A bead slides without friction around a loopthe-loop. The bead is released from a height 18.6 m from the bottom of the loop-the-loop which has a radius 6 m. The acceleration of gravity is 9.8 m/s 2 . 18.6 m 6 m A What is its speed at point A ? Answer in units of m/s.

Answer:

d) Decrease, increase, remain constant

Explanation:

If one tire has a slow leak, the air pressure within the tire will_DECREASE____with time due to outflow of air , the surface area between the tire and the road will__INCREASE__in time,due to flattening of tire.

The net force the tire exerts on the road will_REMAIN CONSTANT____in time. It is so because force does not depend upon area. It is pressure which depends upon area. As there is no change in the weight of the car , force on the road will remain constant.

Answer:

Maximum height attained by the ball will be h = 28.416 m

Explanation:

We have given initial speed of the ball u = 23.6 m /sec

At maximum height velocity will be zero so final velocity v = 0 m/sec

Acceleration due to gravity [tex]g=9.8m/sec^2[/tex]

From law of motion we know that [tex]v^2=u^2-2gh[/tex]

[tex]0^2=23.6^2-2\times 9.8\times h[/tex]

h = 28.416 m

So maximum height attained by the ball will be h = 28.416 m

Answer:

[tex]\rho=4.02\times 10^{-8}\ \Omega-m[/tex]

Explanation:

Let us assume that the radius of the wire, r = 0.8 mm = 0.0008 m

EMF of the battery, V = 12 V

Slope of I versus 1/d, m = 600 A-m

The resistance of any material is given by :

[tex]R=\rho \dfrac{d}{A}[/tex]

d is the length of wire

Since, [tex]I=\dfrac{V}{R}[/tex]

[tex]I=\dfrac{VA}{\rho d}[/tex]

[tex]I=\dfrac{VA}{\rho}.(\dfrac{1}{d})[/tex]

[tex]y=slope\times x[/tex]

[tex]\dfrac{VA}{\rho}=600[/tex]

[tex]\rho=\dfrac{VA}{600}[/tex]

[tex]\rho=\dfrac{12\times \pi \times (0.0008)^2}{600}[/tex]

[tex]\rho=4.02\times 10^{-8}\ \Omega-m[/tex]

So, the resistivity of the material of which the wire is made is [tex]4.02\times 10^{-8}\ \Omega-m[/tex].

The slope of the I vs. 1/d graph represents the resistivity of the wire's material. The given slope is 600 A*m, therefore, the resistivity of the material this wire is made of is 600 Ω*m.

The slope of the I vs. 1/d graph is equal to the resistivity of the material the wire is made of. In this case, the slope is given as 600 A*m, so this means the resistivity of the material the wire is made of is 600 Ω*m. This is derived from Ohm's law V=IR which when arranged as I = V/R, indicates that the slope of the graph is the resistance. Since, the resistance R of a cylindrical conductor is directly related to the resistivity (ρ) of the material as R = ρL/A, where L is the length and A is the cross-sectional area, the slope is a representation of this relationship hence representing resistivity.

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Answer:

10 m/s

Explanation:

mass, M = 2000 kg

Power, P = 100 kW = 100000 W

inclination, θ = 30°

g = 10 m/s^2

Let the velocity is v.

P = F x v

where, F is force and v be the velocity

100000 = mg Sin 30 x v

100000 = 2000 x 10 x 0.5 x v

v = 10 m/s

Thus, the speed is 10 m/s.

The interference principle is responsible for alternating light and dark bands when light passes through two or more narrow slits.

The phenomenon in which two or more waves combine to generate a new wave with a larger, smaller, or equal amplitude. It depends on the alignment of the peaks and troughs of the overlapping waves.

When two or more waves collide, this is known as interference. They may add up, or they may partially or completely cancel each other,

When two waves with the same frequency. We will see varying intensities of light at different points on the screen owing to their superposition.

Hence interference principle is responsible for alternating light and dark bands when light passes through two or more narrow slits.

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Answer:  The correct answer is :  have entered into G0

Explanation:  G0 is the fifth phase, it is named because it is out of the cycle, it is still for an undefined time when new cells are not needed and in this phase the cell is not in division and has lost the ability to perform mitosis.

Answer:a) Each is at same temperature

Explanation:

According to the zeroth law of thermodynamics when two objects are in thermal equilibrium with the third one then they are at thermal equilibrium with each other thus they all are at the same temperature.

Here Also objects are in thermal Equilibrium then they should be at the same temperature.

As Internal Energy is an Extensive Property that depends on the amount of gas Present thus two gases at thermal Equilibrium can have different Temperatures.        

Final answer:

Objects at thermal equilibrium are at the same temperature, by the principle of thermal equilibrium and the Zeroth law of thermodynamics. This equilibrium does not require the objects to have the same internal energy or heat content.

Explanation:

For objects at thermal equilibrium, the correct statement is that each is at the same temperature. This is directly derived from the principle of thermal equilibrium, which states when two or more objects are in thermal contact and no heat flows between them, they are considered to be in thermal equilibrium. According to the Zeroth law of thermodynamics, if object A is in thermal equilibrium with object B, and object A is also in thermal equilibrium with object C, then objects B and C are in thermal equilibrium with one another. This invariably leads to the understanding that all objects at thermal equilibrium share the same temperature, but not necessarily the same internal energy or the same amount of heat.

While the law of conservation of energy ensures that the total energy in an isolated system remains constant, how this energy is distributed among objects (in terms of internal energy or heat) can vary significantly based on each object's specific heat capacity, mass, and other factors. Therefore, the correct answer to the question is: a. Each is at the same temperature.

Answer:

l=24.8 cm

Explanation:

The period of a simple pendulum is given by

[tex]T= 2\pi\sqrt{\frac{l}{g} }[/tex]

l= length of pendulum

g= acceleration due to gravity

taking square on both the sides we get

[tex]T^2= 4\pi^2\frac{l}{g}[/tex]

This can be rewritten as

[tex]l = \frac{T^2}{g}4\pi^2[/tex]

now substituting T= 1 and g= 9.8

[tex]l = \frac{1^2}{9.8}4\pi^2[/tex]

l= 0.248 m = 24.8 cm

Final answer:

The length of a pendulum with a period of 1.00 s can be calculated using the formula L = (T^2/g)π^2, resulting in a length of approximately 0.999 m or 99.9 cm.

Explanation:

The period of a pendulum is determined by its length and the acceleration due to gravity, and it is independent of factors such as mass or amplitude. The period is given by the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

In the given question, the period of the pendulum is 1.00 s. To find the length of the pendulum, we can rearrange the formula and solve for L: L = (T^2/g)π^2.

Using a standard value for acceleration due to gravity of 9.8 m/s^2, we can substitute the values to find the length of the pendulum: L = (1.00 s^2 / 9.8 m/s^2)π^2. Evaluating this expression, we find that the length of the pendulum is approximately 0.999 m, or 99.9 cm.

Answer:

Adjusted forecast for January is 640

Explanation:

given,                                                                  

Demand forecast of a certain product = 800 units      

averaged over all months = 12 months                            

January monthly index = 0.8                                              

We have to find seasonally-adjustment sales for January

Adjusted forecast = ( Demand ) x ( monthly index )

                              =   800 x 0.8                              

                              =  640                                  

Adjusted forecast for January is 640

Answer:

Gold, Platinum and Uranium

Explanation:

A star is nothing but a huge ball of gas. Specifically, Hydrogen, the simplest element of nature. A star is in equilibrium because its immense mass causes it to collapse towards itself, squeezing those hydrogen nuclei or protons, and the union of the protons in its nucleus causes the star to explode, releasing energy. As long as these nuclear reactions exist (the same ones that human beings can cause with their hydrogen bombs), the star will remain in equilibrium.

Protons have a positive charge and tend to repel. But inside the stars they are so tight (there is a lot of pressure and temperature), that they can't avoid crashing. At that time, the electromagnetic force is defeated by what physicists call Strong Force, which holds together protons and neutrons forming more complex atoms. In a typical star, the protons join to form the next element in the periodic table: Helium, consisting of 2 protons and two neutrons. It is a rare element on Earth and was discovered in the Sun rather than on our planet. Hence his name, from the Greek Helios, the sun god.

However, the mass of the sum of the protons that bind to form Helium is less than the total mass of Helium. What happen? Are the laws of physics inside the stars not fulfilled? What happens is impossible to understand if one is born before Albert Einstein, but today it is very easy to explain. The mass that we lack, has actually become energy. The German physicist Albert Einstein (1879-1955) discovered that mass and energy are equivalent while formulating his Theory of Relativity. In fact, let me, for once, write a mathematical equation of an unparalleled beauty:

E = mc2

This equation tells us that the energy E is equal to the mass m times the square of a constant c; that constant c is the speed of light, approximately 300,000 km / s. That is, a very small mass, such as a proton, is equivalent to a very large energy, since the numerical factor by which the mass is multiplied is a very large number. And that energy is what the stars release, the one that our Sun emits and gives us life.

When Hydrogen is depleted, the star collapses until the pressure and temperature increase enough for Helium to fuse with itself; the cycle is repeated and the star ends up generating Carbon, Oxygen, Nitrogen, Silicon, Iron. As you can see, the stars are factories of atoms. When the star explodes, even heavier atoms are generated, such as Gold, Platinum, Uranium, elements that abound on our planet. And they abound, because the Sun is a second or third generation star: that is, it was born from the remains of other stars' explosions, along with the materials that make up our planet, the rest of the planets, the asteroids, the comets, the interstellar dust and ourselves.

Answer:

121 Joules

6.16717 m

Explanation:

m = Mass of the rocket = 2 kg

k = Spring constant = 800 N/m

x = Compression of spring = 0.55 m

Here, the kinetic energy of the spring and rocket will balance each other

[tex]\frac{1}{2}mu^2=\frac{1}{2}kx^2\\\Rightarrow u=\sqrt{\frac{kx^2}{m}}\\\Rightarrow u=\sqrt{\frac{800\times 0.55^2}{2}}\\\Rightarrow u=11\ m/s[/tex]

The initial velocity of the rocket is 11 m/s = u.

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s² = g

[tex]v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-11^2}{2\times -9.81}\\\Rightarrow s=6.16717\ m[/tex]

The maximum height of the rocket will be 6.16717 m

Potential energy is given by

[tex]P=mgh\\\Rightarrow P=2\times 9.81\times \frac{0^2-11^2}{2\times -9.81}\\\Rightarrow P=121\ J[/tex]

The potential energy of the rocket at the maximum height will be 121 Joules

Answer:

785.398 W

444.5698 m

Explanation:

I = Intensity of sound

r = Distance

The intensity of sound is given by

[tex]\beta=10log\frac{I}{I_0}\\\Rightarrow 130=10log\frac{I}{10^{-12}}\\\Rightarrow 13=log\frac{I}{10^{-12}}\\\Rightarrow 10^{13}=\frac{I}{10^{-12}}\\\Rightarrow I=10^{-12}\times 10^{13}\\\Rightarrow I=10\ W/m^2[/tex]

Power

[tex]P=IA\\\Rightarrow P=I4\pi r^2\\\Rightarrow P=10\times 4\pi\times 2.5^2\\\Rightarrow P=785.398\ W[/tex]

The power output of the speaker is 785.398 W

If [tex]\beta=85\ db[/tex]

[tex]\beta=10log\frac{I}{I_0}\\\Rightarrow 85=10log\frac{I}{10^{-12}}\\\Rightarrow 8.5=log\frac{I}{10^{-12}}\\\Rightarrow 10^{8.5}=\frac{I}{10^{-12}}\\\Rightarrow I=10^{-12}\times 10^{8.5}\\\Rightarrow I=10^{-3.5}\ W/m^2[/tex]

[tex]P=IA\\\Rightarrow P=I4\pi r^2\\\Rightarrow r=\sqrt{\frac{P}{I4\pi}}\\\Rightarrow r=\sqrt{\frac{785.398}{10^{-3.5}\times 4\pi}}\\\Rightarrow r=444.5698\ m[/tex]

The distance would be 444.5698 m

To calculate the power output of the speaker, we can convert the sound level from decibels to intensity and then use the formula for spherical spreading of sound. To find the distance where the sound level is 85 dB, we can use the same formula and solve for the distance.

To calculate the power output of the speaker, we first need to convert the sound level from decibels to intensity. We can use the formula I = Io * 10^(B/10), where I is the intensity, Io is a reference intensity, and B is the sound level in decibels. With Io = 10^-12 W/m² and B = 130 dB, we can find I. Since the sound spreads in a sphere, we can use the formula I = P / (4πr²), where P is the power output of the speaker and r is the distance. We know I and r, so we can solve for P.

Using the same formula, we can find the distance r where the sound level is 85 dB. We are given the intensity I and the sound level B, so we can solve for r using the formula r = sqrt(P / (4πI)).

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Answer:

14 billion years

Explanation:

The Hubble – Lemaître law, previously called the Hubble law, is a law of physics that states that the redshift of a galaxy is proportional to the distance it is, which is the same as, the further one galaxy is found from another, more quickly it seems to move away from it.

The Hubble constant is the value that measures the rate at which the expansion speed of the Universe varies with distance, and is one of the fundamental parameters of the Universe and allows, in particular, to determine the age of the Universe as we will see.

Answer:

Flow; Impressed

Explanation:

The electric charge can be think of as the flow rate of electrons in a certain area or point. Voltage is a difference in electrical potential, it makes charges to move in the electrical conductor, therefore it is impressed across a circuit

Final answer:

An ionic bond is the electrostatic attraction that holds together ions with opposite charges in an ionic compound, such as sodium and chlorine forming table salt.

Explanation:

The electrostatic attraction that binds oppositely charged ions together is known as an ionic bond. This type of chemical bond is fundamental in the formation of ionic compounds where electrons are transferred from one atom to another, such as the formation of table salt from sodium and chlorine.

Ions are created when atoms either lose or gain electrons, leading to the formation of cations (positively charged) and anions (negatively charged). The electrostatic attraction between these ions of opposite charge results in a stable ionic structure. For instance, a sodium ion (Na+) will form a stronger ionic bond with a 2+ charge than with a 1+ charge due to the increased electrostatic attraction.

Answer:

a. 2.64 m/s

b. 5.9 m/s

c. 997.92 m3

Explanation:

As this is steady flow, the mass flow rate is constant, and so is the product of flow velocity and cross-sectional area

av = 0.077 * 3.6 = 0.2772 m3/s

We can calculate the speed at various areas by dividing the product above by area

a.[tex]v_1 = 0.2772 / a_1 = 0.2772 / 0.105 = 2.64 m/s[/tex]

b.[tex]v_2 = 0.2772 / a_2 = 0.2772 / 0.047 = 5.9 m/s[/tex]

c. Since the volume discharge rate is 0.2772 cube meters per second. In 1 hour, or 60 * 60 = 3600 seconds, the total volume of water discharged would be

0.2772 * 3600 = 997.92 m3

A water pipe with a varying cross-sectional area has a flow rate of 0.277 m³/s at one point. Over one hour, the pipe discharges 1000 m³ of water.

a. Since the water is incompressible, the volume flow rate at all points in the pipe must remain constant. This means that the product of the cross-sectional area and the fluid velocity must be the same at every point.

Using the continuity equation, we can calculate the fluid velocity at points 2 and 3:

V1 * A1 = V2 * A2

3.60 m/s * 7.70×10−2 m2 = V2 * 0.105 m2

Solving for V2:

V2 = (3.60 m/s * 7.70×10−2 m2) / 0.105 m2

V2 ≈ 2.64 m/s

Similarly, for point 3:

V1 * A1 = V3 * A3

3.60 m/s * 7.70×10−2 m2 = V3 * 0.047 m2

Solving for V3:

V3 = (3.60 m/s * 7.70×10−2 m2) / 0.047 m2

V3 ≈ 5.898 m/s

b. To calculate the volume of water discharged from the open end of the pipe in 1.00 hour, we need to determine the volume flow rate and multiply it by the time.

Volume flow rate = Cross-sectional area * Fluid velocity

Volume flow rate = 0.047 m2 * 5.898 m/s

Volume flow rate ≈ 0.277 m³/s

Volume of water discharged in 1.00 hour:

Volume flow rate * Time

0.277 m³/s * 3600 s/hour

≈ 999.12 m³

Since the volume of water discharged in 1.00 hour is close to 1000 m³, we can round it to 1000 m³.

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Answer:

It is known as the centripetal vector directed to the centre of the fictious circumference

The acceleration vector of a particle in uniform circular motion always points towards the center of the circle

The total acceleration vector of a particle in uniform circular motion always points towards the center of the circle. It is directed perpendicular to the velocity vector and its magnitude is given by [tex]a = v^2/r,[/tex] where v is the magnitude of the velocity vector and r is the radius of the circle.

For example, when a car is moving in a circular path on a banked turn, the acceleration vector points towards the centre of the turn, keeping the car on the circular track. In summary, the acceleration vector of a particle in uniform circular motion is always directed towards the centre of the circle and its magnitude is given by [tex]a = v^2/r,[/tex]

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Answer:

[tex]\omega=32.14\ rad/s[/tex]

Explanation:

Given that,

The compression in the spring, x = 0.0647 m

Speed of the object, v = 2.08 m/s

To find,

Angular frequency of the object.

Solution,

We know that the elation between the amplitude and the angular frequency in SHM is given by :

[tex]v=\omega\times A[/tex]

A is the amplitude

In case of spring the compression in the spring is equal to its amplitude

[tex]\omega=\dfrac{v}{A}[/tex]

[tex]\omega=\dfrac{2.08\ m/s}{0.0647\ m}[/tex]

[tex]\omega=32.14\ rad/s[/tex]

So, the angular frequency of the spring is 32.14 rad/s.

Answer:

D. Nothing will happen; the seesaw will still be balanced.

Explanation:

D. Nothing will happen; the seesaw will still be balanced. Since both toruqes or momentums respect to the center have changed in the same amount (one-half their original distance) the seesaw will remain balanced, if the children change distance in a different amount then it will be out of balance

D. Nothing will happen; the seesaw will still be balanced.

The force acting on a system with static equilibrium is 0

[tex] \large {\boxed {\bold {\sum F = 0}} [/tex]

(forces acting as translational motion only, not including rotational forces)

[tex] \displaystyle \sum F_x = 0 \\\\\ sum F_y = 0 [/tex]

For objects undergoing rotation, the equilibrium must be met

[tex] \large {\boxed {\bold {\sum \tau = 0}} [/tex]

A heavy boy (Hb) and a lightweight girl (Lg) are balanced on a mass-less seesaw

Because there is a balance of rotation, the torque equation:

Στ = 0

Hb.r1-Lg.r2 = 0

Hb.r1 = Lg.r2 (equation 1)

If they both move forward so that they are one-half their original distance from the pivot point, then the distance of the two children to the pivot point is reduced to half

Then the torque equation:

[tex]\rm Hb\times \dfrac{r_1}{2}= Lg\times \dfrac{r_2}{2}\\\\Hb\times r_1=Lg\times r_2[/tex]

This equation remains the same as equation 1, so the seesaw will still be balanced.

tangential force

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displacement of a skateboarder

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The distance of the elevator

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Answer:

[tex]0.57 ms^{-1}[/tex]

Explanation:

k = spring constant of the spring = 40 Nm⁻¹

A = amplitude of the simple harmonic motion = 4 cm = 0.04 m

m = mass of the block attached to spring = 0.20 kg

w = angular frequency of the simple harmonic motion

Angular frequency of the simple harmonic motion is given as [tex]w = \sqrt{\frac{k}{m} } \\w = \sqrt{\frac{40}{0.20} }\\w = 14.14 rads^{-1}[/tex]

[tex]v[/tex] = Speed of the block as it pass the equilibrium point

Speed of the block as it pass the equilibrium point is given as

[tex]v = A w\\v = (0.04) (14.14)\\v = 0.57 ms^{-1}[/tex]

Final answer:

The speed of a 0.20-kg block attached to a spring and released from a displacement of 4.0 cm on a frictionless surface is calculated to be 0.4 m/s when it passes through the equilibrium point, using conservation of mechanical energy.

Explanation:

The question involves calculating the speed of a block when it passes through the equilibrium point after being released from a displacement in a setup involving harmonic motion. In this case, we use the principle of conservation of mechanical energy. The total mechanical energy in a system, including potential and kinetic energy, remains constant if only conservative forces are doing work. Since the surface is frictionless and the only force doing work is conservative (spring force), the potential energy stored in the spring when the block is displaced is fully converted into kinetic energy when the block passes through the equilibrium position.

The potential energy stored in the spring at the maximum displacement is given by ½*k*x², where k is the spring constant (40 N/m) and x is the displacement (0.04 m). Thus, PE = 0.5 * 40 * (0.04)² = 0.032 J. At the equilibrium point, all this potential energy is converted into kinetic energy (KE = 0.5 * m * v²), allowing us to solve for v (speed). Rearranging KE = PE gives v = [tex]\sqrt{(2*PE/m)[/tex]. Plugging in the values, v = [tex]\sqrt{2*0.032/0.20[/tex] = 0.4 m/s.

Answer:

vB = 15.4 m/s

Explanation:

Principle of conservation of energy:

Because there is no friction the mechanical energy is conserve

ΔE = 0

ΔE : mechanical energy change (J)

K : Kinetic energy (J)

U: Potential energy (J)

K = (1/2)mv²

U = m*g*h

Where :

m: mass (kg)

v : speed (m/s)

h : hight (m)

Ef - Ei = 0

(K+U)final - (K+U)initial =0

(K+U)final = (K+U)initial

((1/2)mv²+m*g*h)final = ((1/2)mv²+m*g*h)initial , We divided by m both sides of the equation:

((1/2)vB² + g*hB = (1/2 )vA²+ g*hA

(1/2) (vB)² + (9.8)*(14.7) =  0 + (9.8)(26.8 )

(1/2) (vB)² = (9.8)(26.8 ) - (9.8)*(14.7)

(vB)² = (2)(9.8)(26.8 - 14.7)

(vB)² = 237.16

[tex]v_{B} = \sqrt{237.16}[/tex]

vB = 15.4 m/s : speed of the cart at B

Answer:

the guy above me is correct

Explanation:

Final answer:

The speed of light in air depends on both the wavelength and the frequency of light. Increasing or decreasing the frequency of light leads to changes in the amount of delay.

Explanation:

The speed of light in air depends on both the wavelength and the frequency of light. This relationship is defined by the equation c = fλ, where c is the speed of light, f is the frequency, and λ is the wavelength.

When the frequency of light increases, the wavelength decreases, and vice versa. This means that as you make the frequency higher or lower, there is a corresponding change in the amount of delay.

For example, if you increase the frequency, the wavelength becomes smaller, which leads to a shorter delay. On the other hand, if you decrease the frequency, the wavelength becomes larger, resulting in a longer delay.

Answer: At the period that's between its peaks of brightness and its luminosity.

Explanation:

The two observable properties of a cepheid variable that are directly related to one another at the period between its peaks of brightness and its luminosity. The period-luminosity relation allows us to determine its luminosity from the period between its peaks of brightness. In astronomy, a period-luminosity relation is a relationship linking the luminosity of pulsating variable stars with their pulsation period. The popular relation, for Classical Cepheid variables, is also called Leavitt's law

Answer:

Option (a)

Explanation:

Impulse is defined as the change in momentum of the body. It is a vector quantity and its SI unit is Kg m/s.

mass of ball, m = 0.4 kg

initial velocity, u = - 30 m/s

Final velocity, v = + 20 m/s

Initial momentum, pi = mass x initial velocity = m u = 0.4 x (- 30) = - 12 kg m/ s

Final momentum, pf = mass x final velocity = mv = 0.4 x 20 = 8 Kg m /s

Change in momentum = final momentum - initial momentum = 8 - (- 12 )

So, impulse = 20 kg m /s right

Option (a) is correct

Final answer:

The impulse of the net force on the ball during its collision with the wall is the change in momentum, coming to 32 kg·m/s to the right, leading to option E) none of the above as the correct answer.

Explanation:

The impulse of the net force on a ball during its collision with the wall can be calculated using the change in momentum of the ball, which is equal to the impulse imparted to it. If the ball has a mass of 0.40 kg and changes its velocity from 30 m/s to the left (which we can consider as a negative direction) to 20 m/s to the right (a positive direction), we need to take into account the magnitude and the direction of this change.

The initial momentum of the ball is given by the product of its mass and its initial velocity, which is -0.40 kg × 30 m/s (the negative sign indicates the initial leftward direction). The final momentum after the collision is 0.40 kg × 20 m/s. The impulse is the difference between the final and initial momentum: (0.40 kg × 20 m/s) - (-0.40 kg × 30 m/s), which equals 20 kg·m/s + 12 kg·m/s or 32 kg·m/s to the right. Therefore, the correct answer is E) none of the above.

Answer:

Zero work is done when a vertical force acts on an object moving horizontally

Explanation:

Word is the dot product of force and displacement.

             W = F . s

             W = Fs cosθ

θ is the angle between force and displacement,

We need to find how much work is done when a vertical force acts on an object moving horizontally.

That is angle between force and displacement = 90°

                θ = = 90°

Substituting

              W = Fs cos90 = Fs x 0 = 0

Zero work is done when a vertical force acts on an object moving horizontally    

10 m/sec² acceleration is required for the tow truck to move this vehicle.

The rate at which an item changes its velocity is known as acceleration, a vector quantity. If an object's velocity is changing, it is acceleration.

The net acceleration that objects get as a result of the combined action of gravity and centrifugal force is known as the Earth's gravity, or g. It is a vector quantity whose strength or magnitude is determined by the norm and whose direction correlates with a plumb bob.

force = mass*acceleration

acceleration = force/mass

acceleration = 15000/1500

acceleration = 10 m/sec²

10 m/sec² acceleration is required for the tow truck to move this vehicle.

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Answer:

a) Suzie’s average acceleration = -6.46 m/s²

b) Force exerted to stop Suzie = 271.52 N

Explanation:

a) We have equation of motion, v = u + at

     Final velocity, v = 0 m/s

     Initial velocity, u = 32 mph = 14.22 m/s

     Time, t =2.2 s

Substituting

     0 = 14.22 + a x 2.2

     a = -6.46 m/s²

Suzie’s average acceleration = -6.46 m/s²

b) Mass of Suzie = 42 kg

   Force = Mass x Acceleration

   F = Ma

   F = 42 x -6.46 =-271.52 N

   Force exerted to stop Suzie = 271.52 N

Answer

Given,

Frequency of the ultrasonic pulse = 30 kHz

Speed of the sound = v = 343 m/s

wavelength of the wave emitted = ?

using formula

     [tex]v = \nu \lambda[/tex]                    

     [tex]\lambda= \dfrac{v}{\nu}[/tex]                  

     [tex]\lambda= \dfrac{343}{30\times 10^3}[/tex]

     [tex]\lambda=11.43 \times 10^{-3}\ m[/tex]          

     [tex]\lambda=11.43\ mm[/tex]                    

time taken for a pulse  that reflects off an object 3.0 m away to make a round trip                                                

   [tex]time = \dfrac{\Delta x}{\Delta v}[/tex]

   [tex]time = \dfrac{2\times 3}{343}[/tex]

            t = 0.01749 s

            t = 17.49 ms

The motion detector uses ultrasonic waves to measure distance by timing the round trip of a sound wave. Distance is calculated using the speed of sound and the time taken for the echo to return, and the calculation requires a division by 2 to account for the round trip. Calibration is important for accuracy as the speed of sound changes with temperature.

The motion detector described is a classic example of how ultrasonic waves can be used to measure distance. A similar principle is applied in an automatic focus camera, which generates ultrasonic sound waves, captures their reflections off objects, and calculates the distance based on the time delay of the returning waves. The speed of sound in air at 20 ℃ is approximately 344 m/s. Therefore, if a sound wave returns after 0.150 seconds, we can calculate the distance to the object as follows:

Distance = Speed of Sound × Time / 2
Distance = 344 m/s × 0.150 s / 2
Distance = 25.8 meters
This calculation takes into account that the sound wave must travel to the object and back, making the total distance twice the distance we want to measure, hence the division by 2.

The ultrasonic range finder and technologies such as radar and Doppler shift applications in traffic law enforcement rely on similar concepts of wave reflection and frequency shifts to measure distance and speed.

To understand the effects of temperature on the calibration of such devices, the room temperature is required because the speed of sound in air changes with temperature, potentially influencing the accuracy of these measurements.

Final Answer:

The angle θ at which the wheel comes to rest is approximately θ = tan^(-1)(μ), where μ is the coefficient of static friction. The minimum coefficient of static friction required to prevent slipping is μ = tan^(-1)(m_wheel / m_cylinder), where m_wheel is the mass of the wheel and m_cylinder is the mass of the cylinder.

Explanation:

In this scenario, the forces involved include the gravitational force acting on both the wheel and the cylinder and the tension in the cord. The component of the gravitational force parallel to the incline causes the wheel to roll, and the frictional force opposes slipping. At the point where the wheel comes to rest, the net force along the incline is zero.

Using the equilibrium condition, the gravitational force component along the incline is balanced by the frictional force. This gives us the equation: m_wheel * g * sin(θ) = μ * m_wheel * g * cos(θ), where g is the acceleration due to gravity. Simplifying, we find μ = tan(θ).

To find the minimum coefficient of static friction, we can substitute the masses of the wheel and cylinder: μ_min = tan^(-1)(m_wheel / m_cylinder). This represents the point where the wheel will come to rest without slipping. The tan^(-1) function gives the angle at which the static friction is just sufficient to prevent slipping, and this corresponds to the minimum coefficient of static friction required.

Answer:

1964.8 J

[tex]5.12894\times 10^{-6}\ m^3[/tex]

1150 Joules

Explanation:

m = Mass of bullet = 0.5 kg

[tex]\Delta T[/tex] = Change in temperature = (327-20)

c = Specific heat of lead = 128 J/kg °C

[tex]\beta[/tex] = [tex]84\times 10^{-6}\ /^{\circ}C[/tex]

[tex]L_f[/tex] = Latent heat of fusion of lead = [tex]23000\ J/kg^{\circ}C[/tex]

(Values taken from properties of lead table)

Heat is given by

[tex]Q=mc\Delta T\\\Rightarrow Q=0.05\times 128\times (327-20)\\\Rightarrow Q=1964.8\ J[/tex]

The heat needed to raise the bullet to its final temperature is 1964.8 J

Change in volume is given by

[tex]\Delta V=V_0\beta \Delta T\\\Rightarrow \Delta V=5\times 10^{-6}\times 84\times 10^{-6}\times (327-20)\\\Rightarrow \Delta V=1.2894\times 10^{-7}\ m^3[/tex]

[tex]V=V_0+\Delta V\\\Rightarrow V=5\times 10^{-6}+1.2894\times 10^{-7}\\\Rightarrow V=5.12894\times 10^{-6}\ m^3[/tex]

The volume of the bullet when it comes to rest is [tex]5.12894\times 10^{-6}\ m^3[/tex]

Heat needed for melting

[tex]Q=mL_f\\\Rightarrow Q=0.05\times 23\times 10^3\\\Rightarrow Q=1150\ J[/tex]

The additional heat needed to melt the bullet is 1150 Joules

Final answer:

The calculation involves determining the heat required to increase the bullet's temperature, calculating the change in volume due to thermal expansion, and the additional heat required to melt the bullet, using the specific heat capacity, coefficient of thermal expansion, and latent heat of fusion for lead.

Explanation:

To solve this problem, we will use the specific heat capacity formula and the properties of lead to calculate the heat needed for temperature change and melting.

Heat required to raise the bullet's temperature: The heat (Q) needed can be calculated using the specific heat capacity equation Q = mcΔT, where 'm' is mass, 'c' is specific heat capacity, and ΔT is the change in temperature. For lead, the specific heat capacity (c) is approximately 128 J/(kg·°C).

Volume: To find the volume at the final temperature, we use the formula V = V_0(1+ αΔT), where V_0 is the initial volume, α is the coefficient of thermal expansion for lead, and ΔT is the change in temperature.

Additional heat to melt the bullet: To calculate the additional heat (Q_m) required to melt the bullet, we use the formula Q_m = mL_f, where 'm' is the mass of the bullet and L_f is the latent heat of fusion for lead.

To calculate these values, we also need the initial temperature (T_i), final temperature (T_f), and coefficient of thermal expansion for lead, which is 29.3 × 10⁻⁶ °C-1. For melting lead, the latent heat of fusion (L_f) is 24.7 kJ/kg.