Q: A block of mass $$4.0\ \mathrm{kg}$$ sits on a ramp that makes an angle of $$25^\circ$$ with the horizontal. What is the minimum coefficient of static friction required to keep the crate from sliding down the ramp?

$$\mu_s = \tan(25^\circ) = 0.47$$

Q: A man pulls a girl in a sled (total mass $$23\ \mathrm{kg}) at a $$constant speed on snow with a coefficient of kinetic friction $$\mu_k = 0.14. If $$the rope makes an angle $$\theta = 32^\circ$$ with the horizontal, what is the magnitude of the force required to maintain constant speed?

$$F = \frac{\mu_k m g}{\cos\theta - \mu_k \sin\theta} \approx 45\ \mathrm{N}$$

Q: Calculate the speed required for a $$59\ \mathrm{kg}$$ pole vaulter to just pass over a bar $$5.5\ \mathrm{m}$$ high, if their center of mass starts at $$0.70\ \mathrm{m}$$ above the ground.

$$v = \sqrt{2g(h_f - h_i)} = \sqrt{2 \times 9.8 \times (5.5 - 0.7)} \approx 9.7\ \mathrm{m/s}$$

Q: A $$2.0\ \mathrm{kg}$$ block slides down a frictionless incline of height $$5.0\ \mathrm{m}. $$What is its speed at the bottom?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5.0} \approx 9.9\ \mathrm{m/s}$$

Q: A $$0.2\ \mathrm{kg}$$ ball is thrown horizontally at $$10\ \mathrm{m/s}$$ from a $$20\ \mathrm{m}$$ high cliff. How far from the base does it land? (Neglect air resistance.)

$$x = v_x t = 10 \times \sqrt{\frac{2 \times 20}{9.8}} \approx 20\ \mathrm{m}$$

Q: A $$5.0\ \mathrm{kg}$$ object moves in a circle of radius $$2.0\ \mathrm{m} at$$ $$4.0\ \mathrm{m/s}. $$What is the required centripetal force?

$$F = \frac{mv^2$}{r} = \frac{5.0 \times 16}{2.0} = 40\ \mathrm{N}$$

Q: A $$0.5\ \mathrm{kg}$$ ball is attached to a $$1.0\ \mathrm{m}$$ string and swung in a horizontal circle at $$2.0\ \mathrm{m/s}. $$What is the period of revolution?

$$T = \frac{2\pi r}{v} = \frac{2\pi \times 1.0}{2.0} = \pi\ \mathrm{s}$$

Question 1

A block of mass $$4.0\ \mathrm{kg}$$ sits on a ramp that makes an angle of $$25^\circ$$ with the horizontal. What is the minimum coefficient of static friction required to keep the crate from sliding down the ramp?

Accepted Answer

$$\mu_s = 	an(25^\circ) = 0.47$$

Question 2

A block of mass $$M$$ sits on a rotating circular turntable at a radial distance $$R$$ from the center. The turntable rotates such that the block has velocity $$v$$ but does not slip. What force provides the required centripetal acceleration?

Accepted Answer

The static friction force between the block and the turntable

Question 3

A man pulls a girl in a sled (total mass $$23\ \mathrm{kg}) at a $$constant speed on snow with a coefficient of kinetic friction $$\mu_k = 0.14. If $$the rope makes an angle $$	heta = 32^\circ$$ with the horizontal, what is the magnitude of the force required to maintain constant speed?

Accepted Answer

$$F = \frac{\mu_k m g}{\cos	heta - \mu_k \sin	heta} \approx 45\ \mathrm{N}$$

Question 4

You push very hard on a car with a dead battery, trying to move it. You do work on the car:

Accepted Answer

Only if it starts moving

Question 5

Two blocks of mass $$m_1$$ and $$m_2$$ ($$m_2$$ \u003e $$m_1) $$slide on a frictionless floor and have the same kinetic energy when they hit a rough patch ($$\mu_k \u003e 0) $$and stop. Which block travels farther on the rough patch?

Accepted Answer

They will go the same distance

Question 6

If it requires $$3.0\ \mathrm{J} of $$work to stretch a spring by $$2.0\ \mathrm{cm}$$ from equilibrium, how much more work is required to stretch it an additional $$4.0\ \mathrm{cm} (so $$the total stretch is $$6.0\ \mathrm{cm}$$)?

Accepted Answer

$$12\ \mathrm{J}$$

Question 7

Calculate the speed required for a $$59\ \mathrm{kg}$$ pole vaulter to just pass over a bar $$5.5\ \mathrm{m}$$ high, if their center of mass starts at $$0.70\ \mathrm{m}$$ above the ground.

Accepted Answer

$$v = \sqrt{2g(h_f - h_i)} = \sqrt{2 	imes 9.8 	imes (5.5 - 0.7)} \approx 9.7\ \mathrm{m/s}$$

Question 8

A spring with $$k = 2500\ \mathrm{N/m}$$ and uncompressed length $$L = 8\ \mathrm{cm}$$ sits upright. From what height $$h$$ must you drop a $$3\ \mathrm{kg}$$ block so that the spring is compressed to half its length when the block comes to rest?

Accepted Answer

$$h = 13\ \mathrm{cm}$$

Question 9

A small car and a heavy pickup truck (twice the mass of the car) are both pushed with the same force for the same time. What can you say about their momentum and kinetic energy (ignore friction)?

Accepted Answer

They have the same momentum, but the car has more kinetic energy

Question 10

A billiard ball of mass $$0.5\ \mathrm{kg}$$ with speed $$2.0\ \mathrm{m/s}$$ collides elastically with a wall at $$30^\circ to $$the wall. Its speed after the collision is still $$2.0\ \mathrm{m/s}. $$What is the change in the ball’s momentum $$\Delta \vec{p}$$?

Accepted Answer

$$(-1.0\ \mathrm{kg\ m/s})\ \hat{i}$$

Question 11

A $$4.0\ \mathrm{kg}$$ object moves right at $$9.0\ \mathrm{m/s}$$ and collides inelastically with a $$6.0\ \mathrm{kg}$$ object moving left at $$6.0\ \mathrm{m/s}. $$What is the total kinetic energy after the collision?

Accepted Answer

$$25\ \mathrm{J}$$

Question 12

A $$2.0\ \mathrm{kg}$$ block slides down a frictionless incline of height $$5.0\ \mathrm{m}. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5.0} \approx 9.9\ \mathrm{m/s}$$

Question 13

A $$0.2\ \mathrm{kg}$$ ball is thrown horizontally at $$10\ \mathrm{m/s}$$ from a $$20\ \mathrm{m}$$ high cliff. How far from the base does it land? (Neglect air resistance.)

Accepted Answer

$$x = v_x t = 10 	imes \sqrt{\frac{2 	imes 20}{9.8}} \approx 20\ \mathrm{m}$$

Question 14

A $$5.0\ \mathrm{kg}$$ object moves in a circle of radius $$2.0\ \mathrm{m} at$$ $$4.0\ \mathrm{m/s}. $$What is the required centripetal force?

Accepted Answer

$$F = \frac{mv^2$}{r} = \frac{5.0 	imes 16}{2.0} = 40\ \mathrm{N}$$

Question 15

A $$0.5\ \mathrm{kg}$$ ball is attached to a $$1.0\ \mathrm{m}$$ string and swung in a horizontal circle at $$2.0\ \mathrm{m/s}. $$What is the period of revolution?

Accepted Answer

$$T = \frac{2\pi r}{v} = \frac{2\pi 	imes 1.0}{2.0} = \pi\ \mathrm{s}$$

Question 16

A $$1.0\ \mathrm{kg}$$ object is attached to a spring ($$k = 200\ \mathrm{N/m}) $$and pulled $$0.10\ \mathrm{m}$$ from equilibrium. What is the elastic potential energy stored?

Accepted Answer

$$PE = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.10)^2$ = 1.0\ \mathrm{J}$$

Physics Midterm Study Guidance: Forces, Friction, Circular Motion, Work, Energy, and Momentum

Study Guide - Practice Questions

Study Guide - Flashcards