A\).[/tex] The induced emf  is then given by Faraday's law: [tex]\(\mathcal{E} = -\frac{d\Phi}{dt}\)[/tex]. Taking the derivative with respect to time and using the given values, we find[tex]\(\mathcal{E} = -\mu_0 \cdot N_s \cdot A \cdot \frac{dI}{dt}\).[/tex]

Finally, the induced electric field in the coil is given by [tex]\(E = \frac{\mathcal{E}}{A}\)[/tex]. Substituting the values into this formula provides the magnitude of the average induced electric field in the coil, approximately[tex]\(1.80 \times 10^{-4}\)[/tex]volts per meter. This calculation yields a quantitative measure of the induced electric field strength in response to the changing current in the solenoid.

You are given two resistors, an ammeter, a voltmeter, and a voltage source. By connecting each resistor singly to the voltage source and taking voltage difference and current measurements on the single resistor, you find the following data for each resistor:

Resistor Voltage (V) Current (mA)
1 3.88 43.6
2 4.48 14.45

Using this data, first find the resistance of each resistor and then calculate the following:

(a) The current that would pass through the network of resistors if they were arranged in series and connected to an 7.65 V voltage source.
Iseries =
(b) The current through the circuit if the resistors were arranged in parallel and connected to the same 7.65 V source from part (a).Iparallel =

Answers

Try this solution, note, the resistance of each resistor is marked with green colour, the items (a) and (b) - with red colour.

By using Ohm's law,

a.) Current = 19.17 A

b.) Current = 110.6 A

We are given different voltages and currents for the two resistors.

First resistor:

Voltage [tex]V_{1}[/tex] = 3.88 v

Current [tex]I_{1}[/tex] = 43.6 A

By using Ohm's law, we can calculate [tex]R_{1}[/tex]

V = IR

Make R the subject of formula

R = V/I = 3.88/43.6

R = 0.08899 Ohms

Second resistor

Voltage [tex]V_{2}[/tex] = 4.48 v

Current [tex]I_{2}[/tex] = 14.45 A

By using Ohm's law, we can calculate [tex]R_{2}[/tex]

V = IR

Make R the subject of formula

R = V/I = 4.48/14.45

R = 0.3100 Ohms

a.) Whenever resistors are connected in series, the same current will pass through them

The total resistance in the resistors in series will be achieved by using the below formula

R = [tex]R_{1}[/tex] + [tex]R_{2}[/tex]

R = 0.08899 + 0.3100

R = 0.399 Ohms

By using Ohm's law:

V = IR

Make I the subject of formula

I = V/R = 7.65/0.399

I = 19.17 A

b.) Whenever resistors are arranged in parallel, the same voltage will be supplied to them.

The resultant resistor can be calculated by using the below formula

1/R = 1/[tex]R_{1}[/tex] + 1/[tex]R_{2}[/tex]

1/R = 1/0.08899 + 1/0.3100

1/R = 11.237 + 3.2258

R = 1/14.463

R = 0.069 Ohms

By using Ohm's law,

V = IR

Make I the subject of formula

I = V/R = 7.65/0.069

I = 110.6 A

Learn more here : https://brainly.com/question/18130319

What is the kinetic energy of the rocket with mass 15,000 kg and speed of 5200 m/s? A. 2.01 x 10^11 J B. 2.02x 10^11 J C. 2.03 x 10^11 J D. 2.04 x 10^11 J

Answers

C. [tex]E_{k}=2.03x10^{11}J[/tex]

The kinetic energy of a body is the ability to perform work due to its movement given by the equation [tex]E_{k}=\frac{1}{2}mv^{2}[/tex].

To calculate the kinetic energy of a rocket with mass 15000kg and speed of 5200m/s:

[tex]E_{k}=\frac{1}{2}(15000kg)(5200m/s)^{2}=202800000000J=2.03x10^{11}J[/tex]

Example: Alice is outside ready to begin her morning run when she sees Bob run past her with a constant speed of 10.0 m/s. Alice starts to chase after Bob after 5 seconds How far away is Bob when Alice starts running?

Answers

Answer:

The distance of bob when Alice starts running is 50 m.

Explanation:

Given that,

Speed v = 10.0 m/s

Time t = 5 sec

We need to calculate the distance

Using formula of distance

[tex]D=v\times t[/tex]

[tex]D=10\times5[/tex]

[tex]D=50\ m[/tex]

Hence, The distance of bob when Alice starts running is 50 m.

A photon has a momentum of 5.55 x 10-27 kg-m/s. (a) What is the photon's wavelength? nm (b) To what part of the electromagnetic spectrum does this wavelength correspond? the tolerance is +/-2%

Answers

Explanation:

It is given that,

Momentum of the photon, [tex]p=5.55\times 10^{-27}\ kg-m/s[/tex]

(a) We need to find the wavelength of this photon. It can be calculated using the concept of De-broglie wavelength.

[tex]\lambda=\dfrac{h}{p}[/tex]

h is the Planck's constant

[tex]\lambda=\dfrac{6.67\times 10^{-34}\ Js}{5.55\times 10^{-27}\ kg-m/s}[/tex]

[tex]\lambda=1.2\times 10^{-7}\ m[/tex]

or

[tex]\lambda=120\ nm[/tex]

(b) The wavelength lies in the group of ultraviolet rays. The wavelength of UV rays lies in between 400 nm to 10 nm.

Choose the statement(s) that is/are true about an electric field. (i) The electric potential decreases in the direction of an electric field. (ii) A positive charge experiences a force in the direction of an electric field. (iii) An electron placed in an electric field will move opposite to the direction of the field.

Answers

Answer:

A positive charge experiences a force in the direction of an electric field.

Explanation:

Electric field is defined as the electric force acting per unit positive charge. Mathematically, it is given by :

[tex]E=\dfrac{F}{q}[/tex]

We know that like charges repel each other while unlike charges attract each other. The direction of electric field is in the direction of electric force. For a positive charge the field lines are outwards and for a negative charge the electric field lines are inwards.

So, the correct option is (b) "A positive charge experiences a force in the direction of an electric field".

9) Two mirrors are at right angles to one another. A light ray is incident on the first at an angle of 30° with respect to the normal to the surface. What is the angle of reflection from the second surface?

Answers

Answer:

60°

Explanation:

In the given question it is given that the two mirrors perpendicular to each other.

The light ray will reflect off the first mirror with an angle of 30° (∠i= ∠r) and then arrive at the second mirror. Using geometry of the two mirrors and the fact that the angle between the two of them is 90°, the incident angle for second mirror is 60°, which will again equal to the angle of reflection.

hence, angle of reflection of second mirror is 60°

The angle of reflection from the second surface is (b) 60◦

Explanation:

Two mirrors are at right angles to one another. A light ray is incident on the first at an angle of 30° with respect to the normal to the surface. What is the angle of reflection from the second surface?

(a) 30◦

(b) 60◦

(c) 45◦

(d) 53◦

(e) 75◦

Reflection is the direction change of a wavefront at interface between two different media. The light ray (it is a line (straight or curved) that is perpendicular to the light's wavefronts and its tangent is collinear with the wave vector) will reflect off of the first mirror with an equal angle  of 30◦  then it arrives at the second mirror. By using the geometry (branch of mathematics that concerned with questions of shape, size, relative position of figures, and the properties of space) of the two  mirrors and the angle between the two of them is 90◦ , the  incident angle (the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence called the normal) for the second mirror is 60◦ that equal to the final angle of  reflection.

Learn more about mirrors https://brainly.com/question/13646048

#LearnWithBrainly

Your swimming pool is square and 5.8 m on a side. It is 4.2 m deep in the morning If the temperature changes by 24 degrees C during the afternoon, how much the depth of the water increase?

Answers

Answer:

The increases depth of the water is 0.021 m.

Explanation:

Given that,

One side of square = 5.8 m

Depth = 4.2 m

Temperature = 24°C

Coefficient of volume expansion for water[tex]\beta = 210\times10^{-6}\ /^{\circ}C[/tex]

We need to calculate the volume of the pool

[tex]V= 5.8\times5.8\times4.2[/tex]

[tex]V=141.288\ m^3[/tex]

Using formula of coefficient of volume expansion

[tex]\Delta V=\Beta V_{0}\times\Delta T[/tex]

If the temperature changes by 24 degrees C during the afternoon,

[tex]5.8\times5.8\times h=210\times10^{-6}\times141.288\times24[/tex]

[tex]h=\dfrac{210\times10^{-6}\times141.288\times24}{5.8\times5.8}[/tex]

[tex]h=0.021\ m[/tex]

Hence. The increases depth of the water is 0.021 m.

A 2 meter long bar has a longitudinal/axial wave speed of 5,000 m/s. If the bar is fixed at each end, what is the second natural frequency an for this system in rad/s? a. 12,450 b. 14,850 e 15,710 d. 16,800 e. 18,780 f. None of the above

Answers

Answer:

The second natural frequency an for this system is 15710 rad/s.

(e) is correct option.

Explanation:

Given that,

Length = 2 m

Wave speed = 5000 m/s

We need to calculate the second natural frequency

Using formula of Time period

[tex]T = \dfrac{L}{v}[/tex]

[tex]T=\dfrac{2}{5000}\ s[/tex]

We know that,

The frequency is the reciprocal of time period.

[tex]f=\dfrac{1}{T}[/tex]

[tex]f=\dfrac{5000}{2}[/tex]

[tex]f=2500\ Hz[/tex]

We know that,

[tex]1\ rad/s =\dfrac{1}{2\pi}\ Hz[/tex]

So, The frequency is in rad/s

[tex]f= 15710\ rad/s[/tex]

Hence, The second natural frequency an for this system is 15710 rad/s.

Two 10-cm-diameter charged rings face each other, 23.0 cm apart. Both rings are charged to + 10.0 nC . What is the electric field strength at the center of the left ring?

Answers

The question asks for the electric field strength at the center of a charged ring, which involves using physics concepts related to electric fields and charge distributions. An accurate calculation would require application of formulas for fields due to point charges distributed in a ring, or thorough integration techniques taught at high school level physics.

The subject of the question is Physics, and it pertains to the concept of electric fields created by charged objects. We are considering two identical rings, each with a positive charge of +10.0 nC, facing each other with a separation of 23.0 cm. What is required is to calculate the electric field strength at the center of the left ring. By the symmetry of the setup and since the charges are identical and positive, the electric field at the center of the left ring due only to it would be zero because there is no charge displacement leaving the right ring's field to consider. The electric field strength at a point due to a charged ring on the ring's axis can be calculated using the formula for electric fields due to point charges, since a charged ring can be thought of as a distribution of point charges.

However, without precise formulae for the field due to a ring or detailed integration methods, we cannot calculate the precise value for this field. A good physics course at the high school level will offer the tools necessary to derive such formulae and solve this problem accurately.

If a 76.2 kg patient is exposed to 52.6 rad of radiation from a beta source, then what is the dose (mrem) absorbed by the person's body?

Answers

Answer:

The dose absorbed by the person's body is 52600 mrem.

Explanation:

Given that,

Radiation = 52.6 rad

We need to calculate the absorbed dose

We know that,

The equivalent dose is equal to the absorbed radiation for beta source.

So, The patient is exposed 52.6 rad of radiation.

Therefore, The absorbed radiation is equal to the exposed 52.6 rad of radiation.

[tex]1 rad = \dfrac{1\ rem}{1000\ mrem}[/tex]

So, radiation absorbed = 52.6 rad

[tex]radiation\ absorbed =52.6\times1000\ mrem[/tex]

[tex]radiation\ absorbed = 52600\ mrem[/tex]

Hence, The dose absorbed by the person's body is 52600 mrem.

An airplane starts its takeoff by moving at 1.7 m/s. The plane must then accelerate at 3.0 m/s2 for the next 30s to reach its final takeoff speed. To the nearest tenth of a kilometer, how far does the plane travel while accelerating to its takeoff speed?

Answers

Answer:

The distance is 1.4 km.

Explanation:

Given that,

Initial velocity u= 1.7 m/s

Accelerate a= 3.0 m/s²

Time = 30 s

We need to calculate the distance

Using equation of motion

[tex]s= ut+\dfrac{1}{2}at^2[/tex]

Where, u = initial velocity

a = acceleration

t = time

Put the value in the equation

[tex]s=1.7\times30+\dfrac{1}{2}\times3.0\times(30)^2[/tex]

[tex]s=1401\ m[/tex]

[tex]s=1.4\ km[/tex]

Hence, The distance is 1.4 km.

At time t0 = 0 the mass happens to be at y0 = 4.05 cm and moving upward at velocity v0 = +4.12 m/s. (Mind the units!) Calculate the amplitude A of the oscillating mass. Answer in units of cm.

Answers

The amplitude of the oscillating mass is [tex]\(A = 4.05 \, \text{cm}\).[/tex]

To calculate the amplitude  A of the oscillating mass, we can use the equations of motion for simple harmonic motion (SHM). In SHM, the displacement [tex]\( y(t) \)[/tex] of the mass at time [tex]\( t \)[/tex] is given by:

[tex]\[ y(t) = A \sin(\omega t + \phi) \][/tex]

where:

- [tex]\( A \)[/tex]) is the amplitude,

- [tex]\( \omega \)[/tex] is the angular frequency, and

- [tex]\( \phi \)[/tex] is the phase angle.

Given that at [tex]\( t = t_0 = 0 \)[/tex], the mass is at [tex]\( y_0 = 4.05 \)[/tex] cm and moving upward at velocity [tex]\( v_0 = +4.12 \)[/tex] m/s, we can find the amplitude A

At [tex]\( t = 0 \),[/tex] we have:

[tex]\[ y(0) = A \sin(\phi) = y_0 = 4.05 \, \text{cm} \][/tex]

And also:

[tex]\[ v(0) = \omega A \cos(\phi) = v_0 = +4.12 \, \text{m/s} \][/tex]

To find [tex]\( A \),[/tex]A we'll use the fact that at [tex]\( t = 0 \)[/tex], the mass is at its maximum displacement, which means the velocity is zero at [tex]\( t = 0 \).[/tex] This gives us:

[tex]\[ \omega A \cos(\phi) = 0 \]\[ \cos(\phi) = 0 \][/tex]

Since [tex]\( \cos(\phi) = 0 \) when \( \phi = \frac{\pi}{2} \) or \( \phi = \frac{3\pi}{2} \), we'll consider \( \phi = \frac{\pi}{2} \).[/tex]

Now, from the equation [tex]\( A \sin(\phi) = y_0 \),[/tex] we can find [tex]\( A \):[/tex]

[tex]\[ A \sin\left(\frac{\pi}{2}\right) = 4.05 \]\[ A = 4.05 \, \text{cm} \][/tex]

So, the amplitude[tex]\( A \)[/tex] of the oscillating mass is [tex]\( 4.05 \, \text{cm} \).[/tex]

A 21.6−g sample of an alloy at 93.00°C is placed into 50.0 g of water at 22.00°C in an insulated coffee-cup calorimeter with a heat capacity of 9.20 J/K. If the final temperature of the system is 31.10°C, what is the specific heat capacity of the alloy?

Answers

Final answer:

The specific heat capacity of the alloy can be calculated using the formula q = m * c * ΔT, where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. We can use the principle of conservation of heat to calculate the specific heat capacity of the alloy.

Explanation:

The specific heat capacity of the alloy can be calculated using the formula: q = m * c * ΔT, where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. In this case, the heat transferred to the water can be calculated by q_water = m_water * c_water * ΔT_water. Using the principle of conservation of heat, q_water = -q_alloy. We can rearrange the equation to solve for c_alloy: c_alloy = -q_water / (m_alloy * ΔT_alloy)



Plugging in the values, we have: c_alloy = -q_water / (m_alloy * (ΔT_final - ΔT_initial)). This gives us the specific heat capacity of the alloy.



In this case, the final temperature of the system is 31.10°C, which means that ΔT_alloy = 31.10°C - 93.00°C = -61.90°C. Plugging in the values, we get: c_alloy = -(-50.0 g * 4.184 J/g °C * (31.10°C - 22.00°C)) / (21.6 g * -61.90°C). After calculating, you will find the specific heat capacity of the alloy.

Learn more about specific heat capacitycapacitycapacitycapacity#SPJ12
Final answer:

The specific heat capacity of the alloy can be calculated using the formula: q = m × c × ΔT.

Explanation:

The specific heat capacity of the alloy can be calculated using the formula:

q = m × c × ΔT

where q is the heat transferred, m is the mass of the alloy, c is the specific heat capacity of the alloy, and ΔT is the change in temperature. In this case, the heat transferred to the alloy is equal to the heat transferred from the water:

m1 × c1 × ΔT1 = m2 × c2 × ΔT2

Substituting the given values, we can solve for c2 to find the specific heat capacity of the alloy:

c2 = (m1 × c1 × ΔT1) / (m2 × ΔT2)

Learn more about specific heat capacity here:

https://brainly.com/question/28302909

#SPJ3

At takeoff, a commercial jet has a speed of 72 m/s. Its tires have a diameter of 0.89 m. Part (a) At how many rev/min are the tires rotating? Part (b) What is the centripetal acceleration at the edge of the tire in m/s^2?

Answers

Answer:

a) Revolutions per minute = 2.33

b) Centripetal acceleration = 11649.44 m/s²

Explanation:

a) Angular velocity is the ratio of linear velocity and radius.

Here linear velocity = 72 m/s

Radius, r  = 0.89 x 0. 5 = 0.445 m

Angular velocity

         [tex]\omega =\frac{72}{0.445}=161.8rad/s[/tex]

Frequency

         [tex]f=\frac{2\pi}{\omega}=\frac{2\times \pi}{161.8}=0.0388rev/s=2.33rev/min[/tex]

Revolutions per minute = 2.33

b) Centripetal acceleration

               [tex]a=\frac{v^2}{r}[/tex]

  Here linear velocity = 72 m/s

  Radius, r  = 0.445 m

Substituting

   [tex]a=\frac{72^2}{0.445}=11649.44m/s^2[/tex]

Centripetal acceleration = 11649.44m/s²

To find the revolutions per minute of the tires, calculate the circumference of the tire and divide the jet's speed in meters per minute by this circumference. For the centripetal acceleration, first find the tire's angular velocity in radians per second and plug it, along with the tire's radius, into the centripetal acceleration formula.

For part (a), to calculate how many revolutions per minute (rev/min) the tires are rotating, you must determine the circumference of the tire first. The circumference (C) is given by [tex]C = \pi d[/tex], where d is the diameter. Given d = 0.89 m, the circumference is [tex]C = \pi (0.89 m)[/tex]. This value represents the distance the tire covers in one revolution.

To find out how many rev/min the tires make, we need to consider the speed of the jet which is 72 m/s. Since there are 60 seconds in a minute, the distance covered in one minute is [tex]72 m/s * 60 s/min.[/tex] Dividing this distance by the tire's circumference gives us the number of revolutions per minute:

[tex]rev/min = \(\frac{(72 m/s) \* (60 s/min)}{\\(pi)(0.89 m)}\)[/tex]

After calculating, you get the tires' rotation rate in rev/min.

For part (b), to calculate the centripetal acceleration (ac) at the edge of the tire, use the formula [tex]ac = \(r\omega^2\),[/tex]where r is the radius of the tire, and [tex]\(\omega\)[/tex] is the angular velocity in radians per second. The angular velocity can be found by converting the rev/min to revolutions per second (rev/s), and then multiplying by [tex]2\pi[/tex] to convert to radians per second.

Lastly, replacing [tex]\(\omega\)[/tex] and r in the centripetal acceleration formula will give you the edge's centripetal acceleration in m/s2.

The frequency factor and activation energy for a chemical reaction are A = 4.23 x 10–12 cm3/(molecule·s) and Ea = 12.9 kJ/mol at 384.7 K, respectively. Determine the rate constant for this reaction at 384.7 K.

Answers

Final answer:

The rate constant for this reaction at 384.7 K is 7.945 x 10^-4 cm^3/(molecule·s).

Explanation:

The rate constant, denoted by k, can be determined using the Arrhenius equation: k = Ae^-Ea/RT, where A is the frequency factor, Ea is the activation energy, R is the ideal gas constant, and T is the temperature in Kelvin. To find the rate constant at 384.7 K, we first need to convert Ea from kJ/mol to J/mol by multiplying it by 1000, giving us 12,900 J/mol. Plugging in the values A = 4.23 x 10^-12 cm^3/(molecule·s), Ea = 12,900 J/mol, and R = 8.314 J/mol/K, into the Arrhenius equation, we can calculate k as follows:

k = (4.23 x 10^-12 cm^3/(molecule·s)) * e^(-12,900 J/mol / (8.314 J/mol/K * 384.7 K))

k = 7.945 x 10^-4 cm^3/(molecule·s)

The same 1710 kg artificial satellite is placed into circular orbit at the same altitude of 2.6x10° m around an exoplanet with the same radius as the Earth, but twice the mass. a. What is the orbital speed of the satellite? b. What is the period of the satellite? C. What is the kinetic energy of the satellite? d. What is the total energy of the satellite?

Answers

Given:

mass of satellite, m = 1710 kg

altitude, h = [tex]2.6\times 10^{6} m[/tex]

G =  [tex]6.67\times 10^{-11} [/tex]

we know

mass of earth, [tex]M_{E}[/tex] =  [tex]5.972\times 10^{24} kg[/tex]

Here, according to question we will consider

[tex]2M_{E}[/tex] =  [tex]11.944\times 10^{24} kg[/tex]

radius of earth,  [tex]R_{E}[/tex] =  [tex]6.371\times 10^{6} m[/tex]

Formulae Used and replacing [tex]M_{E}[/tex] by  [tex]2M_{E}[/tex] :

1). [tex]v = \sqrt{\frac{2GM_{E}}{R_{E} + h}}[/tex]

2). [tex]T = \sqrt{\frac{4\pi ^{2}(R_{E} + h)^{3}}{2GM_{E}}}[/tex]

3). [tex]KE = \frac{1}{2}mv^{2}[/tex]

4). [tex]Total Energy, E = -\frac{2GM_E\times m}{2(R_{E} + h)}[/tex]

where,

v = orbital velocity of satellite

T = time period

KE = kinetic energy

Solution:

Now, Using Formula (1), for orbital velocity:

 [tex]v = \sqrt{\frac{6.67 \times 10^{-11} \times 11.944 \times 10^{24}}{6.371 \times 10^{6} + 2.6 \times 10^{6}}[/tex]

v =  [tex]9.423 \times 10^{3}[/tex]  m/s

Using Formula (2) for time period:

[tex]T = \sqrt{\frac{4\pi ^{2}(6.371\times 10^{6} + 2\times 10^{6})^{3}}{6.67\times 10^{-11}\times 9.44\times 10^{24}}}[/tex]

[tex]T = 6.728\times 10^{3} s[/tex]

Now, Using Formula(3) for kinetic energy:

[tex]KE = \frac{1}{2}(9.44\times 10^{24})(9.42\times 10^{3})^{2}[/tex]

[tex]KE = \frac{1}{2}(1710)(9.42\times 10^{3})^{2} = 7.586\times 10^{10} J[/tex]

Now, Using Formula(4) for Total energy:

[tex]E = -\frac{6.67\times 10^{-11}\times 9.44\times 10^{24}\times 1710}{2( 6.371\times 10^{6} + 2.6\times 10^{6})}[/tex]

[tex]E = - 7.59\times 10^{10} J[/tex]

The plug-in transformer for a laptop computer puts out 7.50 V and can supply a maximum current of 1.6 A. What is the maximum input current Ip in amps, if the input voltage is 240 V? Assume 100% efficiency

Answers

Answer:

The input current is 0.05 A.

Explanation:

Given that,

Output voltage = 7.50 V

Output current = 1.6 A

Input voltage = 240 v

We need to calculate the input current

The efficiency is 100% so.

Input power = output power

[tex]\dfrac{V_{i}}{V_{o}}=\dfrac{I_{o}}{I_{i}}[/tex]

[tex]\dfrac{240}{7.50}=\dfrac{1.6}{I_{i}}[/tex]

[tex]I_{i}=\dfrac{1.6\times7.50}{240}[/tex]

[tex]I_{i}=0.05\ A[/tex]

Hence, The input current is 0.05 A.

The input current Ip for the plug-in transformer for a laptop computer in amps is 0.05 A.

What is the function of transformer?

The primary winding of the transformer converts the electric power into the magnetic power, and the secondary winding of the transformer converts it back into the required electric power.

The ratio of the input voltage to the output voltage is equal to the ratio of output current to the input current of the transformer (for 100 percent efficiency). Therefore

[tex]\dfrac{V_i}{V_o}=\dfrac{I_o}{I_i}[/tex]

The input and output voltage of the transformer is 240 V and 7.50 V respectively and the output current is 1.6 amp.

As, the efficiency of the transformer is 100 percent. Thus, put the values in the above formula as,

[tex]\dfrac{240}{7.50}=\dfrac{1.6}{I_i}\\I_i=0.05\rm A[/tex]

Thus, the input current Ip for the plug-in transformer for a laptop computer in amps is 0.05 A.

Learn more about the transformer here;

https://brainly.com/question/1312500

A concave lens has a focal length of 20 cm. A real object is 30 cm from the lens. Where is the image? What is the magnification?

Answers

Answer:

12 cm and 0.4

Explanation:

f = - 20 cm, u = - 30 cm

Let v be the position of image and m be the magnification.

Use lens equation

1 / f = 1 / v - 1 / u

- 1 / 20 = 1 / v + 1 / 30

1 / v = - 5 / 60

v = - 12 cm

m = v / u = - 12 / (-30) = 0.4

Consider two charges, q1=3C and q2=2C 2m apart from each other. Calculate the electric force between them. Is the force attractive or repulsive?

Answers

Answer:

Electric force between the charges, [tex]F=1.35\times 10^{10}\ N[/tex]

Explanation:

It is given that,

Charge 1, q₁ = 3 C

Charge 2, q₂ = 2 C

Distance between them, r = 2 m

We need to find the electric force between them. The formula for electric force is given by :

[tex]F=k\dfrac{q_1q_2}{r^2}[/tex]

k is the electrostatic constant

[tex]F=9\times 10^9\times \dfrac{3\ C\times 2\ C}{(2\ m)^2}[/tex]

[tex]F=1.35\times 10^{10}\ N[/tex]

So, the force between the charges is [tex]1.35\times 10^{10}\ N[/tex]. Hence, this is the required solution.

A girl is standing on a trampoline. Her mass is 65 kg and she is able to jump 3 m. What is the spring constant for the trampoline? (logger pro?)

Answers

Answer:

k = 212.55 newton per meter

Explanation:

A girl is standing on a trampoline. Her mass is 65 kg and she is able to jump 3 meters.

We have to find the spring constant.

Since by Hooke's law,

F = -kx

Where F = force applied by the spring

k = spring constant

x = displacement

And we know force applied by the spring will be equal to the weight of the girl.

So, F = mg

Therefore, (-mg) = -kx

65×(9.81) = k×(3)

k = [tex]\frac{(65)(9.81)}{3}[/tex]

k = 212.55 N per meter

Therefore, spring constant of the spring is 212.55 Newton per meter.

The electic field inside a spherical volume of radius a is given by: vector E = p_0 r^2 / 4 epsilon r cap Find an expression for the charge density inside the spherical volume that gives rise to this electric field.

Answers

Answer:

[tex]\rho = \rho_0 r[/tex]

Explanation:

As we know by Gauss law

[tex]\int E. dA = \frac{q}{\epsilon}[/tex]

here we know that

[tex]E = \frac{\rho_0 r^2}{4\epsilon}[/tex]

so here we have

[tex](\frac{\rho_0 r^2}{4\epsilon})(4\pi r^2) = \frac{(\int\rho dV)}{\epsilon}[/tex]

now we have

[tex]\frac{\pi \rho_0 r^4}{\epsilon} = \frac{(\int\rho dV)}{\epsilon}[/tex]

[tex]\pi \rho_0 r^4 = (\int\rho dV)[/tex]

now differentiate both sides by volume

[tex]\frac{d(\pi \rho_0 r^4)}{dV} = \rho [/tex]

[tex]\frac{\pi \rho_0 4r^3 dr}{4\pi r^2 dr} = \rho[/tex]

[tex]\rho = \rho_0 r[/tex]

How much current must flow through a wire to make a magnetic field as strong as Earth's field (5.00 x 10^-5 T) 1.00 m away from the wire?

Answers

Answer:

250 A

Explanation:

B = 5 x 10^-5 T, r = 1 m

Let current be i.

the magnetic field due to a straight current carrying conductor is given by

B = μ0 / 4π x 2i / r

5 x 10^-5 = 10^-7 x 2 x i / 1

i = 250 A

A brick in the shape of a cube with sides 10 cm has a density of 2500 kg/m^3. What is its weight? a.) 250 N
b.) 2.5 N
c.) 25 N
d.) 0.001 N

Answers

Answer:

c.) 25 N

Explanation:

 We find the volume of the brick, knowing that the volume of a cube is given by the formula:

[tex]l=0,1 metros \\V=l^{3}\\V=(0,1\: \: m)^{3}=0,001\: \: m^{3}[/tex]

being l the side of the cube, which in this case is 10 cm or 0,1 m. Now we find the mass of the object, knowing the density and the Volume of the cube:

[tex]m=V*d\\m=(0,001 \:\:m^{3})(2500 \: \: \frac{Kg}{m^{3}})=2,5 \:\: Kg[/tex]

We find the weight by multiplying the mass of the object with the gravity constant.

[tex]W=m*g=(2.5 \:Kg)*(9,81 \:m/s^{2} )=24,5 N\approx25\: N[/tex]

Final answer:

The weight of the brick is 24.5 N.

Explanation:

To find the weight of the brick, we can use the formula weight = density × volume × gravitational acceleration.

First, we need to calculate the volume of the cube. The volume of a cube is given by the formula V = side³, where side is the length of one side of the cube.

Given that the side of the cube is 10 cm, the volume of the cube is V = 10 cm × 10 cm × 10 cm = 1000 cm³.

Next, we convert the volume from cm³ to m³ by dividing by 100^3: V = 1000 cm³ ÷ (100 cm/m)³ = 0.001 m³.

Now, we can calculate the weight of the brick: weight = 2500 kg/m³ × 0.001 m³ × 9.8 m/s² = 24.5 N.

Therefore, the weight of the brick is 24.5 N, which is not one of the given options.

An electron moving with a velocity v⃗ = 5.0 × 107 m/s i^ enters a region of space where perpendicular electric and a magnetic fields are present. The electric field is E⃗ = 104 V/m j^. What magnetic field will allow the electron to go through the region without being deflected?

Answers

Final answer:

To allow the electron to pass through the region without being deflected, the magnetic field should be equal and opposite to the electric field with a magnitude of 5.0 x 10^3 T in the -i^ direction.

Explanation:

The force experienced by an electron moving in a magnetic field is given by the formula F = qvB sin(θ), where q is the charge of the electron, v is its velocity, B is the magnetic field, and θ is the angle between the direction of velocity and the magnetic field. To allow the electron to pass through the region without being deflected, the magnetic force should be equal and opposite to the electric force. Since the electric field is in the j^ direction, the magnetic field should be in the -i^ direction with a magnitude of 5.0 x 10^3 T.

Learn more about Magnetic field here:

https://brainly.com/question/36936308

#SPJ12

To prevent the electron from being deflected, the magnetic field should be [tex]2.0 \times 10{^-4} T[/tex]. This is calculated by balancing the electric and magnetic forces acting on the electron.

To determine the magnetic field that allows an electron to pass through a region with perpendicular electric and magnetic fields without being deflected, we use the concept of force balance. When the forces from the electric field and the magnetic field are equal and opposite, the electron will move in a straight line without deflection. Given the electron's velocity[tex]v = 5.0 \times 10^7 m/s \hat i[/tex] and the electric field [tex]E = 10^4 V/m \hat j[/tex], we can use the formula:

[tex]qE = qvB[/tex]

Here, q is the charge of the electron, E is the magnitude of the electric field, v is the electron's velocity, and B is the magnetic field strength. Solving for B, we get:

[tex]B = E/v[/tex]

Plug in the given values:

[tex]B = 10^4 V/m / 5.0 \times 10^7 m/s[/tex]

This simplifies to:

[tex]B = 2.0 \times 10^{-4} T[/tex]

Therefore, the magnetic field required is [tex]2.0 \times 10^{-4} T[/tex].

Other Questions
The following best describes the bourgeoisieO a wealthy social class that exploits the working classesaffluent middle-class people who hire workersO a category so-named by the Bolshevikso the predecessors of the Russian Communist PartyWhat the answer ? how to create a conducive environment for learning? How does classical literature compare with enlightment literature Find the area of the rhombus. (4) Cognitive development to explain Dimitri's antisocial behavior in the scenario below why is his mother's comment unlikely to influence his behavior? how would you encourage Dimitri to stop behaving this ways? Which of these is most likely to lead someone to decrease his or her level of physical activity? A.Internet articles with information about healthful lifestyles B.Advertising for exercise apps C.Marketing campaigns for online video games D.Advertising for community events that promote an active lifestyle often times when countries are at war, they will decide what news of the war they want the public to know about. With that in mind, respond to this question: Do you think governments are justified in censoring news? Why or why not? Consider a 150 turn square loop of wire 17.5 cm on a side that carries a 42 A current in a 1.7 T. a) What is the maximum torque on the loop of wire in N.m? b) What is the magnitude of the torque in Nm when the angle between the field and the normal to the plane of the loop is 14? Solve for x -2x + 5 what is the inverse of the function f(x)=2x+1 If the specific gravity of a fluid is 0.721, its mass density is a. 44.99 lb/ft3 -b. 44.99 slugs/ft. c. 1.397 lb/ft d. 1.397 slugs/t e. none of these 11. A fluid a. is a gas. b. is a liquid. _c. is incompressible d. has a definite volume regardless of the size of the container e. a. and b. above. The domain of r:(3,-2)(1,2)(-1,-4)(-1,2) Write an equation: 1/5 of a shipment of books weights 25 pounds Vista Seating Company is currently selling 2 comma 200 oversized bean bag chairs a month at a price of $75 per chair. The variable cost of each chair sold includes $40 to purchase the bean bag chairs from suppliers and a $9 sales commission. Fixed costs are $ 14 comma 000 per month. The company is considering making several operational changes and wants to know how the change will impact its operating income. Read the requirements LOADING.... Requirement 1. Prepare the company's current contribution margin income statement. (Use parentheses or a minus sign for an operating loss.) Vista Seating Company Contribution Margin Income Statement Sales revenue Variable expenses: Cost of goods sold Operating expenses Contribution margin Fixed expenses Operating income (loss) Requirement 2. Calculate the change in operating income that would result from implementing each of the following independent strategy alternatives. Compare each alternative to the current operating income as you calculated in Requirement 1. Consider each alternative separately. a. Alternative 1: The company believes volume will increase by 16% if salespeople are paid a commission of 15% of the sales price rather than the current $9 per unit. (Use parentheses or a minus sign for an operating loss.) Vista Seating Company Contribution Margin Income Statement Sales revenue Variable expenses: Cost of goods sold Operating expenses Contribution margin Fixed expenses Operating income (loss) I Need Help!! Answer Please!! ConsGrough, Inc. has increased its annual common dividend by 3% in each of the years that the company has existed. If you believe that the company can continue to do so indefinitely, then what price would you be will to pay for ConsGrough if the required rate of return is 6% and the dividend that it paid yesterday was $5? The British gold sovereign coin is an alloy of gold and copper having a total mass of 7.988 g, and is 22-karat gold 24 x (mass of gold)/(total mass) (a) Find the mass of gold in the sovereign in kilograms using the fact that the number of karats kc (b) Calculate the volumes of gold and copper, respectively, used to manufacture the coin. m3 volume of gold m3 volume of copper (c) Calculate the density of the British sovereign coin. kg/m3 Knowing that the protease shows highest activity between pH 4-6, what could be the identity of the base residue acting as a in the reaction? Explain and write the expected mechanism for the reaction. b. Assuming that the optimal pH for the reaction strictly depends exclusively on the protonation state of the active site residues at which pH do you expect maximal enzymatic activity? Explain your rationale. c. What is the fraction of deprotonated Cys and protonated B at the calculated optimum pH? d. How these fractions are changing at 1 pH unit below the optimal pH? Which fraction of the enzyme will be active at this pH? a slice of bread has 1.5 g of fat, 19 g carbohydrate and 4 g protein. how many kcal in the slice? please show all of you work in a dimensional analysis format. HELP!! Seasonal variations in ocean temperatures can impact the populations of living organisms in the ocean. How would a phytoplankton population be affected by these changes?