Question 1

A mass M = 5.6 kg on a horizontal table is pulled by a horizontal string that passes over a frictionless pulley to a free-hanging mass m = 3.4 kg. The coefficient of friction between M and the table is 0.28. The acceleration of M is A) 3.7 m/s². B) 2.0 m/s². C) 2.2 m/s². D) 0.20 m/s². E) 0.49 m/s².

Accepted Answer

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Question 2

A tired worker pushes a heavy 100-kg) crate that is resting on a thick pile carpet. The coefficients of static and kinetic friction are 0.6 and 0.4, respectively. The worker pushes with a horizontal force of 490 N. The frictional force exerted by the surface is
A) 980 N.
B) 588 N.
C) 490 N.
D) 392 N.
E) 100 N.

Accepted Answer

The maximum static friction is 588 N (0.6 * 980 N), but since the worker's force is 490 N, which is less than 588 N, the frictional force equals the applied force, 490 N.

Question 3

A worker pushes a heavy 100-kg) crate that is resting on a thick pile carpet. The coefficients of static and kinetic friction are 0.6 and 0.4, respectively. The worker pushes with a horizontal force of 600 N. Use g = 9.8 m/s². The frictional force exerted by the surface is A) 980 N. B) 588 N. C) 490 N. D) 392 N. E) 98 N.

Accepted Answer

The answer of A worker pushes a heavy 100-kg) crate...

Question 4

A worker pushes a heavy 100-kg) crate that is resting on a thick pile carpet. The coefficients of static and kinetic friction are 0.6 and 0.4, respectively. The worker pushes with a horizontal force of 600 N. Use g = 9.8 m/s². The acceleration of the crate will be A) 9.8 m/s². B) 4.9 m/s². C) 3.5 m/s². D) 2.1 m/s². E) 0 m/s².

Accepted Answer

The force of friction acting on the crate can be found using the formula:
friction = coefficient of friction * normal force
where the normal force is equal to the weight of the crate (since it is on a horizontal surface).
friction = 0.6 * 100 * 9.8 = 588 N
Since the force of the worker's push is greater than the force of friction, the crate will accelerate. The acceleration can be found using the formula:
net force = mass * acceleration
where the net force is the force of the worker's push minus the force of friction.
net force = 600 N - 588 N = 12 N
acceleration = net force / mass = 12 N / 100 kg = 0.12 m/s^2
Finally, since the coefficient of kinetic friction is less than the coefficient of static friction, once the crate starts moving, the force of friction will decrease to 0.4 * 100 * 9.8 = 392 N. Thus, the crate will continue to move with a constant velocity (i.e. no more acceleration). Therefore, the acceleration of the crate is 2.1 m/s^2.

Question 5

An object with a mass of 5.5 kg is allowed to slide from rest down an inclined plane. The plane makes an angle of 30^o with the horizontal. The coefficient of friction between the plane and the object is 0.35. The acceleration of the object is A) 5.3 m/s². B) 2.8 m/s². C) 3.4 m/s². D) 9.8 m/s². E) 1.9 m/s².

Accepted Answer

The answer of An object with a mass of 5.5...

Question 6

A block is placed on an inclined plane with an angle of inclination $\theta$ in degrees) with respect to horizontal. The coefficient of static friction between the block and the inclined plane is 0.7. For what maximum value of $\theta$ will the block remain stationary on the inclined surface? A) 35^o B) 82^o C) 44^o D) 30^o E) 18^o

Accepted Answer

The maximum value of $\theta$ for which the block will remain stationary on the inclined surface is given by:$$\theta = \tan^{-1}(\mu_s)$$where $\mu_s$ is the coefficient of static friction.In this case, $\mu_s$ = 0.7, so:$$\theta = \tan^{-1}(0.7) = 35^o$$

Question 7

A block is placed on a plane whose angle of inclination is 30^o. The coefficients of static and kinetic friction for the block on the inclined plane are 0.5 and 0.4, respectively. The block A) remains stationary on the inclined plane. B) accelerates down the inclined plane. C) travels down the inclined plane at constant velocity. D) travels up the inclined plane at constant velocity. E) accelerates up the inclined plane.

Accepted Answer

The answer of A block is placed on a plane...

Question 8

A 100-kg block is pushed up a 30^o incline at constant velocity. If the coefficient of friction between the block and the incline is 0.1, what constant force parallel to the incline is required to move the block? A) 0.49 kN B) 0.085 kN C) 0.22 kN D) 0.80 kN E) 0.58 kN

Accepted Answer

The answer of A 100-kg block is pushed up a...

Question 9

A block of mass m is pulled in the direction shown in the figure across a rough surface at a constant velocity. The magnitude of the frictional force is A) µ_kmg. B) µ_kT cos $\theta$ C) µ_kT - mg). D) µ_kT sin $\theta$ E) µ_kmg - T sin $\theta$).

Accepted Answer

The answer of  A block of mass m is...

Question 10

Which of the following statements is NOT true about friction? A) µ_k is less than µ_s. B) µ_k is independent of the relative speed of the surfaces in the range of about 1 cm/s to several meters per second. C) µ_k depends on the relative speed of the surfaces at speeds over several meters per second. D) The coefficients of friction depend on the nature of the surfaces. E) The force of static friction depends on the area of contact between the two surfaces.

Accepted Answer

The force of static friction does not depend on the area of contact between the two surfaces; it depends on the normal force and the materials in contact, represented by the coefficient of static friction.

Question 11

A worker pulls horizontally on a rope that is attached to a 10-kg crate resting on a rough floor. The coefficients of static and kinetic friction are 0.5 and 0.3, respectively. The worker pulls with a force of 40 N. The frictional force exerted by the surface is
A) 30 N.
B) 50 N.
C) 10 N.
D) 100 N.
E) 40 N.

Accepted Answer

The answer of A worker pulls horizontally on a rope...

Question 12

A block of mass m is pulled in the direction shown in the figure across a rough surface at a constant velocity. The magnitude of the frictional force is A) µ_kmg. B) T cos $\theta$ C) T - µ_kmg). D) µ_kT sin $\theta$ E) µ_kmg - T sin $\theta$).

Accepted Answer

The answer of  A block of mass m is...

Question 13

A mass m is placed on a rough incline at an angle $\theta$ to the horizon. A force F is applied up the incline so that the mass slides up the incline. Using the compass rose, the direction of the frictional force is along 
A) a.
B) b.
C) c.
D) d.
E) e.

Accepted Answer

The answer of A mass m is placed on a...

Question 14

An object with a mass of 5.5 kg is allowed to slide from rest down an inclined plane. The plane makes an angle of 30^o with the horizontal and is 72 m long. The coefficient of friction between the plane and the object is 0.35. The speed of the object at the bottom of the plane is A) 5.3 m/s. B) 15 m/s. C) 24 m/s. D) 17 m/s. E) 11 m/s.

Accepted Answer

First, we need to find the acceleration of the object down the plane using the equation:

a = gsinθ - μgcosθ

where g is the acceleration due to gravity (9.8 m/s2), θ is the angle of the plane (30°), and μ is the coefficient of friction (0.35).

a = (9.8 m/s2)sin(30°) - (0.35)(9.8 m/s2)cos(30°)
a = 4.53 m/s2

Next, we can use the equation for acceleration to find the final velocity of the object at the bottom of the plane:

v^2 = u^2 + 2as

where u is the initial velocity (0 m/s), s is the distance down the plane (72 m), and a is the acceleration we just calculated.

v^2 = 2(4.53 m/s2)(72 m)
v = 16.9 m/s

However, this is just the speed without considering the force of friction. We need to adjust for the work done against friction:

Wfriction = μmgd

where m is the mass of the object (5.5 kg) and d is the distance down the plane (72 m).

Wfriction = (0.35)(5.5 kg)(9.8 m/s2)(72 m) = 135.51 J

The work-energy principle states that the work done on an object is equal to its change in kinetic energy. In this case, the work done on the object is:

W = Fd = μmgd

where F is the force of friction. So we can write:

Fd = 1/2mvf^2 - 1/2mu^2

Solving for vf, we get:

vf = sqrt[2Fd/m + u^2]

Substituting in the values we know:

vf = sqrt[2(135.51 J)/(5.5 kg) + 0^2] = 17 m/s

Therefore, the answer is D) 17 m/s.

Question 15

A block is placed on a plane whose angle of inclination is 30^o. The coefficients of static and kinetic friction for the block on the inclined plane are 0.7 and 0.5, respectively. The block A) remains stationary on the inclined plane. B) accelerates down the inclined plane. C) travels down the inclined plane at constant velocity. D) travels up the inclined plane at constant velocity. E) accelerates up the inclined plane.

Accepted Answer

The block remains stationary on the inclined plane because the force of gravity acting downhill is balanced by the force of static friction uphill, which is equal to the force of gravity in this case (since the block is not moving). The coefficient of static friction is greater than the force trying to move the block, so it stays in place.

Question 16

A block is placed on a plane whose angle of inclination is 30^o. The coefficients of static and kinetic friction for the block on the inclined plane are both 0.2. The block A) remains stationary on the inclined plane. B) accelerates down the inclined plane. C) travels down the inclined plane at constant velocity. D) travels up the inclined plane at constant velocity. E) accelerates up the inclined plane.

Accepted Answer

The gravitational component down the plane (mg sin 30°) is greater than the maximum static friction (μs mg cos 30°), causing the block to accelerate down the plane.

Question 17

A 50-kg block rests on a horizontal surface. The coefficient of static friction $\mu$_s = 0.50. The coefficient of kinetic friction $\mu$_k = 0.35. A force of 250 N is applied as shown. Which of the following statemen best describes the subsequent motion? A) The block remains at rest. B) The block moves and continues to move at constant velocity. C) The block accelerates to the right. D) The block does not move until is increased to greater than 490 N. E) No conclusions can be drawn concerning the movement of the block from the information given.

Accepted Answer

The force applied is greater than the force of static friction, so the block will begin to move. The coefficient of kinetic friction is less than the coefficient of static friction, so the force required to maintain a constant velocity is less than the force required to start moving the block. Therefore, the block will accelerate to the right.

Question 18

An object with a mass M = 250 g is at rest on a plane that makes an angle $\theta$ = 30^o above the horizontal. The coefficient of kinetic friction between M and the plane is µ_k = 0.100. Mass M is attached by a string to another mass, m = 200 g, which hangs freely. When mass m has fallen 30.0 cm, its speed is A) 83 cm/s. B) 48 cm/s. C) 160 cm/s. D) 59 cm/s. E) 72 cm/s.

Accepted Answer

The answer of  An object with a mass M...

Question 19

A mass m is placed on a rough incline at an angle $\theta$ to the horizon. A force F is applied up the incline, to prevent the mass from sliding down the incline, and it is just enough to prevent the mass from sliding down the incline. Using the compass rose, the direction of the frictional force is along 
A) a.
B) b.
C) c.
D) d.
E) e.

Accepted Answer

The frictional force always acts opposite to the direction of motion or the impending motion. Here, the force F is preventing the mass from sliding down the incline and hence the frictional force will act opposite to the direction of F, which is along the incline in the downward direction. Therefore, the direction of the frictional force is along b.

Question 20

A 100-kg block is pushed up a 30^o incline that is 10 m long. If the coefficient of friction between the block and the incline is 0.1, the constant force parallel to the incline that is required to move the block from rest at the bottom of the incline to the top in 3 s is approximately A) 0.49 kN. B) 0.085 kN. C) 0.22 kN. D) 0.80 kN. E) 0.58 kN.

Accepted Answer

First, we need to calculate the angle of incline:

tan θ = opposite / adjacent = 1/3

θ = tan^-1(1/3) = 18.4°

Next, we need to calculate the normal force:

N = mg cos θ = 100 kg x 9.8 m/s^2 x cos 18.4° = 942.5 N

Then, we need to calculate the force of friction:

f = μN = 0.1 x 942.5 N = 94.3 N

Finally, we can use Newton's second law to calculate the force parallel to the incline:

F = ma = mgsinθ - f = 100 kg x 9.8 m/s^2 x sin 18.4° - 94.3 N = 787.2 N

This is the force required to move the block up the incline. However, we need to find the force required to move the block from rest to the top of the incline in 3 seconds, which means we need to calculate the average force:

Fave = F / t = 787.2 N / 3 s = 262.4 N

This is the force required to move the block on average. To convert this to kilonewtons:

Fave = 0.2624 kN

Rounding to two decimal places, the answer is D) 0.80 kN.

Quiz 5: Forces and Motion II: Applications

A mass M = 5.6 kg on a horizontal table is pulled by a horizontal string that passes over a frictionless pulley to a free-hanging mass m = 3.4 kg. The coefficient of friction between M and the table is 0.28. The acceleration of M is

A tired worker pushes a heavy 100-kg) crate that is resting on a thick pile carpet. The coefficients of static and kinetic friction are 0.6 and 0.4, respectively. The worker pushes with a horizontal force of 490 N. The frictional force exerted by the surface is

A worker pushes a heavy 100-kg) crate that is resting on a thick pile carpet. The coefficients of static and kinetic friction are 0.6 and 0.4, respectively. The worker pushes with a horizontal force of 600 N. Use g = 9.8 m/s2. The frictional force exerted by the surface is

A worker pushes a heavy 100-kg) crate that is resting on a thick pile carpet. The coefficients of static and kinetic friction are 0.6 and 0.4, respectively. The worker pushes with a horizontal force of 600 N. Use g = 9.8 m/s2. The acceleration of the crate will be

An object with a mass of 5.5 kg is allowed to slide from rest down an inclined plane. The plane makes an angle of 30 o with the horizontal. The coefficient of friction between the plane and the object is 0.35. The acceleration of the object is

A block is placed on an inclined plane with an angle of inclination θ\thetaθ in degrees) with respect to horizontal. The coefficient of static friction between the block and the inclined plane is 0.7. For what maximum value of θ\thetaθ will the block remain stationary on the inclined surface?

A block is placed on a plane whose angle of inclination is 30 o . The coefficients of static and kinetic friction for the block on the inclined plane are 0.5 and 0.4, respectively. The block

A 100-kg block is pushed up a 30 o incline at constant velocity. If the coefficient of friction between the block and the incline is 0.1, what constant force parallel to the incline is required to move the block?

A block of mass m is pulled in the direction shown in the figure across a rough surface at a constant velocity. The magnitude of the frictional force is

Which of the following statements is NOT true about friction?

A worker pulls horizontally on a rope that is attached to a 10-kg crate resting on a rough floor. The coefficients of static and kinetic friction are 0.5 and 0.3, respectively. The worker pulls with a force of 40 N. The frictional force exerted by the surface is

A block of mass m is pulled in the direction shown in the figure across a rough surface at a constant velocity. The magnitude of the frictional force is

A mass m is placed on a rough incline at an angle θ\thetaθ to the horizon. A force F is applied up the incline so that the mass slides up the incline. Using the compass rose, the direction of the frictional force is along

An object with a mass of 5.5 kg is allowed to slide from rest down an inclined plane. The plane makes an angle of 30 o with the horizontal and is 72 m long. The coefficient of friction between the plane and the object is 0.35. The speed of the object at the bottom of the plane is

A block is placed on a plane whose angle of inclination is 30 o . The coefficients of static and kinetic friction for the block on the inclined plane are 0.7 and 0.5, respectively. The block

A block is placed on a plane whose angle of inclination is 30 o . The coefficients of static and kinetic friction for the block on the inclined plane are both 0.2. The block

A 50-kg block rests on a horizontal surface. The coefficient of static friction μ\muμ s = 0.50. The coefficient of kinetic friction μ\muμ k = 0.35. A force of 250 N is applied as shown. Which of the following statemen best describes the subsequent motion?

A 100-kg block is pushed up a 30 o incline that is 10 m long. If the coefficient of friction between the block and the incline is 0.1, the constant force parallel to the incline that is required to move the block from rest at the bottom of the incline to the top in 3 s is approximately

A worker pushes a heavy 100-kg) crate that is resting on a thick pile carpet. The coefficients of static and kinetic friction are 0.6 and 0.4, respectively. The worker pushes with a horizontal force of 600 N. Use g = 9.8 m/s². The frictional force exerted by the surface is

A worker pushes a heavy 100-kg) crate that is resting on a thick pile carpet. The coefficients of static and kinetic friction are 0.6 and 0.4, respectively. The worker pushes with a horizontal force of 600 N. Use g = 9.8 m/s². The acceleration of the crate will be

An object with a mass of 5.5 kg is allowed to slide from rest down an inclined plane. The plane makes an angle of 30^o with the horizontal. The coefficient of friction between the plane and the object is 0.35. The acceleration of the object is

A block is placed on an inclined plane with an angle of inclination $\theta$ in degrees) with respect to horizontal. The coefficient of static friction between the block and the inclined plane is 0.7. For what maximum value of $\theta$ will the block remain stationary on the inclined surface?

A block is placed on a plane whose angle of inclination is 30^o. The coefficients of static and kinetic friction for the block on the inclined plane are 0.5 and 0.4, respectively. The block

A 100-kg block is pushed up a 30^o incline at constant velocity. If the coefficient of friction between the block and the incline is 0.1, what constant force parallel to the incline is required to move the block?

An object with a mass of 5.5 kg is allowed to slide from rest down an inclined plane. The plane makes an angle of 30^o with the horizontal and is 72 m long. The coefficient of friction between the plane and the object is 0.35. The speed of the object at the bottom of the plane is

A block is placed on a plane whose angle of inclination is 30^o. The coefficients of static and kinetic friction for the block on the inclined plane are 0.7 and 0.5, respectively. The block

A block is placed on a plane whose angle of inclination is 30^o. The coefficients of static and kinetic friction for the block on the inclined plane are both 0.2. The block

A 100-kg block is pushed up a 30^o incline that is 10 m long. If the coefficient of friction between the block and the incline is 0.1, the constant force parallel to the incline that is required to move the block from rest at the bottom of the incline to the top in 3 s is approximately