Question 1

A 50.0-kg block is being pulled up a 16.0° slope by a force of 250 N that is parallel to the slope.The coefficient of kinetic friction between the block and the slope is 0.200.What is the acceleration of the block?
A)0.528 m/ $\mathrm { s }^2$
B)0.158 m/ $\mathrm { s }^2$
C)0.412 m/ $\mathrm { s }^2$
D)0.983 m/ $\mathrm { s }^2$
E)0.260 m/ $\mathrm { s }^2$

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Question 2

A 7.5-kg stone moves up frictionless hill that slopes upward at 41° above the horizontal.If the stone has an initial velocity of 8.5 m/s at the bottom,how far (as measured along the surface of the hill)will it go before stopping?

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Question 3

A 200-g hockey puck is launched up a ramp that is inclined at a 30° angle above the horizontal.The coefficients of static and kinetic friction between the puck and the ramp are µ_s = 0.40 and µ_k = 0.30,respectively,and the puck's initial velocity at the base is 3.8 m/s parallel to the sloping surface of the ramp.What speed does the puck have when it slides back down to its starting point?

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Question 4

A 150-N crate is being pulled up a perfectly smooth ramp that slopes upward at 15° by a pull that is directed at 30° above the surface of the ramp.What is the magnitude of the pull required to make the crate move up the ramp at a constant velocity of 1.75 m/s?

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Question 5

A slanted roof rises at 35° above the horizontal,and the straight-line distance from the top of the roof to the bottom edge is 4.5 m.The roof is covered with ice,so it offers no friction to objects sliding on it.A piece of ice at the top suddenly breaks loose and begins to slide down from rest.
(a)How long will it take for the ice to reach the bottom edge of the roof?
(b)How fast will the ice be traveling just as it reaches the bottom edge?

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Question 6

You push horizontally on a 120-N box that is initially resting on a horizontal table.The coefficient of static friction between the box and the table is 0.75,and the coefficient of kinetic friction is 0.40.Find the friction force exerted on the box by the table if the push is equal to (a)84 N; (b)94 N.

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Question 7

As shown in the figure,block B on a horizontal tabletop is attached by very light horizontal strings to two hanging blocks,A and C.The pulleys are ideal,and the coefficient of kinetic friction between block B and the tabletop is 0.100.The masses of the three blocks are m_A = 12.0 kg,m_B = 7.00 kg,and m_C = 10.0 kg.Find the magnitude and direction of the acceleration of block B after the system is gently released and has begun to move.

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Question 8

A system consisting of blocks,a light frictionless pulley,a frictionless incline,and very light connecting wires is shown in the figure.The wires pull on the left-hand blocks parallel to the surface of the ramp.The 9.0-kg block accelerates downward when the system is released gently from rest.
(a)What is the magnitude of the acceleration of the 9.0-kg block?
(b)What is the tension force that the wire connecting the two blocks on the incline exerts on the blocks?

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Question 9

A 6.0-kg box slides down an inclined plane that makes an angle of 39° with the horizontal.If the coefficient of kinetic friction is 0.40,at what rate does the box accelerate down the slope? A)3.1 m/s² B)3.4 m/s² C)3.7 m/s² D)4.1 m/s²

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Question 10

The figure shows a block of mass m resting on a 20° slope.The coefficients of friction between the block and the surface of the slope are $\mu _ { \mathrm { S } } = 0.64$ and $\mu _ { \mathrm { k } } = 0.54$ It is connected using a very light string over an ideal pulley to a hanging block of mass 2.0 kg.The string above the slope pulls parallel to the surface.What is the minimum mass m so the system will remain at rest when it is released from rest? 
A)2.1 kg
B)3.3 kg
C)1.3 kg
D)3.6 kg

Accepted Answer

To find the minimum mass, we need to consider the maximum force of friction that can act on the block.

The weight of the hanging block is 2.0 kg * 9.81 m/s^2 = 19.62 N.

The force that the string exerts on the block is also 19.62 N (because the system is at rest).

This force is parallel to the slope, so we need to find the component of the weight that is parallel to the slope:

19.62 N * sin 20° = 6.70 N

The maximum force of friction is $\mu _ { \mathrm { S } } m g \cos \theta$ = 0.64 * m * 9.81 m/s^2 * cos 20° = 6.28 m N.

Since the system is at rest, the force of friction must be equal to the force parallel to the slope:

6.28 m N = 6.70 N

Solving for m, we get:

m = 2.1 kg

Question 11

A 15-kg block is on a frictionless ramp that is inclined at 20° above the horizontal.It is connected by a very light string over an ideal pulley at the top edge of the ramp to a hanging 19-kg block,as shown in the figure.The string pulls on the 15-kg block parallel to the surface of the ramp.Find the magnitude of the acceleration of the 19-kg block after the system is gently released. A)4.0 m/s² B)3.8 m/s² C)4.2 m/s² D)4.5 m/s²

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Question 12

A flatbed truck is carrying a 20-kg crate up a sloping road.The coefficient of static friction between the crate and the bed is 0.40,and the coefficient of kinetic friction is 0.30.What is the maximum angle of slope that the truck can climb at constant speed if the crate is to stay in place?
A)0.38°
B)13°
C)17°
D)22°
E)68°

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Question 13

A 200-g hockey puck is launched at an initial speed of 16 m/s up a metal ramp that is inclined at a 30° angle.The coefficients of static and kinetic friction between the hockey puck and the metal ramp are µ_s = 0.40 and µ_k = 0.30,respectively.What vertical height does the puck reach above its starting point? A)8.6 cm B)17 cm C)13 cm D)4.2 cm

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Question 14

A 2.8-kg tool can move on a perfectly smooth ramp that slants at 42° above the horizontal.What are the magnitude and direction of the acceleration of this tool if it is sliding (a)up the ram,(b)down the ramp?

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Question 15

Jason takes off across level water on his jet-powered skis.The combined mass of Jason and his skis is 75 kg (the mass of the fuel is negligible).Water exerts a force of 200 N on the skis.The coefficient of kinetic friction between the skis and water is 0.10.Unfortunately,the skis run out of fuel after only 41 s.How far from his starting point has Jason traveled when he finally coasts to a stop?
A)3900 m
B)2900 m
C)2000 m
D)1400 m

Accepted Answer

Explanation:The force of kinetic friction is:$$f_k=\mu_kn=\mu_kmg=0.10(75	ext{ kg})(9.8	ext{ m/s}^2)=73.5	ext{ N}$$The net force on the skis is:$$F_{net}=F_w-f_k=200	ext{ N}-73.5	ext{ N}=126.5	ext{ N}$$The acceleration of the skis is:$$a=\frac{F_{net}}{m}=\frac{126.5	ext{ N}}{75	ext{ kg}}=1.69	ext{ m/s}^2$$The distance traveled by the skis is:$$d=\frac{1}{2}at^2=\frac{1}{2}(1.69	ext{ m/s}^2)(41	ext{ s})^2=\boxed{2900	ext{ m}}$$

Question 16

A 5.0-kg box slides on the surface on a ramp that rises at 37° above the horizontal.The coefficient of kinetic friction between the box and the surface of the ramp is 0.60.What are the magnitude and direction of the acceleration of the box if it is sliding (a)up the ramp,(b)down the ramp?

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Question 17

Two packages are connected by a very light string that goes over an ideal pulley as shown in the figure.Package A has a mass of 3.0 kg and can slide along a rough plane inclined at 30° above the horizontal.The string pulls on package A parallel to the surface of the plane.The coefficient of static friction between package A and the plane is 0.40.What minimum mass should package B have in order to start package A sliding up the ramp?

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Question 18

The figure shows a system consisting of three blocks,a light frictionless pulley,and light connecting ropes that act horizontally on the upper two blocks.The 9.0-kg block is on a perfectly smooth horizontal table.The surfaces of the 12-kg block are rough,with µ_k = 0.30 between the 12-kg and 9.0-kg blocks.The mass M of the hanging block is set so that it descends at a constant velocity of 3.25 m/s. (a)What is the mass M of the hanging block? (b)The mass M is now changed to 5.0 kg,causing it to accelerate downward after it is released.What is the acceleration of the hanging block?

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Quiz 4: Applying Newtons Laws

A 50.0-kg block is being pulled up a 16.0° slope by a force of 250 N that is parallel to the slope.The coefficient of kinetic friction between the block and the slope is 0.200.What is the acceleration of the block?

A 7.5-kg stone moves up frictionless hill that slopes upward at 41° above the horizontal.If the stone has an initial velocity of 8.5 m/s at the bottom,how far (as measured along the surface of the hill)will it go before stopping?

A 150-N crate is being pulled up a perfectly smooth ramp that slopes upward at 15° by a pull that is directed at 30° above the surface of the ramp.What is the magnitude of the pull required to make the crate move up the ramp at a constant velocity of 1.75 m/s?

A 6.0-kg box slides down an inclined plane that makes an angle of 39° with the horizontal.If the coefficient of kinetic friction is 0.40,at what rate does the box accelerate down the slope?

A flatbed truck is carrying a 20-kg crate up a sloping road.The coefficient of static friction between the crate and the bed is 0.40,and the coefficient of kinetic friction is 0.30.What is the maximum angle of slope that the truck can climb at constant speed if the crate is to stay in place?

A 2.8-kg tool can move on a perfectly smooth ramp that slants at 42° above the horizontal.What are the magnitude and direction of the acceleration of this tool if it is sliding (a)up the ram,(b)down the ramp?

A 5.0-kg box slides on the surface on a ramp that rises at 37° above the horizontal.The coefficient of kinetic friction between the box and the surface of the ramp is 0.60.What are the magnitude and direction of the acceleration of the box if it is sliding (a)up the ramp,(b)down the ramp?