Two balls have the same mass of 5.00 kg. Suppose that these two balls are attached to a rigid massless rod of length 2L, where L = 0.550 m.
One is attached at one end of the rod and the other at the middle of the rod.
If the rod is held by the open end and rotates in a circular motion with angular speed of 45.6 revolutions per second,

(a) What is the tension for the first half of the rod, i.e., between 0 and L if the pivot point is chosen as origin?

(b) What is the tension for the second half of the rod, i.e., between L and 2L if the pivot point is chosen as origin?

To develop this problem it is necessary to apply the law of Pascal. The pressure exerted on an incompressible and equilibrium fluid within a container of non-deformable walls is transmitted with equal intensity in all directions and at all points of the fluid. For which the pressure is defined as,

[tex]P = P_{atm}+P_{oil}+P_{water}[/tex]

The pressure of an object can be expressed by means of density, gravity and height

[tex]P = \rho*g*h[/tex]

Our values are given as,

[tex]g=9.8m/s^2\\h_w = 0.17m\\h_o = 0.34\\\gamma_g = 0.9\rightarrow \rho=0.9*10^{-3}[/tex]

Replacing we have to,

[tex]P = P_{atm}+P_{oil}+P_{water}[/tex]

[tex]P = P_{atm}+\rho_{oil}gh_{oil}+\rho_{water}gh_{water}[/tex]

[tex]P = 1.013*10^5+(0.9*10^3)(9.8)(0.34)+(10^3)(9.8)(0.17)[/tex]

[tex]P = 105964.8Pa[/tex]

To solve the exercise it is necessary to apply the concepts given in Newton's second law and the equations of motion description.

Let's start by defining acceleration based on speed and time, that is

[tex]a = \frac{v}{t}[/tex]

On the other hand according to Newton's second law we have to

F=ma

where

m= Mass

a = Acceleration

Replacing the value of acceleration in this equation we have

[tex]F=m(\frac{v}{t})[/tex]

Substituting with our values we have

[tex]100N=(5Kg)\frac{v}{0.2}[/tex]

Re-arrange to find v

[tex]v=\frac{100*0.2}{5}[/tex]

[tex]v = 2m/s[/tex]

Therefore the speed of the glider is 2m/s

Using the Heisenberg Uncertainty Principle in quantum mechanics, which states that position and momentum of a particle cannot both be precisely measured at the same time, we can calculate the smallest box in which an electron can be confined with a specified maximum speed. The mass of the electron and the given speed are used to compute the uncertainty in momentum, which is then used in the Heisenberg inequality formula to find the size of the box.

This question can be addressed using the Heisenberg Uncertainty Principle, which in quantum mechanics, states that the position and the momentum of a particle cannot both be precisely measured at the same time. The more precisely we know the position (Δx), the less precisely we can know the velocity (Δv), and vice versa.

Considering an electron, which has a mass (m) of 9.11×10-31 kg, and wanting the speed to be no more than 13 m/s, we can use the Heisenberg inequality formula:

Δx* Δp ≥ ℏ/2,

where ℏ is the reduced Planck constant, and Δp is the uncertainty in momentum. Since momentum (p) is equal to the mass (m) times the velocity (v), we find the uncertainty in momentum (Δp) to be m* Δv which is (9.11×10-31 kg * 13 m/s). Now, we can solve for the smallest uncertainty in position (Δx), also known as the linear size of the box.

Using these calculations, we must first find Δp, then substitute into the above inequality and solve for Δx. This will give you the minimum size of the box in which the electron can be confined.

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Answer:

option C

Explanation:

The correct answer is option C.

For negative velocity  

Negative velocity is when the velocity of the object in a negative direction.

so, for the velocity of the car to be negative, it should be in -x-direction.

For positive acceleration

Positive acceleration is the change of the velocity of the object with respect to time in a positive direction

but when the velocity of the object is in negative direction the slowing down of the vehicle will give positive acceleration.

hence, the correct answer is an option  -x-direction decreasing in speed.

Final answer:

The heat loss per unit length of the tube due to convection is approximately 141.7 W/m, calculated using the formula for heat transfer by convection with the provided temperatures and convection coefficient.

Explanation:

To estimate the heat loss per unit length of tube in W/m due to convection, we use the formula for heat transfer by convection which is Q = hA(Tsur - Tair). The convection coefficient 'h' is given as 11 W/m²·K, the temperature of the oil 'Tsur' is 150°C, and the air temperature 'Tair' is 20°C.

We need to find the surface area 'A' which for a pipe is calculated using A = π x d x L, where 'd' is the diameter and 'L' is the length of the pipe. Since we need the heat loss per unit length, L will be 1 meter.

Firstly, calculate the surface area per meter of the pipe: A = π x 0.025 m x 1 m = 0.0785 m². Then, plug these values into the convection formula to find heat loss per meter: Q = 11 W/m²·K x 0.0785 m² x (150°C - 20°C) = 141.7 W/m. Therefore, the heat loss per unit length of the tube is approximately 141.7 W/m.

Answer:

The speed of the crate after the beanbag hits it is 1.2 m/s.

Explanation:

Hi there!

The momentum of the system beanbag-crate remains the same after the collision, i.e., the momentum of the system is conserved. The momentum of the system is calculated by adding the momenta of each object. So, the initial momentum (before the collision) is calculated as follows:

initial momentum = momentum of the crate + momentum of the beanbag

initial momentum = mc · vc + mb · vb

Where:

mc = mass of the crate.

vc = initial velocity of the crate.

mb = mass of the beanbag

vb = initial mass of the beanbag

With the data we have, we can calculate the initial momentum:

initial momentum  = 20 kg · 0 m/s + 1.5 kg · 10 m/s = 15 kg · m/s

Now, let´s write the equation of the momentum of the system after the collision:

final momentum = mc · vc´ + mb · vb´

Where vc´ and vb´ are the final velocity of the crate and the beanbag respectively. Let´s replace with the data we have:

final momentum = 20 kg · vc´ + 1.5 · (-6 m/s)

Since

initial momentum = final momentum

Then:

15 kg · m/s = 20 kg · vc´ + 1.5 kg · (-6 m/s)

Solving for vc´:

(15 kg · m/s + 9 kg · m/s) / 20 kg = vc´

vc´ = 1.2 m/s

The speed of the crate after the beanbag hits it is 1.2 m/s.

Using the law of conservation of momentum, the speed of the crate after the beanbag hits it is found to be 1.2 m/s in the +x direction.

The situation described can be solved using the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision. The momentum (p) of an object is its mass (m) times its velocity (v), or p = mv.

Before the collision, the 1.5-kg beanbag has a momentum of 1.5 kg * 10 m/s = 15 kg*m/s in the +x direction, and the 20-kg crate has a momentum of 0, as it is at rest. Therefore, the total momentum before the collision is 15 kg*m/s.

After the collision, the beanbag has a momentum of 1.5 kg * -6 m/s = -9 kg*m/s in the -x direction. Since the total momentum must be conserved, the crate must have a momentum of 15 kg*m/s (total initial momentum) + 9 kg*m/s (final momentum of beanbag) = 24 kg*m/s in the +x direction. Therefore, the speed (v) of the crate after the collision is its momentum divided by its mass, or v = p/m = 24 kg*m/s / 20 kg = 1.2 m/s.

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Answer:

option A

Explanation:

The correct answer is option A

given,

mass of ball and bean bag is same

golf ball rebound with certain velocity where as the bean bag stops.

Impulse = Change in momentum

I = m v_f - m v_i

When the golf ball rebound there will be negative velocity on the ball.

Which will add up and increase the impulse of the golf ball.

But in the case of beam bag velocity after the collision is zero the impulse will be less.

The golf ball experiences the greater impulse from the ground.

Impulse refers to the force acting over time to change the momentum of an object. It is represented by J and usually expressed in Newton-seconds or kg m/s so we can conclude that the golf ball experiences the greater impulse from the ground because of the structure and elasticity.

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Answer:

The buoyant force is 2964500 N.

Explanation:

Given that,

Density of water = 1000 kg/m³

Area = 550 m²

Height = 2.0 m

Depth = 0.55 m

Suppose we need to write an equation for the buoyant force on the empty barge in terms of the known data and find the value of force

We need to write the buoyant force equation

[tex]F_{b}=\rho\times V\times g[/tex]

The volume is

[tex]V=A\times h_{0}[/tex]

Put the value of volume into the buoyant force

[tex]F_{b}=\rho\times A\times h_{0}\times g[/tex]

We need to calculate the buoyant force

Put the value into the formula

[tex]F_{b}=1000\times550\times0.55\times9.8[/tex]

[tex]F_{b}=2964500\ N[/tex]

Hence, The buoyant force is 2964500 N.

The question describes a scenario involving Archimedes' Principle and the concept of density. It compares the submerged portions of a barge when it's empty versus when it's loaded. The difference in the submerged parts describes how the barge displaces more water to balance the increased weight.

The phenomenon described in the question involves Archimedes' Principle and the concept of density, both of which are topics in Physics. The principle states that the buoyant force (upward force) that acts on an object submerged in a fluid is equal to the weight of the fluid the object displaces.

Initially, when the barge is empty, only a small part (H0 = 0.55 m) of it is submerged in the water, meaning it displaces a smaller volume of water equivalent to 0.55 m * 550 m². When it is loaded with coal, a larger part (H1 = 1.7 m) is submerged, and it displaces a larger volume of water (1.7 m * 550 m²).

The change in the submerged height of the barge when it's loaded compared to when it's empty can be attributed to increased weight which, to maintain equilibrium, is matched by the displacement of greater volume of water and hence increasing water's buoyant force.

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Answer:

[tex]\theta=144\ rad[/tex]

Explanation:

given,

α=( 10+6 t ) rad/s²

[tex]\alpha =\dfrac{d\omega}{dt}[/tex]

[tex]d\omega= \alpha dt[/tex]

integrating both side

[tex]\omega= \int (10+6 t )dt[/tex]

[tex]\omega=10 t+6\dfrac{t^2}{2}[/tex]

[tex]\omega=10 t+3t^2[/tex]

we know

[tex]\omega =\dfrac{d\theta}{dt}[/tex]

[tex]d\theta= \alpha dt[/tex]

integrating both side

[tex]\theta= \int (10 t+3t^2 )dt[/tex]

[tex]\theta=10\dfrac{t^2}{2}+3\dfrac{t^3}{3}[/tex]

[tex]\theta=5 t^2+t^3[/tex]

now, at t = 4 s θ will be equal to

[tex]\theta=5\times 4^2+4^3[/tex]

[tex]\theta=144\ rad[/tex]

Answer:C.

Explanation: the hoop is the right answer

Answer:

During this motion, 0.133 J of heat energy was created

Explanation:

Hi there!

Let´s calculate the energy of the object in each phase of the motion.

At first, the object has only kinetic energy (KE):

KE = 1/2 · m · v²

Where:

m = mass of the object.

v = velocity.

KE = 1/2 · 0.01 kg · (9 m/s)²

KE = 0.405 J

When the object goes up the ramp, it gains some gravitational potential energy (PE). Due to the conservation of energy, the object must convert some of its kinetic energy to obtain potential energy. By calculating the potential energy that the object acquires, we can know the loss of kinetic energy:

PE = m · g · h

Where:

m = mass of the object.

g = acceleration due to gravity (9.81 m/s²)

h = height.

PE = 0.01 kg · 9.81 m/s² · 1.5 m

PE = 0.147 J

The object "gives up" 0.147 J of kinetic energy to be converted into potential energy.

Then, after going up the ramp, the kinetic energy of the object will be:

0.405 J - 0.147 J = 0.258 J

When the object reaches the spring, kinetic energy is used to compress the spring and the object obtains elastic potential energy (EPE). Let´s calculate the EPE obtained by the object:

EPE = 1/2 · k · x²

Where:

k = spring constant.

x = compression of the spring

EPE = 1/2 · 100 N/m · (0.05 m)² = 0.125 J

Then, only 0.125 J of kinetic energy was converted into elastic potential energy. The object is at rest at the end of the motion, i.e., the object does not have kinetic energy when it compresses the spring by 5.0 cm. Since energy can´t be lost, the rest of the kinetic energy, that was not used to compress the spring, had to be converted into heat energy:

Heat energy = initial kinetic energy - obtained elastic potential energy

Heat energy = 0.258 J - 0.125 J = 0.133 J

During this motion, 0.133 J of heat energy was created.

Final answer:

The question asks to calculate the heat energy produced when a 0.01-kg object sliding at 9.0 m/s is stopped by a spring after going up a ramp. Using conservation of energy, the heat energy can be found by subtracting the spring's elastic potential energy from the total initial kinetic and gravitational potential energies.

Explanation:

The student's question involves determining the amount of heat energy created during the motion of a 0.01-kg object as it slides, goes up a ramp, and is stopped by a compressed spring. To solve this problem, we need to apply the principles of conservation of energy and mechanics.

Initially, the object has kinetic energy since it is sliding at 9.0 m/s. As it goes up a ramp with a height increase of 1.5 m, it gains gravitational potential energy and loses some kinetic energy. Finally, when it strikes and compresses the spring (of constant k = 100 N/m) by 5.0 cm, it loses all its kinetic energy, which gets converted into the energy stored in the spring (elastic potential energy) and heat energy due to non-conservative forces.

The formula to find the elastic potential energy (Ep) stored in a compressed spring is:

Ep = 1/2 * k * x2

Where k is the spring constant and x is the compression length. Since the initial kinetic energy and the gravitational potential energy are converted into the elastic potential energy and heat, we can find the heat energy by subtracting the elastic potential energy from the sum of the initial kinetic and gravitational potential energies.

Heat energy = Initial kinetic energy + Gravitational potential energy - Elastic potential energy

Answer:

So the acceleration of the child will be [tex]8.05m/sec^2[/tex]

Explanation:

We have given angular speed of the child [tex]\omega =1.25rad/sec[/tex]

Radius r = 4.65 m

Angular acceleration [tex]\alpha =0.745rad/sec^2[/tex]

We know that linear velocity is given by [tex]v=\omega r=1.25\times 4.65=5.815m/sec[/tex]

We know that radial acceleration is given by [tex]a=\frac{v^2}{r}=\frac{5.815^2}{4.65}=7.2718m/sec^2[/tex]

Tangential acceleration is given by

[tex]a_t=\alpha r=0.745\times 4.65=3.464m/sec^[/tex]

So total acceleration will be [tex]a=\sqrt{7.2718^2+3.464^2}=8.05m/sec^2[/tex]

The magnitude of the linear acceleration of the child is mathematically given as

a=8.05m/sec^2

Question Parameters:

A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s2.

Generally the equation for the linear velocity  is mathematically given as

v=wr

Therefore

v=1.25*4.65

v=5.815

radial acceleration is given by

a=v^2/r

Hence

a=5.815/4.65

a=7.2718

Tangential acceleration is

a_t=\alpha r

a_t=0.745*4.65

a_t=3.464m/sec

Hence, total acceleration will be

[tex]a=\sqrt{7.2718^2+3.464^2}[/tex]

a=8.05m/sec^2

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Answer:

S = 2266.67 m/s

Explanation:

Given,

length of the metal = 3.4 m

pulses are separated in time = 8.4 ms

speed of sound in air= 343 m/s

speed of sound in this metal = ?

time taken

[tex]t = \dfrac{distance}{speed}[/tex]

[tex]t = \dfrac{3.4}{343}[/tex]

t = 9.9 ms

speed of sound in the metal is fast

t = 9.9 - 8.4 = 1.5 ms

time for which sound is in metal is equal to 1.5 ms

speed of sound in metal

 [tex]speed= \dfrac{distance}{time}[/tex]

[tex]S = \dfrac{3.4}{1.5 \times 10^{-3}}[/tex]

S = 2266.67 m/s

Speed of sound in metal is equal to S = 2266.67 m/s

Final answer:

The speed of sound in the metal is approximately 404.76 m/s.

Explanation:

To determine the speed of sound in the metal, we need to use the time difference between the two pulses and the length of the metal bar. The time difference between the pulses is 8.40 ms and the length of the bar is 3.4 m. The speed of sound in the metal can be calculated using the formula: speed = distance / time. In this case, the distance is the length of the bar and the time is the time difference between the pulses.

So, by substituting the values into the formula, we get: speed = 3.4 m / (8.40 * 10^-3 s).

Simplifying the equation, we get: speed = 404.76 m/s.

Therefore, the speed of sound in the metal is approximately 404.76 m/s.

Answer:

t = 120.5 nm

Explanation:

given,    

refractive index of the oil = 1.4

wavelength of the red light = 675 nm

minimum thickness of film = ?

formula used for the constructive interference

[tex]2 n t = (m+\dfrac{1}{2})\lambda[/tex]

where n is the refractive index of oil

t is thickness of film

for minimum thickness

m = 0

[tex]2 \times 1.4 \times t = (0+\dfrac{1}{2})\times 675[/tex]

[tex]t = \dfrac{0.5\times 675}{2\times 1.4}[/tex]

        t = 120.5 nm

hence, the thickness of the oil is t = 120.5 nm

Final answer:

The minimum thickness t of the oil film that will give constructive interference of reflected red light with a wavelength of 675 nm is 202.5 nm.

Explanation:

Constructive interference of reflected light occurs when the path difference between the two waves is equal to an integer multiple of the wavelength. In this case, we have constructive interference for red light with a wavelength of 675 nm.

The path difference can be represented as 2nt, where n is the index of refraction of the oil and t is the thickness of the oil film. Since we are viewing the film from air, we need to consider the difference in indices of refraction.

For constructive interference, the path difference must be equal to mλ, where m is the order of the interference. In this case, we have m = 1.

Using the formula for the path difference, we can set up the following equation:

2nt = (m + 1/2)λ

Plugging in the values, we have:

2(1.4)(t) = (1 + 1/2)(675 nm)

Simplifying, we get:

t = 202.5 nm

Therefore, the minimum thickness t of the oil film that will give constructive interference of reflected red light with a wavelength of 675 nm is 202.5 nm.

Answer:

L = 0.109 H

Explanation:

Given that,

Number of loops in the solenoid, N = 1500

Radius of the wire, r = 4 cm = 0.04 m

Length of the rod, l = 13 cm = 0.13 m

To find,

Self inductance in the solenoid

Solution,

The expression for the self inductance of the solenoid is given by :

[tex]L=\dfrac{\mu_o N^2 A}{l}[/tex]

[tex]L=\dfrac{4\pi \times 10^{-7}\times (1500)^2\times \pi (0.04)^2}{0.13}[/tex]

L = 0.109 H

So, the self inductance of the solenoid is 0.109 henries.

Answer:

The separation distance between the slits is 16710.32 nm.

Explanation:

Given that,

Wavelength = 641 nm

Angle =4.4°

(a). We need to calculate the separation distance between the slits

Using formula of young's double slit

[tex]d\sin\theta=m\lambda[/tex]

[tex]d=\dfrac{m\lambda}{\sin\theta}[/tex]

Where, d = the separation distance between the slits

m = number of order

[tex]\lambda[/tex] =wavelength

Put the value into the formula

[tex]d=\dfrac{2\times641\times10^{-9}}{\sin4.4}[/tex]

[tex]d=0.00001671032\ m[/tex]

[tex]d=16710.32\ nm[/tex]

Hence, The separation distance between the slits is 16710.32 nm.

The separation distance between the slits in Young's double slit experiment can be calculated using the formula d = λx / sin(θ), where d is the separation distance, λ is the wavelength of light, θ is the angle of the fringe, and x is the distance between the fringe and the screen.

In Young's double slit experiment, the separation distance between the slits can be determined using the formula:

d = λx / sin(θ)

Where d is the separation distance between the slits, λ is the wavelength of light, θ is the angle of the fringe, and x is the distance between the fringe and the screen. In this example, the second dark fringe on either side of the central maximum is given as θ = 4.4 degrees. To calculate the separation distance between the slits, we also need to know the wavelength of the red light, which is given as λ = 641 nm.

Using the formula, we have:

d = (641 nm) * x / sin(4.4 degrees)

To find the value of d, we need to know the value of x, which is the distance between the fringe and the screen.

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Let's dimension the horizontal length with the name X and the vertical dimensions as Y.

In this way the total volume will be given under the function

[tex]V = x^2 y[/tex]

The cost for the bottom is given by [tex](x^2)(20)=20x^2[/tex]

While the cost for performing the top by [tex](x^2)(16) = 16x^2[/tex]

The cost for performing the sides would be given by [tex](1.5)(xy)(4) = 6xy[/tex]

Therefore the total cost would be

[tex]c_{total}= 36x^2 +6xy[/tex]

The total volume is equivalent to

[tex]784 = x^2y[/tex]

[tex]xy = \frac{784}{x}[/tex]

Replacing in our cost function

[tex]c_{total}= 36x^2 +6xy[/tex]

[tex]c_{total}= 36x^2 +6(\frac{784}{x})[/tex]

Obtaining the first derivative and equalizing to zero we will obtain the ideal measure, therefore

[tex]c' = 0[/tex]

[tex]c' = 72x-\frac{4707}{x^2}[/tex]

[tex]0= 72x-\frac{4707}{x^2}[/tex]

[tex]x = (\frac{523}{2})^{1/3}[/tex]

[tex]x = 6.3947ft[/tex]

Then,

[tex]784 = x^2y[/tex]

[tex]y = \frac{784}{x^2}[/tex]

[tex]y = \frac{784}{6.3947^2}[/tex]

[tex]y = 19.17ft[/tex]

In this way the measures of the base should be 6.3947ft (width and length) and the height of 19.17ft.

Answer:

37.34372 kg

Explanation:

m = Mass

[tex]\Delta T[/tex] = Change in temperature

1 denotes water

2 denotes copper

c = Heat capacity

Heat is given by

[tex]Q=mc\Delta T[/tex]

In this case the heat transfer will be equal

[tex]m_1c_1\Delta T_1=m_2c_2\Delta T_2\\\Rightarrow m_2=\frac{m_1c_1\Delta T_1}{c_2\Delta T_2}\\\Rightarrow m_2=\frac{95.7\times 4.18(24.2-22.7)}{0.39(65.4-24.2)}\\\Rightarrow m_2=37.34372\ kg[/tex]

Mass of copper block is 37.34372 kg

Answer:

Magnetic force, F = 0.262 N

Explanation:

It is given that,

Magnetic field of an electromagnet, B = 0.52 T

Length of the wire, [tex]l = 2r =2\times 2.4=4.8\ cm=0.048\ m[/tex]

Current in the straight wire, i = 10.5 A

Let F is the magnitude of force is exerted on the wire. The magnetic force acting on an object of length l is given by :

[tex]F=ilB[/tex]

[tex]F=10.5\ A\times 0.048\ m\times 0.52\ T[/tex]

F = 0.262 N

So, the magnitude of force is exerted on the wire is 0.262 N.

Answer:

0.875 m/s

5 N

Explanation:

[tex]m_1[/tex] = Mass of person = 50 kg

[tex]m_2[/tex] = Mass of log = 200 kg

[tex]v_1[/tex] = Velocity of person = 1.5 m/s

[tex]v_2[/tex] = Velocity of log

v = Velocity of log with respect to shore = 1 m/s

t = Time taken = 5 seconds

As the momentum of system is conserved we have

[tex](m_1+m_2)v=m_1v_1+m_2v_2\\\Rightarrow v_2=\frac{(m_1+m_2)v-m_1v_1}{m_2}\\\Rightarrow v_2=\frac{(50+200)1-50\times 1.5}{200}\\\Rightarrow v_2=0.875\ m/s[/tex]

Velocity of the log at the end of the 5 seconds is 0.875 m/s

Force is given by

[tex]F=\frac{m(v-u)}{t}\\\Rightarrow F=\frac{50(1.5-1)}{5}\\\Rightarrow F=5\ N[/tex]

The average force between you and the log during those 5 seconds is 5 N

Answer:

850N

Explanation:

The step by step is in the attachment.

To develop this problem it is necessary to apply the concepts related to Broglie hypothesis.

The hypothesis defines that

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

Where,

P = momentum

h = Planck's constant

The momentum is also defined as,

P = mv

Where,

m = mass

v = Velocity

PART A) Replacing at the first equation

[tex]\lambda = \frac{h}{mv}[/tex]

Our values are given as,

[tex]h = 6.626*10^{-34}Js[/tex]

[tex]m = 65Kg[/tex]

[tex]\lambda = 0.76m[/tex]

Re-arrange to find v, we have:

[tex]v = \frac{h}{m\lambda}[/tex]

[tex]v = \frac{6.626*10^{-34}}{65*0.76}[/tex]

[tex]v = 1.341*10^{-35}m/s[/tex]

PART B) From the kinematic equations of movement description we know that velocity is defined as displacement over a period of time, that is

[tex]v = \frac{x}{t}[/tex]

Re-arrange to find t,

[tex]t = \frac{d}{v}[/tex]

[tex]t = \frac{0.001}{ 1.341*10^{-35}}[/tex]

[tex]t = 7.455*10^{31}s[/tex]

[tex]7.455*10^{31} > 4*10^{17} \rightarrow[/tex]the age of the universe.

Answer:

6.47385 N

Explanation:

m = Mass of stone = 0.538 kg

t = Time taken to hit the rock = 0.964 seconds

v = Velocity of rock = 11.6 m/s

Force is given by

[tex]F=\frac{mv}{t}\\\Rightarrow F=\frac{0.538\times 11.6}{0.964}\\\Rightarrow F=\frac{6.2408}{0.964}\\\Rightarrow F=6.47385\ N[/tex]

The magnitude of the average force experienced by the boat during this process is 6.47385 N

The momentum of each thrown rock is 6.241 kg·m/s. The force or thrust on the boat is the rate of change of this momentum, which equates to an average force of 6.47 N.

The topic of this question falls under the domain of Physics, specifically momentum. The phenomenon at hand is the principle of conservation of momentum which states that the momentum of an isolated system remains constant if no external forces are acting on it.

The momentum of each rock thrown is given by the product of its mass and its velocity, which is (0.538 kg)(11.6 m/s)= 6.241 kg·m/s. Given that a rock is thrown every 0.964 second, the rate of change of momentum, which is equal to the force, can be calculated by dividing the momentum of each rock by the time between each throw. So, the average force experienced by the boat is 6.241 kg·m/s / 0.964 s = 6.47 N (rounded to 2 decimal places).

Therefore, each time a rock is thrown out of the boat, there is an equal and opposite thrust on the boat which averages to a force of 6.47 N.

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Answer:

solid

Explanation:

they molecules are closely together

Answer:

[tex]m_l=0.619\ kg[/tex]

Explanation:

Given:

For the whole ice to melt in lemonade and result a temperature of 11.8°C the total heat lost by the lemonade will be equal to the total heat absorbed by the ice to come to 0°C from -10.2°C along with the latent heat absorbed in the melting of ice at 0°C and the heat absorbed by the ice water of 0°C to reach a temperature of 11.8°C.

Now, mathematically:

[tex]Q_l=Q_i+Q_m+Q_w[/tex]

[tex]m_l.c_w.\Delta T_l=m_i.c_i.\Delta T_i_i+m_i.L+m_i.c_w.\Delta T_w[/tex]

[tex]m_l.c_w.(T_{il}-T_f)=m_i(c_i.\Delta T_i_i+L+c_w.\Delta T_w)[/tex]

[tex]m_l\times 4186\times (20.5-11.8)=0.055(2000\times (0-(-10.2))+340000+4186\times (11.8-0))[/tex]

[tex]m_l=0.619\ kg[/tex] (mass of lemonade)

True

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Answer:

[tex] \lambda = 3.21 \ cm[/tex]

Explanation:

given,                                                                            

width of narrow slit = 4.8 cm                                

minimum angle of diffraction = θ = 42°                

wavelength of the microwave = ?                            

condition for the diffraction for single slit diffraction

      [tex]d sin \theta = m \lambda[/tex]              

for the first minima m = 1                          

      [tex]d sin \theta = \lambda[/tex]                  

wavelength of microwave radiation is equal to

      [tex] \lambda = d sin \theta[/tex]                

      [tex] \lambda = 4.8\times sin 42^0[/tex]  

      [tex] \lambda = 3.21 \ cm[/tex]                

the wavelength of microwaves is equal to [tex] \lambda = 3.21 \ cm[/tex]

The wavelength of the microwaves is approximately 0.032 m or 3.2 cm.

To find the wavelength of the microwaves given the slit width and the angle of the first diffraction minimum, you can use the diffraction formula for a single slit:

where:

Given:

Rearrange the formula to solve for the wavelength [tex]\(\lambda\)[/tex]:

Plug in the values:

First, calculate [tex]\(\sin 42^\circ\)[/tex]:

Now compute the wavelength:

So, the wavelength of the microwaves is approximately [tex]\(0.032 \text{ m}\) or \(3.2 \text{ cm}\)[/tex].

Answer:8.8 m/s

Explanation:

Given

mass of train [tex]m_1=0.6 kg[/tex]

velocity of Train [tex]v_1=20 m/s[/tex]

mass of another train [tex]m_2=1.5 kg[/tex]

Final velocity of both train [tex]v=12 m/s[/tex]

Let [tex]v_2[/tex] be the velocity of [tex]m_2[/tex] before collision

As external Force is zero therefore change in momentum is zero

conserving Momentum

[tex]m_1v_1+m_2v_2=(m_1+m_2)v[/tex]

[tex]0.6\times 20+1.5\times v_2=(0.6+1.5)\cdot 12[/tex]

[tex]1.5\times v_2=25.2-12[/tex]

[tex]v=\frac{13.2}{1.5}=8.8 m/s[/tex]    

The magnetic flux through an object like a bracelet can change a) because the bracelet is moving in the magnetic field, field direction, or if the bracelet moves through the field. Examples include loops moving into or rotating within a magnetic field.

The reason why the magnetic flux through the bracelet is changing can be due to various factors. These include a change in the magnitude of the magnetic field, a) a change in the field's direction relative to the bracelet, or the bracelet moving through the magnetic field. Magnetic flux changes when a loop moves into a magnetic field or rotates within it. Specifically, in part (a) as the loop moves into the field, and in part (b) as the loop rotates, thus changing the orientation.

It is also indicated that the change in magnetic flux through a loop or coil can result from the spinning of a magnet nearby, causing the magnetic field within the coil to change rapidly, as described with a rotating magnet affecting coil current due to the variation in the number and direction of magnetic field lines passing through it.

The correct option is c. The bracelet is moving in the magnetic field.

Magnetic flux through a surface, such as a bracelet, is defined as the product of the magnetic field (B), the area of the surface (A), and the cosine of the angle (θ) between the magnetic field lines and the normal to the surface. Mathematically, this is expressed as:

[tex]\[ \Phi_B = B \cdot A \cdot \cos(\theta) \][/tex]

 For the magnetic flux to change, one or more of the following must occur:

 1. The magnitude of the magnetic field (B) changes.

2. The area of the surface (A) changes.

3. The orientation of the surface with respect to the magnetic field changes, i.e., the angle (θ) changes.

4. The surface moves within the magnetic field, changing the amount of field lines passing through it.

 Given the options:

 a. The magnitude of the magnetic field is changing. - This would indeed change the magnetic flux, but it is not one of the given scenarios.

 b. The magnetic field is changing direction with respect to the bracelet. - This would also change the magnetic flux, as it would change the angle θ between the magnetic field lines and the normal to the surface of the bracelet. However, this option does not explicitly state that the direction of the magnetic field is changing; it only mentions the direction with respect to the bracelet, which could imply a change in orientation of the bracelet itself.

 c. The bracelet is moving in the magnetic field. - This option indicates that the bracelet is changing its position within the magnetic field. As the bracelet moves, the amount of magnetic field lines passing through it can change, even if the magnetic field itself is uniform and constant. This movement can alter the effective area through which the field lines pass (A) and/or the angle (θ), thus changing the magnetic flux.

Since the question asks for the reason why the magnetic flux through the bracelet is changing, and option c directly describes a scenario where the bracelet's movement within the field would cause a change in flux, it is the correct answer. The other options either do not apply to the given scenario or are not explicitly described as occurring.

The calculated tension is in the cable at the end of the scaffolding is 208.94 N.

First, let's calculate the weights acting on the system: the weight of the watermelon (Wm) and the weight of the scaffolding (Ws). Wm = mass of the watermelon × gravity = 7.1 kg × 9.8 m/s2 = 69.58 N, and Ws = 260 N given. Next, we choose the pivot point at the end of the scaffolding opposite the watermelon to find the tension in the cable at that end. The distance from the watermelon to the supporting cable is (4.8 m - 0.53 m) = 4.27 m, and the distance from the pivot to the scaffold's center of mass (assuming it's uniform) is half its length, or 2.4 m.

Applying the equilibrium condition for torques (Τclockwise = Τcounterclockwise), we have:

(69.58 N × 4.27 m) + (260 N × 2.4 m) = T × 4.8 m

⇒ T = ((69.58 N × 4.27 m) + (260 N × 2.4 m)) / 4.8 m

⇒ T = 208.94 N.

The tension in the cable at the end of the scaffolding where the watermelon is placed is [tex]{34.79 \text{ N}} \)[/tex].

Given:

- Mass of the watermelon, [tex]\( m = 7.1 \)[/tex] kg

- Acceleration due to gravity, [tex]\( g = 9.8 \)[/tex] m/s²

- Length of the scaffolding, [tex]\( L = 4.8 \)[/tex] m

- Distance of the watermelon from one end, [tex]\( d = 0.53 \)[/tex] m

1. Calculate the weight of the watermelon:

[tex]\[ W = mg = 7.1 \times 9.8 = 69.58 \text{ N} \][/tex]

2. Determine the tensions in the cables:

 Since the system is in equilibrium, the tension [tex]\( T_1 \)[/tex] at the end where the watermelon is placed and the tension [tex]\( T_2 \)[/tex] at the opposite end satisfy:

[tex]\[ T_1 + T_2 = W \][/tex]

3. Find [tex]\( T_2 \)[/tex]:

From the equilibrium condition:

[tex]\[ T_2 = \frac{W}{2} = \frac{69.58}{2} = 34.79 \text{ N} \][/tex]

4. Calculate [tex]\( T_1 \)[/tex]:

  Since [tex]\( T_1 + T_2 = W \)[/tex] and [tex]\( T_1 = -T_2 \)[/tex] (because [tex]\( T_1 \)[/tex] and [tex]\( T_2 \)[/tex] act in opposite directions):

[tex]\[ T_1 = W - T_2 = 69.58 - 34.79 = 34.79 \text{ N} \][/tex]

Therefore, the tension in the cable at the end of the scaffolding where the watermelon is placed is [tex]{34.79 \text{ N}} \)[/tex].