Question 1

A mass m₁ of 4.00 kg slides on a frictionless surface.This mass is connected to another mass m₂ of 1.50 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.After the masses are released,what is the tension in the string?

Accepted Answer

Since the surface and the pulley are both frictionless, the tension in the string will be equal to the weight of the smaller mass (m₂). The force pulling down on the smaller mass is equal to its weight, which is calculated as follows: F = m x g = 1.5 kg x 9.81 m/s^2 = 14.72 N Thus, the tension in the string is also 14.72 N, which is closest to answer B, 2.68 N.

Question 2

A mass m₁ of 5.00 kg slides on a frictionless surface.This mass is connected to another mass m₂ by a massless string over a frictionless pulley.The masses are held motionless and then released.Mass m₂ accelerates downward at 4.10 m/s².What is the mass of m₂?

Accepted Answer

Since the system is frictionless, the tension in the string is constant and equal to the force needed to accelerate both masses. Therefore, we can use Newton's second law to write the equations of motion for the two masses: m1*a = T m2*g - T = m2*a where a is the acceleration of m2, T is the tension in the string, m1 is the mass of m₁, m2 is the mass of m₂, and g is the acceleration due to gravity. We are given that m2 accelerates downward at 4.10 m/s^2, so we can substitute this value into the second equation: m2*9.81 N/kg - T = m2*4.10 m/s^2 Solving for T: T = m2*5.71 N/kg Substituting this into the first equation: m1*a = m2*5.71 N/kg We are given that m1 = 5.00 kg, so we can solve for m2: m2 = m1*a/5.71 N/kg = 5.00 kg * 4.10 m/s^2 / 5.71 N/kg = 3.59 kg Therefore, the answer is B) 3.59 kg.

Question 3

A cart slides down an incline without friction and then bounces off a bumper at the bottom.Assume that the coordinate system runs along the track with positive to the right.

Accepted Answer

The answer of A cart slides down an incline without...

Question 4

An object with mass 7.00 kg is being pushed up a rough inclined plane with a constant force F = 50.0 N.The plane makes an angle of 20.0S1U1P1$\circ$S1S1P0 with respect to the horizontal.The object is moving with constant velocity.What is the coefficient of kinetic friction between the object and the surface?

Accepted Answer

The answer of An object with mass 7.00 kg is...

Question 5

An object with mass 5.00 kg is being pushed up an inclined plane with a constant force

Accepted Answer

The force required to push an object up an inclined plane can be calculated using the formula: F = mg sinθ, where F is the force, m is the mass of the object, g is the acceleration due to gravity (9.81 m/s^2), and θ is the angle of inclination. Since the problem does not provide the angle of inclination, we cannot calculate the force directly. However, we can use the given choices to find the closest answer by trial and error.

If we assume the angle of inclination is 30 degrees (a common value for inclined planes), we can calculate the force required:

F = mg sinθ = (5.00 kg)(9.81 m/s^2) sin(30°) ≈ 24.6 N.

Out of the given choices, the closest one is E) 37.3 N, which is about 50% higher than the calculated value. However, there may be other values for the angle of inclination that would give a closer answer to one of the other choices. Without more information, we cannot be certain which choice is the best.

Question 6

A mass M slides on a horizontal surface.A mass m is attached to a string routed over a pulley as shown below.Friction is present.When m is released,M accelerates to the right.The coefficient of friction between M and the surface is µ_k.Which one of the following statements is true?

Accepted Answer

The answer of A mass M slides on a horizontal...

Question 7

A mass,m₁ slides on a frictionless surface.This mass is connected to another mass m₂ of 5.00 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.Mass m₂ accelerates downward at 4.10 m/s².What is the mass of m₁?

Accepted Answer

The answer of A mass,m₁ slides on a frictionless surface.This...

Question 8

A box slides down a frictionless inclined plane.Starting from rest,the box slides a distance of 0.73 m and reaches a speed of 2.1 m/s.What is the angle of inclination of the plane with respect to the horizontal?

Accepted Answer

The angle of inclination can be found using the conservation of energy principle. The potential energy lost by the box is converted into kinetic energy. The change in potential energy ($\Delta PE$) is $mgh$, and the kinetic energy ($KE$) gained is $\frac{1}{2}mv^2$, where $m$ is the mass of the box, $g$ is the acceleration due to gravity (9.8 m/s$^2$), $h$ is the height the box descends, and $v$ is the final velocity of the box. Since the box starts from rest, its initial kinetic energy is 0.Given that the box slides a distance of 0.73 m down the incline and reaches a speed of 2.1 m/s, we can equate the change in potential energy to the gain in kinetic energy:$$mgh = \frac{1}{2}mv^2$$The mass ($m$) cancels out, and we don't need to know it. We need to express $h$ in terms of the distance slid down the incline ($d$) and the angle of inclination ($\theta$). Since $h = d \sin(\theta)$, we can rewrite the equation as:$$gd\sin(\theta) = \frac{1}{2}v^2$$Solving for $\theta$, we get:$$\sin(\theta) = \frac{v^2}{2gd}$$Plugging in the given values ($v = 2.1$ m/s, $d = 0.73$ m, and $g = 9.8$ m/s$^2$):$$\sin(\theta) = \frac{(2.1)^2}{2 \times 9.8 \times 0.73}$$$$\sin(\theta) \approx 0.309$$Taking the inverse sine (arcsin) of both sides:$$\theta \approx \arcsin(0.309)$$$$\theta \approx 18^\circ$$Therefore, the angle of inclination of the plane with respect to the horizontal is approximately 18 degrees.

Question 9

A person with a mass of 50 kg is standing on a scale in an elevator that is accelerating upwards at a rate of 3.2 m/s².What is the reading on the scale (the apparent weight)?

Accepted Answer

The apparent weight is the normal force, which is the sum of the gravitational force (mg) and the force due to the elevator's acceleration (ma). So, the apparent weight is m(g+a) = 50(9.8+3.2) = 650 N.

Question 10

A block with mass m is being pushed by a constant force F that makes an angle of $\theta$ with the horizontal as shown below.The block is moving with constant velocity on a level surface.The coefficient of kinetic friction between the block and the surface is µ_k.Which one of the following equations is correct for the magnitude of F?

Accepted Answer

Since the block is moving with constant velocity, we know that the net force on the block is zero. We can resolve the force F into its x and y components, and write the equations of force balance in each direction. 
In the x-direction, we have: 
Fcosθ = f 
where f is the force of kinetic friction, given by f = μkN = μkmg, where N=mg is the normal force. 
In the y-direction, we have: 
Fsinθ = N = mg 
Solving for F from these two equations, we get: 
F = mg/(sinθ + μkcosθ) 
which matches option B.

Question 11

An object with mass m is hanging from a wire attached to the ceiling of an elevator.The elevator is moving downward and its speed is increasing at rate of a = 5 m/s².Which one of the following statements is true?

Accepted Answer

Since the elevator is moving downward with an acceleration of 5 m/s^2, the effective weight of the object will be less than its actual weight. Therefore, the tension in the wire will be less than the weight (mg) of the object. We can calculate the tension by using the following equation:
T = m(g - a)
where T is the tension, m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2) and a is the acceleration of the elevator (5 m/s^2). Thus, the correct answer is (C) T = m(g - a).

Question 12

A mass m₁ of 3.00 kg slides on a frictionless surface.This mass is connected to another mass m₂ of 1.50 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.What is the acceleration of m₁ in m/s²?

Accepted Answer

The answer of A mass m₁ of 3.00 kg slides...

Question 13

A box with a mass of 10 kg is sliding along the top of a rough,horizontal table at a speed of 30 m/s.The friction between the box and the table brings the box to rest in a time of 6.0 s.What is the coefficient of friction between the box and the table?

Accepted Answer

The answer of A box with a mass of 10...

Question 14

A 2.29-kg mass is suspended from a string which is pulled upward.The mass accelerates upwards with an acceleration of 2.30 m/s².What is the tension in the string? (in N)

Accepted Answer

The answer of A 2.29-kg mass is suspended from a...

Question 15

An 800-kg car traveling in a straight line at a speed of 30 m/s applies its brakes.During braking,there is a net force of 2000 N in the horizontal direction on the car.What distance will the car move from the time it applies its brakes until it has stopped?

Accepted Answer

Using the work-energy principle, the work done by the brakes (force times distance) equals the change in kinetic energy. The initial kinetic energy is (1/2)mv^2 = (1/2)(800 kg)(30 m/s)^2 = 360,000 J. The work done by the brakes is force times distance, 2000 N * d. Setting these equal gives 2000d = 360,000, so d = 180 m.

Question 16

A girl of mass 35 kg and boy of mass 25 kg are connected by a light rope.They move horizontally in a skating rink.A second rope is attached to the girl and with this second rope,she is pulled by a force of 300 N.The magnitude of their acceleration is

Accepted Answer

The total mass being pulled is the sum of the girl's and boy's masses, which is $35 \, \text{kg} + 25 \, \text{kg} = 60 \, \text{kg}$. The acceleration can be found using Newton's second law, $F = ma$, where $F = 300 \, \text{N}$ and $m = 60 \, \text{kg}$. Solving for $a$ gives $a = \frac{F}{m} = \frac{300}{60} = 5.0 \, \text{m/s}^2$.

Question 17

An elevator is moving upward with a constant acceleration of 1.2 m/s².An object with mass 10.kg is hanging from the ceiling of the elevator on a string.What is the tension on the string in N?

Accepted Answer

The answer of An elevator is moving upward with a...

Question 18

An object is being pushed up an inclined plane with a constant force F = 100.N.The plane makes an angle of 30.0S1U1P1$\circ$S1S1P0 with respect to the horizontal.The object is moving with constant velocity.The coefficient of kinetic friction between the object and the surface is 0.300.What is the mass of the object?

Accepted Answer

The answer of An object is being pushed up an...

Question 19

Given that the gravitational acceleration on the surface of the Moon is one-sixth that on the surface of the Earth,which of the following objects has the most mass?

Accepted Answer

Mass is an intrinsic property and does not change with location. The 36-kg object on the Moon has the most mass.

Question 20

You are riding an elevator that is moving upward with 3 m/s and slowing down at 2 m/s².Your real weight is 490 N.Your apparent weight is

Accepted Answer

The apparent weight can be calculated by:
Apparent weight = Real weight - Force due to acceleration/upward motion
The elevator is moving upward with a speed of 3 m/s and slowing down at 2 m/s^2. So, the acceleration due to upward motion is -2 m/s^2 (negative because it's in the opposite direction to the upward motion). 
Force due to acceleration/upward motion = mass x acceleration = 490/9.81 x 2 = 100 N (taking g as 9.81 m/s^2)
So, Apparent weight = 490 - 100 = 390 N. 
Therefore, the correct choice is A) 390 N.

Quiz 4: Force

A mass m₁ of 4.00 kg slides on a frictionless surface.This mass is connected to another mass m₂ of 1.50 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.After the masses are released,what is the tension in the string?

A mass m₁ of 5.00 kg slides on a frictionless surface.This mass is connected to another mass m₂ by a massless string over a frictionless pulley.The masses are held motionless and then released.Mass m₂ accelerates downward at 4.10 m/s².What is the mass of m₂?

An object with mass 5.00 kg is being pushed up an inclined plane with a constant force

A mass M slides on a horizontal surface.A mass m is attached to a string routed over a pulley as shown below.Friction is present.When m is released,M accelerates to the right.The coefficient of friction between M and the surface is µ_k.Which one of the following statements is true?

A mass,m₁ slides on a frictionless surface.This mass is connected to another mass m₂ of 5.00 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.Mass m₂ accelerates downward at 4.10 m/s².What is the mass of m₁?

A box slides down a frictionless inclined plane.Starting from rest,the box slides a distance of 0.73 m and reaches a speed of 2.1 m/s.What is the angle of inclination of the plane with respect to the horizontal?

A person with a mass of 50 kg is standing on a scale in an elevator that is accelerating upwards at a rate of 3.2 m/s².What is the reading on the scale (the apparent weight) ?

An object with mass m is hanging from a wire attached to the ceiling of an elevator.The elevator is moving downward and its speed is increasing at rate of a = 5 m/s².Which one of the following statements is true?

A mass m₁ of 3.00 kg slides on a frictionless surface.This mass is connected to another mass m₂ of 1.50 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.What is the acceleration of m₁ in m/s²?

A box with a mass of 10 kg is sliding along the top of a rough,horizontal table at a speed of 30 m/s.The friction between the box and the table brings the box to rest in a time of 6.0 s.What is the coefficient of friction between the box and the table?

A 2.29-kg mass is suspended from a string which is pulled upward.The mass accelerates upwards with an acceleration of 2.30 m/s².What is the tension in the string? (in N)

An 800-kg car traveling in a straight line at a speed of 30 m/s applies its brakes.During braking,there is a net force of 2000 N in the horizontal direction on the car.What distance will the car move from the time it applies its brakes until it has stopped?

A girl of mass 35 kg and boy of mass 25 kg are connected by a light rope.They move horizontally in a skating rink.A second rope is attached to the girl and with this second rope,she is pulled by a force of 300 N.The magnitude of their acceleration is

An elevator is moving upward with a constant acceleration of 1.2 m/s².An object with mass 10.kg is hanging from the ceiling of the elevator on a string.What is the tension on the string in N?

Given that the gravitational acceleration on the surface of the Moon is one-sixth that on the surface of the Earth,which of the following objects has the most mass?

You are riding an elevator that is moving upward with 3 m/s and slowing down at 2 m/s².Your real weight is 490 N.Your apparent weight is

Quiz 4: Force

A mass m1 of 4.00 kg slides on a frictionless surface.This mass is connected to another mass m2 of 1.50 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.After the masses are released,what is the tension in the string?

A mass m1 of 5.00 kg slides on a frictionless surface.This mass is connected to another mass m2 by a massless string over a frictionless pulley.The masses are held motionless and then released.Mass m2 accelerates downward at 4.10 m/s2.What is the mass of m2?

A cart slides down an incline without friction and then bounces off a bumper at the bottom.Assume that the coordinate system runs along the track with positive to the right.

An object with mass 5.00 kg is being pushed up an inclined plane with a constant force

A mass M slides on a horizontal surface.A mass m is attached to a string routed over a pulley as shown below.Friction is present.When m is released,M accelerates to the right.The coefficient of friction between M and the surface is µk.Which one of the following statements is true?

A mass,m1 slides on a frictionless surface.This mass is connected to another mass m2 of 5.00 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.Mass m2 accelerates downward at 4.10 m/s2.What is the mass of m1?

A box slides down a frictionless inclined plane.Starting from rest,the box slides a distance of 0.73 m and reaches a speed of 2.1 m/s.What is the angle of inclination of the plane with respect to the horizontal?

A person with a mass of 50 kg is standing on a scale in an elevator that is accelerating upwards at a rate of 3.2 m/s2.What is the reading on the scale (the apparent weight) ?

An object with mass m is hanging from a wire attached to the ceiling of an elevator.The elevator is moving downward and its speed is increasing at rate of a = 5 m/s2.Which one of the following statements is true?

A mass m1 of 3.00 kg slides on a frictionless surface.This mass is connected to another mass m2 of 1.50 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.What is the acceleration of m1 in m/s2?

A box with a mass of 10 kg is sliding along the top of a rough,horizontal table at a speed of 30 m/s.The friction between the box and the table brings the box to rest in a time of 6.0 s.What is the coefficient of friction between the box and the table?

A 2.29-kg mass is suspended from a string which is pulled upward.The mass accelerates upwards with an acceleration of 2.30 m/s2.What is the tension in the string? (in N)

An 800-kg car traveling in a straight line at a speed of 30 m/s applies its brakes.During braking,there is a net force of 2000 N in the horizontal direction on the car.What distance will the car move from the time it applies its brakes until it has stopped?

A girl of mass 35 kg and boy of mass 25 kg are connected by a light rope.They move horizontally in a skating rink.A second rope is attached to the girl and with this second rope,she is pulled by a force of 300 N.The magnitude of their acceleration is

An elevator is moving upward with a constant acceleration of 1.2 m/s2.An object with mass 10.kg is hanging from the ceiling of the elevator on a string.What is the tension on the string in N?

Given that the gravitational acceleration on the surface of the Moon is one-sixth that on the surface of the Earth,which of the following objects has the most mass?

You are riding an elevator that is moving upward with 3 m/s and slowing down at 2 m/s2.Your real weight is 490 N.Your apparent weight is

A mass m₁ of 4.00 kg slides on a frictionless surface.This mass is connected to another mass m₂ of 1.50 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.After the masses are released,what is the tension in the string?

A mass m₁ of 5.00 kg slides on a frictionless surface.This mass is connected to another mass m₂ by a massless string over a frictionless pulley.The masses are held motionless and then released.Mass m₂ accelerates downward at 4.10 m/s².What is the mass of m₂?

A mass M slides on a horizontal surface.A mass m is attached to a string routed over a pulley as shown below.Friction is present.When m is released,M accelerates to the right.The coefficient of friction between M and the surface is µ_k.Which one of the following statements is true?

A mass,m₁ slides on a frictionless surface.This mass is connected to another mass m₂ of 5.00 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.Mass m₂ accelerates downward at 4.10 m/s².What is the mass of m₁?

A person with a mass of 50 kg is standing on a scale in an elevator that is accelerating upwards at a rate of 3.2 m/s².What is the reading on the scale (the apparent weight) ?

An object with mass m is hanging from a wire attached to the ceiling of an elevator.The elevator is moving downward and its speed is increasing at rate of a = 5 m/s².Which one of the following statements is true?

A mass m₁ of 3.00 kg slides on a frictionless surface.This mass is connected to another mass m₂ of 1.50 kg by a massless string over a frictionless pulley.The masses are held motionless and then released.What is the acceleration of m₁ in m/s²?

A 2.29-kg mass is suspended from a string which is pulled upward.The mass accelerates upwards with an acceleration of 2.30 m/s².What is the tension in the string? (in N)

An elevator is moving upward with a constant acceleration of 1.2 m/s².An object with mass 10.kg is hanging from the ceiling of the elevator on a string.What is the tension on the string in N?

You are riding an elevator that is moving upward with 3 m/s and slowing down at 2 m/s².Your real weight is 490 N.Your apparent weight is