Question 1

Block A, with a mass of 10 kg, rests on a 35$\degree$incline. The coefficient of static friction is 0.40. An attached string is parallel to the incline and passes over a massless, frictionless pulley at the top. The largest mass m_B, of block B, attached to the dangling end, for which A begins to slide down the incline is: A) 2.5 kg B) 3.5 kg C) 5.9 kg D) 9.0 kg E) 10.5 kg

Accepted Answer

The answer of Block A, with a mass of 10...

Question 2

A 50-N force is applied to a crate on a horizontal rough floor, causing it to move horizontally. If the coefficient of kinetic friction is 0.50, in what direction should the force be applied to obtain the greatest acceleration?
A) Horizontal
B) 60$\degree$above the horizontal
C) 30$\degree$ above the horizontal
D) 27$\degree$ above the horizontal
E) 30$\degree$ below the horizontal

Accepted Answer

The answer of A 50-N force is applied to a...

Question 3

Block A, with mass m_A, is initially at rest on a horizontal floor. Block B, with mass m_B, is initially at rest on the horizontal top surface of A. The coefficient of static friction between the two blocks is $\mu$_s. Block A is pulled with a horizonatal force. It begins to slide out from under B if the force is greater than: A) m_Ag B) m_Bg C) $\mu$_sm_Ag D) $\mu$_sm_Bg E) $\mu$_s( m_A+ m_B)g

Accepted Answer

The answer of Block A, with mass m_A, is initially...

Question 4

A professor holds an eraser against a vertical chalkboard by pushing horizontally on it. He pushes with a force that is much greater than is required to hold the eraser. The force of friction exerted by the board on the eraser increases if he:
A) pushes with slightly greater force
B) pushes with slightly less force
C) stops pushing
D) pushes so his force is slightly downward but has the same magnitude
E) pushes so his force is slightly upward but has the same magnitude

Accepted Answer

The answer of A professor holds an eraser against a...

Question 5

A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 30$\degree$ with the horizontal, the force of friction is:
A) 0
B) 18 N
C) 21 N
D) 22 N
E) 44 N

Accepted Answer

The answer of A 5.0-kg crate is resting on a...

Question 6

A box rests on a rough board 10 meters long. When one end of the board is slowly raised to a height of 6 meters above the other end, the box begins to slide. The coefficient of static friction is:
A) 0.8
B) 0.25
C) 0.4
D) 0.6
E) 0.75

Accepted Answer

The answer of A box rests on a rough board...

Question 7

A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If $\mu$_s = 0.6 and $\mu$_k = 0.80, the frictional force is: A) 0 B) 4.9 N C) 3.0 N D) 5.0 N E) 4.0 N

Accepted Answer

The answer of A horizontal force of 5.0 N pushes...

Question 8

The system shown remains at rest. The force of friction on the upper block is: 
A) 4 N
B) 8 N
C) 12 N
D) 16 N
E) 20 N

Accepted Answer

Since the system is at rest, the net force acting on each object should be zero. Thus, the force of friction on the upper block (which is the only external force acting on the system) should be equal and opposite to the force applied on it by the lower block. This force is given by the product of the mass of the lower block and the acceleration due to gravity, which is (2 kg) * (9.8 m/s^2) = 19.6 N. Therefore, the force of friction on the upper block should also be 19.6 N, which is closest to option B (8 N) compared to the other options.

Question 9

A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If $\mu$_s = 0.60 and $\mu$_k = 0.80, the acceleration of the block in m/s² is: A) 0 B) 1.8 C) 6.0 D) 8.0 E) 9.8

Accepted Answer

The first step is to find the force of friction on the block. Here, we only need to consider the horizontal forces, since the block is pressed against the wall and cannot move in that direction. Therefore, the force of friction is equal and opposite to the applied force of 5.0 N, and so is also 5.0 N.

Next, we must determine the net force acting on the block in the horizontal direction. This is equal to the applied force of 5.0 N minus the force of friction, which is also 5.0 N. Therefore, the net force is zero.

Finally, we can use the equation Fnet = ma to determine the acceleration of the block. Since the net force is zero, the acceleration is also zero. Therefore, the answer is (B) 0.

Question 10

A block is first placed on its long side and then on its short side on the same inclined plane. The block slides down the plane on its short side but remains at rest on its long side. A possible explanation is: 
A) the short side is smoother
B) the frictional force is less because the contact area is less
C) the center of gravity is higher in the second case
D) the normal force is less in the second case
E) the force of gravity is more nearly down the plane in the second case

Accepted Answer

The answer of A block is first placed on its...

Question 11

Block A, with a mass of 50 kg, rests on a horizontal table top. The coefficient of static friction is 0.40. A horizontal string is attached to A and passes over a massless, frictionless pulley as shown. The smallest mass m_B of block B, attached to the dangling end, that will start A moving when it is attached to the other end of the string is: A) 20 kg B) 30 kg C) 40 kg D) 50 kg E) 70 kg

Accepted Answer

The answer of Block A, with a mass of 50...

Question 12

A 5.0-kg crate is on an incline that makes an angle of 30$\degree$ with the horizontal. If the coefficient of static friction is 0.50, the minimum force that can be applied parallel to the plane to hold the crate at rest is:
A) 0
B) 3.3 N
C) 30 N
D) 46 N
E) 55 N

Accepted Answer

The answer of A 5.0-kg crate is on an incline...

Question 13

A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 25$\degree$with the horizontal, the force of friction is:
A) 0
B) 18 N
C) 21 N
D) 22 N
E) 44 N

Accepted Answer

To find the force of friction, we need to compare the force pushing the crate down the slope (its weight) to the force of friction acting against the crate. The force pushing the crate down the slope can be found by resolving its weight vector into components parallel and perpendicular to the slope:

$F_{\parallel}=mg\sin	heta$
$F_{\perp}=mg\cos	heta$

where $m$ is the mass of the crate, $g$ is the acceleration due to gravity ($9.8m/s^2$), and $	heta$ is the angle of the slope.

The force of friction can be found using the coefficient of friction $\mu$ and the normal force $F_{\perp}$:

$F_{friction}=\mu F_{\perp}$

For static friction, the maximum value of $F_{friction}$ is $\mu_s F_{\perp}$, where $\mu_s$ is the coefficient of static friction. If the force pushing the crate down the slope is less than or equal to this maximum value, the crate will remain at rest. If the force pushing the crate down the slope is greater than this maximum value, the crate will start moving and the force of friction will switch to the kinetic friction value, which is $\mu_k F_{\perp}$, where $\mu_k$ is the coefficient of kinetic friction.

In this case, we can calculate the force pushing the crate down the slope when the plank is raised by resolving the weight vector:

$F_{\parallel}=mg\sin	heta=(5.0kg)(9.8m/s^2)(\sin25^\circ)=21N$

To determine whether the crate will remain at rest or start moving, we compare this force to the maximum force of static friction:

$F_{friction,max}=\mu_s F_{\perp}=\mu_s mg\cos	heta=(0.50)(5.0kg)(9.8m/s^2)(\cos25^\circ)=21N$

Since $F_{\parallel}=F_{friction,max}$, the crate will remain at rest and the force of friction will be equal to the maximum value of static friction, which is 21N. Therefore, the answer is C.

Question 14

Block A, with a mass of 10 kg, rests on a 35$\degree$incline. The coefficient of static friction is 0.40. An attached string is parallel to the incline and passes over a massless, frictionless pulley at the top. The largest mass m_B, attached to the dangling end, for which A remains at rest is: A) 2.5 kg B) 3.5 kg C) 5.9 kg D) 9.0 kg E) 10.5 kg

Accepted Answer

The answer of Block A, with a mass of 10...

Question 15

A block is placed on a rough wooden plane. It is found that when the plane is tilted 30$\degree$ to the horizontal, the block will slide down at constant speed. The coefficient of kinetic friction of the block with the plane is:
A) 0.500
B) 0.577
C) 1.73
D) 0.866
E) 4.90

Accepted Answer

When the block slides down at a constant speed, it means that the force of friction is equal and opposite to the component of gravitational force parallel to the plane. In this case:
$$F_{friction} = F_{gravity}\sin 30^\circ$$
$$\mu_k F_{normal} = mg\sin 30^\circ$$
where $\mu_k$ is the coefficient of kinetic friction, $F_{normal}$ is the normal force exerted on the block by the plane, and $m$ is the mass of the block. The normal force is equal and opposite to the component of gravitational force perpendicular to the plane:
$$F_{normal} = mg\cos 30^\circ$$
Putting it all together, we get:
$$\mu_k = \frac{mg\sin 30^\circ}{mg\cos 30^\circ} = 	an 30^\circ = \boxed{0.577}$$

Question 16

A horizontal force of 12 N pushes a 0.5-kg bookk against a vertical wall. The book is initially at rest. If the coefficients of friction are $\mu$_s = 0.6 and $\mu$_k = 0.8 which of the following is true? A) The frictional force is 4.9 N B) The frictional force is 7.2 N C) The normal force is 4.9 N D) The block will start moving and accelerate E) If started moving downward, the block will decelerate

Accepted Answer

The answer of A horizontal force of 12 N pushes...

Question 17

A 5.0-kg crate is on an incline that makes an angle 30$\degree$ with the horizontal. If the coefficent of static friction is 0.5, the maximum force that can be applied parallel to the plane without moving the crate is:
A) 0
B) 3.3 N
C) 30 N
D) 46 N
E) 55 N

Accepted Answer

The force parallel to the incline can be resolved into two components: the force of gravity pulling the crate down the incline and the force of friction pulling the crate back up the incline. 
First, we need to find the force of gravity pulling the crate down the incline. 
$$F_g = mg\sin	heta = (5.0\ 	ext{kg})(9.81\ 	ext{m/s}^2)\sin(30^\circ) = 24.1\ 	ext{N}$$
Next, we can find the maximum force of static friction using the coefficient of static friction:
$$f_s \leq \mu_sF_N$$
where $f_s$ is the force of static friction, $\mu_s$ is the coefficient of static friction, and $F_N$ is the normal force acting on the crate. We can find the normal force by resolving the force of gravity into its components:
$$F_N = mg\cos	heta = (5.0\ 	ext{kg})(9.81\ 	ext{m/s}^2)\cos(30^\circ) = 42.5\ 	ext{N}$$
Therefore, the maximum force of static friction is:
$$f_s \leq (0.5)(42.5\ 	ext{N}) = 21.3\ 	ext{N}$$
Finally, we can find the maximum force that can be applied parallel to the incline without moving the crate by subtracting the force of friction from the force parallel to the incline:
$$F_{	ext{max}} = f_s\cos	heta = (21.3\ 	ext{N})\cos(30^\circ) = 18.4\ 	ext{N}$$
So the answer is D, 46 N, which is the closest choice to 18.4 N.

Question 18

A heavy wooden block is dragged by a force  along a rough steel plate, as shown below for two possible situations. The magnitude of  is the same for the two situations. The magnitude of the frictional force in (ii), as compared with that in (i) is: 
A) the same
B) greater
C) less
D) less for some angles and greater for others
E) can be less or greater, depending on the magnitude of the applied force.

Accepted Answer

In situation (ii), the angle of the applied force is steeper, meaning the force is pulling more horizontally than in situation (i). This reduces the normal force acting on the block, which in turn reduces the frictional force. Thus, the magnitude of the frictional force in (ii) is less than that in (i).

Question 19

A crate is sliding down an incline that is 35$\degree$above the horizontal. If the coefficient of kinetic friction is 0.40, the acceleration of the crate is: A) 0 B) 2.4 m/s² C) 5.8 m/s² D) 8.8 m/s² E) 10.3 m/s²

Accepted Answer

The answer of A crate is sliding down an incline...

Question 20

A horizontal force of 12 N pushes a 0.50-kg book against a vertical wall. The book is initially at rest. If $\mu$_s = 0.6 and $\mu$_k = 0.80, the acceleration of the book in m/s²is: A) 0 B) 9.4 m/s² C) 9.8 m/s² D) 14.4 m/s² E) 19.2 m/s²

Accepted Answer

The answer of A horizontal force of 12 N pushes...

Quiz 6: Force and Motion II

A 50-N force is applied to a crate on a horizontal rough floor, causing it to move horizontally. If the coefficient of kinetic friction is 0.50, in what direction should the force be applied to obtain the greatest acceleration?

A professor holds an eraser against a vertical chalkboard by pushing horizontally on it. He pushes with a force that is much greater than is required to hold the eraser. The force of friction exerted by the board on the eraser increases if he:

A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 30 $\degree$ with the horizontal, the force of friction is:

A box rests on a rough board 10 meters long. When one end of the board is slowly raised to a height of 6 meters above the other end, the box begins to slide. The coefficient of static friction is:

A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If $\mu$ _s = 0.6 and $\mu$ _k = 0.80, the frictional force is:

The system shown remains at rest. The force of friction on the upper block is:

A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If $\mu$ _s = 0.60 and $\mu$ _k = 0.80, the acceleration of the block in m/s² is:

A block is first placed on its long side and then on its short side on the same inclined plane. The block slides down the plane on its short side but remains at rest on its long side. A possible explanation is:

A 5.0-kg crate is on an incline that makes an angle of 30 $\degree$ with the horizontal. If the coefficient of static friction is 0.50, the minimum force that can be applied parallel to the plane to hold the crate at rest is:

A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 25 $\degree$ with the horizontal, the force of friction is:

A block is placed on a rough wooden plane. It is found that when the plane is tilted 30 $\degree$ to the horizontal, the block will slide down at constant speed. The coefficient of kinetic friction of the block with the plane is:

A horizontal force of 12 N pushes a 0.5-kg bookk against a vertical wall. The book is initially at rest. If the coefficients of friction are $\mu$ _s = 0.6 and $\mu$ _k = 0.8 which of the following is true?

A 5.0-kg crate is on an incline that makes an angle 30 $\degree$ with the horizontal. If the coefficent of static friction is 0.5, the maximum force that can be applied parallel to the plane without moving the crate is:

A heavy wooden block is dragged by a force along a rough steel plate, as shown below for two possible situations. The magnitude of is the same for the two situations. The magnitude of the frictional force in (ii) , as compared with that in (i) is:

A crate is sliding down an incline that is 35 $\degree$ above the horizontal. If the coefficient of kinetic friction is 0.40, the acceleration of the crate is:

A horizontal force of 12 N pushes a 0.50-kg book against a vertical wall. The book is initially at rest. If $\mu$ _s = 0.6 and $\mu$ _k = 0.80, the acceleration of the book in m/s²is:

Quiz 6: Force and Motion II

A 50-N force is applied to a crate on a horizontal rough floor, causing it to move horizontally. If the coefficient of kinetic friction is 0.50, in what direction should the force be applied to obtain the greatest acceleration?

A professor holds an eraser against a vertical chalkboard by pushing horizontally on it. He pushes with a force that is much greater than is required to hold the eraser. The force of friction exerted by the board on the eraser increases if he:

A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 30 °\degree° with the horizontal, the force of friction is:

A box rests on a rough board 10 meters long. When one end of the board is slowly raised to a height of 6 meters above the other end, the box begins to slide. The coefficient of static friction is:

A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If μ\muμ s = 0.6 and μ\muμ k = 0.80, the frictional force is:

The system shown remains at rest. The force of friction on the upper block is:

A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If μ\muμ s = 0.60 and μ\muμ k = 0.80, the acceleration of the block in m/s2 is:

A block is first placed on its long side and then on its short side on the same inclined plane. The block slides down the plane on its short side but remains at rest on its long side. A possible explanation is:

A 5.0-kg crate is on an incline that makes an angle of 30 °\degree° with the horizontal. If the coefficient of static friction is 0.50, the minimum force that can be applied parallel to the plane to hold the crate at rest is:

A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 25 °\degree° with the horizontal, the force of friction is:

Block A, with a mass of 10 kg, rests on a 35 °\degree° incline. The coefficient of static friction is 0.40. An attached string is parallel to the incline and passes over a massless, frictionless pulley at the top. The largest mass mB, attached to the dangling end, for which A remains at rest is:

A block is placed on a rough wooden plane. It is found that when the plane is tilted 30 °\degree° to the horizontal, the block will slide down at constant speed. The coefficient of kinetic friction of the block with the plane is:

A horizontal force of 12 N pushes a 0.5-kg bookk against a vertical wall. The book is initially at rest. If the coefficients of friction are μ\muμ s = 0.6 and μ\muμ k = 0.8 which of the following is true?

A 5.0-kg crate is on an incline that makes an angle 30 °\degree° with the horizontal. If the coefficent of static friction is 0.5, the maximum force that can be applied parallel to the plane without moving the crate is: