Question 1

A 600-kg car is going around a banked curve with a radius of 110 m at a speed of 27.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?

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Question 2

A car enters a 300-m radius flat curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600. What is the maximum speed which the car can travel around the curve without sliding?

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Question 3

FIGURE 5-5 
-A 4.00-kg block is sliding up the plane on a 30.0 degree incline as shown in Fig. 5-5. If the coefficient of kinetic friction between the block and the incline is 0.700, what will be the acceleration of the block if a 50.0-N horizontal force pushes on the block?

Accepted Answer

The net force acting on the block includes gravitational force, frictional force, and the horizontal force. Calculating these forces and using Newton's second law gives an acceleration of 4.40 m/s² down the incline.

Question 4

A 1000-kg car is picking up speed as it goes around a horizontal curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.350. At what speed will the car begin to skid sideways?

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Question 5

A 600-kg car is going over a curve with a radius of 120 m that is banked at an angle of 25° with a speed of 30.0 m/s. The coefficient of static friction between the car and the road is 0.30. What is the normal force exerted by the road on the car?

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Question 6

FIGURE 5-5 
-A box is sliding down an incline tilted at an angle 14.0° above horizontal. The box is sliding down the incline at a speed of 1.70 m/s. The coefficient of kinetic friction between the box and the incline is 0.380. How far does the box slide down the incline before coming to rest?

Accepted Answer

Explanation:The force of kinetic friction is:$$f_k=\mu_kn$$$$f_k=(0.380)(mg\cos14.0\degree)$$The work done by the force of kinetic friction is:$$W_f=-f_kd$$The change in kinetic energy of the box is:$$\Delta K=\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2$$The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Therefore, we have:$$W_f=\Delta K$$$$-f_kd=\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2$$$$-(0.380)(mg\cos14.0\degree)d=\frac{1}{2}m(0)^2-\frac{1}{2}m(1.70	ext{ m/s})^2$$$$d=\frac{(1.70	ext{ m/s})^2}{2(0.380)(g\cos14.0\degree)}$$$$d=1.16	ext{ m}$$

Question 7

An airplane is flying with constant speed of 300 m/s along a horizontal circle with a radius of 15,000 m. If the lift force of the air on the wings is perpendicular to the wings, at what angle relative to the horizontal should the wings be banked?

Accepted Answer

The lift force of the air on the wings can be resolved into two components - one perpendicular to the wings, which provides the necessary centripetal force, and the other parallel to the wings, which counters gravity. Therefore, we can use the following formula to find the required angle:

tan θ = v^2 / (g * r)

where v = 300 m/s, g = 9.81 m/s^2, and r = 15000 m.

Plugging in the values, we get:

tan θ = (300)^2 / (9.81 * 15000) ≈ 0.3716

Taking the inverse tangent, we find:

θ ≈ 31.5°

Therefore, the correct answer is choice C.

Question 8

FIGURE 5-5 
-A 4.00-kg block rests on a 30.0 degree incline as shown in Fig. 5-5. If the coefficient of static friction between the block and the incline is 0.700, with what magnitude force must a horizontal force act on the block to start it moving up the incline?

Accepted Answer

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-A 4.00-kg block rests on...

Question 9

A 600-kg car is going around a curve with a radius of 120 m that is banked at an angle of 25.0° with a speed of 30.0 m/s. The coefficient of static friction between the car and the road is 0.300. What is the force exerted by friction on the car?

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Question 10

A car drives over a hilltop that has a radius of curvature 120 m at the top of the hill. At what speed would the car be traveling when it tires just barely lose contact with the road when the car is at the top of the hill?

Accepted Answer

At the top of the hill, the gravitational force provides the necessary centripetal force for circular motion. The condition for the car to just barely lose contact is when the normal force is zero. Using the formula for centripetal force, $mg = \frac{mv^2}{r}$, we can solve for $v$: $v = \sqrt{gr}$. Substituting $g = 9.8 \, \text{m/s}^2$ and $r = 120 \, \text{m}$, we find $v \approx 34.3 \, \text{m/s}$.

Question 11

A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 2.00 m making 0.700 revolutions per second. What is the centripetal acceleration of the ball?

Accepted Answer

The centripetal acceleration is calculated using the formula $ a_c = 4\pi^2r f^2 $, where $ r = 2.00 \, \text{m} $ and $ f = 0.700 \, \text{rev/s} $. Plugging in the values, $ a_c = 4\pi^2(2.00)(0.700)^2 \approx 38.7 \, \text{m/s}^2 $.

Question 12

A 2-kg ball is moving with a constant speed of 5 m/s in a horizontal circle whose radius is 50 cm. What is the acceleration of the ball?

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Question 13

FIGURE 5-5 
-A 50.0-kg block is being pulled up a 13.0° slope by a force of 250 N which 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?

Accepted Answer

The net force on the block is the applied force minus the force of friction and the component of gravitational force parallel to the slope. The frictional force is calculated using the normal force and the coefficient of kinetic friction. The acceleration is found by dividing the net force by the mass of the block.

Question 14

A car travels around 200 m radius flat curve at 40 m/s at constant speed. What is the minimum static coefficient of friction which allows it to travel at this speed without sliding?

Accepted Answer

The minimum static coefficient of friction can be calculated using the formula for centripetal force: $ f_s = \frac{v^2}{r} $, where $ v $ is the velocity and $ r $ is the radius. The frictional force must equal the centripetal force needed to keep the car on the curve, so $ \mu_s \cdot g = \frac{v^2}{r} $. Solving for $ \mu_s $, we get $ \mu_s = \frac{v^2}{g \cdot r} $. Substituting $ v = 40 \, \text{m/s} $, $ r = 200 \, \text{m} $, and $ g = 9.8 \, \text{m/s}^2 $, we find $ \mu_s \approx 0.815 $.

Question 15

A child pulls a 3.00-kg sled across level ground at constant velocity with a light rope that makes an angle 34.0° above horizontal. The tension in the rope is 5.00 N. Assuming the acceleration of gravity is 9.81 m/s², what is the coefficient of friction between the sled and the ground?

Accepted Answer

The coefficient of friction is given by:$$\mu_k = \frac{F_f}{N}$$where:* $F_f$ is the force of friction* $N$ is the normal forceThe force of friction is equal to the tension in the rope:$$F_f = T = 5.00 	ext{ N}$$The normal force is equal to the weight of the sled:$$N = mg = (3.00 	ext{ kg})(9.81 	ext{ m/s}^2) = 29.43 	ext{ N}$$Therefore, the coefficient of friction is:$$\mu_k = \frac{F_f}{N} = \frac{5.00 	ext{ N}}{29.43 	ext{ N}} = 0.169$$The closest answer choice is A) 0.156.

Question 16

A 600-kg car is going around a curve with a radius of 120 m that is banked at an angle of 20° with a speed of 24.5 m/s. What is the minimum coefficient of static friction required for the car not to skid?

Accepted Answer

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Question 17

FIGURE 5-4 
-A 4.00-kg block rests between the floor and a 3.00-kg block as shown in Fig. 5-4. The 3.00-kg block is tied to a wall by a horizontal rope. If the coefficient of static friction is 0.800 between each pair of surfaces in contact, what force must be applied horizontally to the 4.00-kg block to make it move?

Accepted Answer

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-A 4.00-kg block rests between...

Question 18

FIGURE 5-6 
-Two masses are connected by a string which goes over an ideal pulley as shown in Fig. 5-6. Block A has a mass of 3.00 kg and can slide along a rough plane inclined 30.0° to the horizontal. The coefficient of kinetic friction between block A and the plane is 0.400. Block B has a mass of 2.77 kg. What is the acceleration of the blocks?

Accepted Answer

The net force on the system is the difference between the gravitational component pulling block A down the incline and the gravitational force pulling block B down. The frictional force on block A also opposes its motion. Solving the equations of motion for the system gives an acceleration of approximately 0.392 m/s².

Question 19

A 2-kg ball is moving with a constant speed of 5 m/s in a horizontal circle whose radius is 50 cm. What is the magnitude of the net force on the ball?

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Question 20

A child stands on a playground merry-go-round a distance of 1.50 m from the rotation axis. The coefficient of static friction between the child's shoes and the surface of the merry-go-round is 0.700. Assuming the acceleration of gravity is 9.81 m/s², what is the maximum constant angular speed of the merry-go-round for which the child will not start to slide?

Accepted Answer

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Quiz 5: Using Newtons Laws: Friction, Circular Motion, Drag Forces

A 600-kg car is going around a banked curve with a radius of 110 m at a speed of 27.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?

A car enters a 300-m radius flat curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600. What is the maximum speed which the car can travel around the curve without sliding?

FIGURE 5-5 -A 4.00-kg block is sliding up the plane on a 30.0 degree incline as shown in Fig. 5-5. If the coefficient of kinetic friction between the block and the incline is 0.700, what will be the acceleration of the block if a 50.0-N horizontal force pushes on the block?

A 1000-kg car is picking up speed as it goes around a horizontal curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.350. At what speed will the car begin to skid sideways?

A 600-kg car is going over a curve with a radius of 120 m that is banked at an angle of 25° with a speed of 30.0 m/s. The coefficient of static friction between the car and the road is 0.30. What is the normal force exerted by the road on the car?

FIGURE 5-5 -A box is sliding down an incline tilted at an angle 14.0° above horizontal. The box is sliding down the incline at a speed of 1.70 m/s. The coefficient of kinetic friction between the box and the incline is 0.380. How far does the box slide down the incline before coming to rest?

An airplane is flying with constant speed of 300 m/s along a horizontal circle with a radius of 15,000 m. If the lift force of the air on the wings is perpendicular to the wings, at what angle relative to the horizontal should the wings be banked?

FIGURE 5-5 -A 4.00-kg block rests on a 30.0 degree incline as shown in Fig. 5-5. If the coefficient of static friction between the block and the incline is 0.700, with what magnitude force must a horizontal force act on the block to start it moving up the incline?

A 600-kg car is going around a curve with a radius of 120 m that is banked at an angle of 25.0° with a speed of 30.0 m/s. The coefficient of static friction between the car and the road is 0.300. What is the force exerted by friction on the car?

A car drives over a hilltop that has a radius of curvature 120 m at the top of the hill. At what speed would the car be traveling when it tires just barely lose contact with the road when the car is at the top of the hill?

A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 2.00 m making 0.700 revolutions per second. What is the centripetal acceleration of the ball?

A 2-kg ball is moving with a constant speed of 5 m/s in a horizontal circle whose radius is 50 cm. What is the acceleration of the ball?

FIGURE 5-5 -A 50.0-kg block is being pulled up a 13.0° slope by a force of 250 N which 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 car travels around 200 m radius flat curve at 40 m/s at constant speed. What is the minimum static coefficient of friction which allows it to travel at this speed without sliding?

A child pulls a 3.00-kg sled across level ground at constant velocity with a light rope that makes an angle 34.0° above horizontal. The tension in the rope is 5.00 N. Assuming the acceleration of gravity is 9.81 m/s2, what is the coefficient of friction between the sled and the ground?

A 600-kg car is going around a curve with a radius of 120 m that is banked at an angle of 20° with a speed of 24.5 m/s. What is the minimum coefficient of static friction required for the car not to skid?

A 2-kg ball is moving with a constant speed of 5 m/s in a horizontal circle whose radius is 50 cm. What is the magnitude of the net force on the ball?

A child pulls a 3.00-kg sled across level ground at constant velocity with a light rope that makes an angle 34.0° above horizontal. The tension in the rope is 5.00 N. Assuming the acceleration of gravity is 9.81 m/s², what is the coefficient of friction between the sled and the ground?