Q: A frog jumps upward from level ground, reaching a maximum height of $$1.0 m. $$The frog pushes off the ground with a constant force for $$0.15 s. $$What is the magnitude of the acceleration during the jump?

$$a = \\dfrac{4.427 \\text{ m/s}}{0.15 \\text{ s}} = 29.51 \\text{ m/s}^2$$

Q: A car is parked on a $$30^\\circ$$ inclined surface. If the brakes fail and the wheels are free to roll, what is the car's acceleration down the incline (neglecting friction)?

$$a = g \\sin(30^\\circ) = 4.9 \\text{ m/s}^2$$

Q: Two boxes, one of mass $$m$$ and one of mass $$2m$$, are stacked and the table is frictionless. What is the smallest possible static coefficient of friction $$\\mu_s$$ between the boxes so that the top box does not slide when a force is applied to the bottom box?

$$f_{s,\\text{max}} = \\mu_s n = \\mu_s 2mg$$

Q: An object moves in a circle of radius $$5 m $$with a constant speed of $$10 m/s. $$What is the centripetal acceleration of the object?

$$a_c = \\dfrac{v^2$}{r} = \\dfrac{(10 \\text{ m/s})^2$}{5 \\text{ m}} = 20 \\text{ m/s}^2$$

Q: A car travels along a $$100 m $$radius banked curve. What is the fastest speed at which the car can travel without slipping if the coefficient of static friction is $$0.2$$ and the banking angle is $$20^\\circ$$?

$$v_{\\text{max}} = \\sqrt{r g (\\tan\\theta + \\mu_s)}$$

Question 1

A skier descends the face of a mountain inclined at $$30^\circ$$ above the horizontal. Which of the following forces acts perpendicular to the surface of the mountain?

Accepted Answer

The normal force ($$n)$$

Question 2

A skier is sliding down a frictional slope. Which force acting on the skier will have the greatest magnitude?

Accepted Answer

The weight of the skier ($$w)$$

Question 3

You push your sister on a skateboard, causing her to accelerate along the floor while you remain stationary. According to Newton's Third Law, how does the magnitude of the force you exert on your sister compare to that exerted on you by your sister?

Accepted Answer

The forces are equal in magnitude.

Question 4

A frog jumps upward from level ground, reaching a maximum height of $$1.0 m. $$The frog pushes off the ground with a constant force for $$0.15 s. $$What is the magnitude of the acceleration during the jump?

Accepted Answer

$$a = \dfrac{4.427 \text{ m/s}}{0.15 \text{ s}} = 29.51 \text{ m/s}^2$$

Question 5

A piano is pulled straight upward with vertically attached ropes at a constant velocity. What is the relationship between the tension force ($$T) $$and the weight ($$w) of $$the piano?

Accepted Answer

The tension force must equal the weight of the piano ($$T = w).$$

Question 6

A car is parked on a $$30^\circ$$ inclined surface. If the brakes fail and the wheels are free to roll, what is the car's acceleration down the incline (neglecting friction)?

Accepted Answer

$$a = g \sin(30^\circ) = 4.9 \text{ m/s}^2$$

Question 7

Two boxes, one of mass $$m$$ and one of mass $$2m$$, are stacked and the table is frictionless. What is the smallest possible static coefficient of friction $$\mu_s$$ between the boxes so that the top box does not slide when a force is applied to the bottom box?

Accepted Answer

$$f_{s,\text{max}} = \mu_s n = \mu_s 2mg$$

Question 8

A car and a truck are moving at $$10 m/s on $$level pavement. Both vehicles' tires have a coefficient of rolling friction $$\mu = 0.10$$ with the pavement. Which force is greater: the force of friction acting on the car or the truck?

Accepted Answer

The force of friction is greater on the truck.

Question 9

If the mass of the car is $$1,000 kg $$and the mass of the truck is $$1,500 kg$$, what is the size of the force exerted by the car on the truck during a collision?

Accepted Answer

Equal in magnitude to the force exerted by the truck on the car.

Question 10

An object moves in a circle of radius $$5 m $$with a constant speed of $$10 m/s. $$What is the centripetal acceleration of the object?

Accepted Answer

$$a_c = \dfrac{v^2$}{r} = \dfrac{(10 \text{ m/s})^2$}{5 \text{ m}} = 20 \text{ m/s}^2$$

Question 11

A car travels along a $$100 m $$radius banked curve. What is the fastest speed at which the car can travel without slipping if the coefficient of static friction is $$0.2$$ and the banking angle is $$20^\circ$$?

Accepted Answer

$$v_{\text{max}} = \sqrt{r g (\tan\theta + \mu_s)}$$

Question 12

You ride a roller coaster at a steady $$30 m/s. $$How does your apparent weight compare to your actual weight when you are at the top of a $$75 m $$radius loop?

Accepted Answer

Your apparent weight is less than your actual weight.

Question 13

A satellite is to be placed in geostationary orbit directly above the Earth's surface. Earth has a mass of $$6.0 \times 10$$^{24}$$ kg. What is the period T$ of the satellite's orbit?

Accepted Answer

$$T = 24 H \times \dfrac{3600 s}{1 H} = 86,400 s$$

Question 14

A car is moving in a circular banked curve. Which force provides the necessary centripetal force for the car to stay on the curve?

Accepted Answer

The horizontal component of the normal force and friction.

Question 15

A car of mass $$m is $$pulled by a rope with tension $$T at $$constant velocity. What is the value of $$T$$?

Accepted Answer

$$T = mg$$

Forces, Newton's Laws, Friction, and Circular Motion: Quizzes 4-6 Key Study Guide

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