Q: A projectile is launched from the ground at an angle $$\theta$$ above the horizontal with initial speed $$v_0. $$Neglecting air resistance, which of the following best describes the time it takes to reach its maximum height?

$$t = \dfrac{v_0$ \sin\theta}{g}$$

Question 1

A car accelerates uniformly from rest to a speed of $$30\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the magnitude of its acceleration?

Accepted Answer

$$3.0\ \mathrm{m/s^2$}$$

Question 2

A projectile is launched from the ground at an angle $$	heta$$ above the horizontal with initial speed $$v_0. $$Neglecting air resistance, which of the following best describes the time it takes to reach its maximum height?

Accepted Answer

$$t = \dfrac{v_0$ \sin	heta}{g}$$

Question 3

A block of mass $$5\ \mathrm{kg} is $$pulled across a horizontal surface with a force of $$20\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. If the coefficient of kinetic friction is $$0.2$$, what is the acceleration of the block? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.0\ \mathrm{m/s^2$}$$

Question 4

A $$2\ \mathrm{kg}$$ object moves in a circle of radius $$4\ \mathrm{m} at a $$constant speed of $$6\ \mathrm{m/s}. $$What is the magnitude of the net force acting on the object?

Accepted Answer

$$18\ \mathrm{N}$$

Question 5

A $$0.5\ \mathrm{kg}$$ ball is dropped from a height of $$10\ \mathrm{m}. $$What is its speed just before hitting the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$14\ \mathrm{m/s}$$

Question 6

A $$3\ \mathrm{kg}$$ block slides down a frictionless incline of height $$5\ \mathrm{m}. $$What is the work done by gravity?

Accepted Answer

$$147\ \mathrm{J}$$

Question 7

A $$0.2\ \mathrm{kg}$$ ball moving at $$5\ \mathrm{m/s}$$ collides elastically with a stationary $$0.3\ \mathrm{kg}$$ ball. What is the velocity of the $$0.2\ \mathrm{kg}$$ ball after the collision?

Accepted Answer

$$-1\ \mathrm{m/s}$$

Question 8

A solid disk of mass $$2\ \mathrm{kg}$$ and radius $$0.5\ \mathrm{m}$$ rotates about its center with angular velocity $$10\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$25\ \mathrm{J}$$

Question 9

A uniform beam of length $$4\ \mathrm{m}$$ and mass $$20\ \mathrm{kg} is $$supported at its ends. A $$60\ \mathrm{kg}$$ person stands $$1\ \mathrm{m}$$ from the left end. What is the force exerted by the right support?

Accepted Answer

$$250\ \mathrm{N}$$

Question 10

A $$0.1\ \mathrm{kg}$$ mass attached to a spring oscillates with amplitude $$0.2\ \mathrm{m}$$ and period $$0.5\ \mathrm{s}. $$What is the maximum speed of the mass?

Accepted Answer

$$1.26\ \mathrm{m/s}$$

Question 11

A satellite orbits Earth in a circular orbit of radius $$2R_E$$, where $$R_E is $$Earth's radius. What is the satellite's orbital speed?

Accepted Answer

$$\sqrt{\dfrac{GM_E}{2R_E}}$$

Question 12

A gas in a sealed container is heated at constant volume. According to the ideal gas law, what happens to the pressure?

Accepted Answer

It increases linearly with temperature.

Question 13

A $$1.0\ \mathrm{kg}$$ block at $$20^\circ\mathrm{C}$$ absorbs $$4200\ \mathrm{J} of $$heat. If the specific heat of the material is $$420\ \mathrm{J/(kg\cdot K)}$$, what is the final temperature?

Accepted Answer

$$40^\circ\mathrm{C}$$

Question 14

A Carnot engine operates between $$500\ \mathrm{K}$$ and $$300\ \mathrm{K}. $$What is its maximum possible efficiency?

Accepted Answer

$$0.40$$

Question 15

A $$2\ \mathrm{kg}$$ object moves with velocity $$\vec{v} = (3\hat{i} + 4\hat{j})\ \mathrm{m/s}. $$What is its momentum vector?

Accepted Answer

$$\vec{p} = (6\hat{i} + 8\hat{j})\ \mathrm{kg\cdot m/s}$$

Question 16

A $$0.5\ \mathrm{kg}$$ mass is attached to a string and swung in a horizontal circle of radius $$1.5\ \mathrm{m} at a $$speed of $$3\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$4.5\ \mathrm{N}$$

Question 17

A $$10\ \mathrm{kg}$$ box is pushed up a $$30^\circ$$ incline at constant speed. If the coefficient of kinetic friction is $$0.1$$, what is the required applied force parallel to the incline? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$63.7\ \mathrm{N}$$

Question 18

A $$0.3\ \mathrm{kg}$$ mass attached to a spring oscillates with a frequency of $$2\ \mathrm{Hz}. $$What is the spring constant?

Accepted Answer

$$47.4\ \mathrm{N/m}$$

Question 19

A $$5\ \mathrm{kg}$$ object is moving at $$10\ \mathrm{m/s}$$ and collides inelastically with a $$3\ \mathrm{kg}$$ object at rest. What is their final velocity after the collision?

Accepted Answer

$$6.25\ \mathrm{m/s}$$

Question 20

A $$0.2\ \mathrm{kg}$$ ball is attached to a string and swung in a vertical circle of radius $$0.8\ \mathrm{m}. $$What is the minimum speed at the top of the circle so the string remains taut?

Accepted Answer

$$2.8\ \mathrm{m/s}$$

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