Q: A projectile is launched from ground level with an initial velocity of $$v_0 at an $$angle $$\theta$$ above the horizontal. Neglecting air resistance, what is the maximum height $$H$$ reached by the projectile?

$$H = \dfrac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: A car rounds a banked curve of radius $$r at $$speed $$v. If $$the curve is banked at angle $$\theta$$ and there is no friction, what is the correct expression for the banking angle to allow the car to make the turn safely?

$$\tan \theta = \dfrac{v^2$}{rg}$$

Q: A 5 kg object is moving at 10 m/s and collides with a stationary 3 kg object. If the collision is perfectly inelastic, what is the final velocity $$v_f of $$the combined mass?

$$v_f = \dfrac{5 \times 10}{5 + 3} = 6.25\ \text{m/s}$$

Question 1

A projectile is launched from ground level with an initial velocity of $$v_0 at an $$angle $$	heta$$ above the horizontal. Neglecting air resistance, what is the maximum height $$H$$ reached by the projectile?

Accepted Answer

$$H = \dfrac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 2

A block of mass $$m$$ slides down a frictionless incline of height $$h. $$What is its speed $$v at $$the bottom of the incline?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 3

A car rounds a banked curve of radius $$r at $$speed $$v. If $$the curve is banked at angle $$	heta$$ and there is no friction, what is the correct expression for the banking angle to allow the car to make the turn safely?

Accepted Answer

$$	an 	heta = \dfrac{v^2$}{rg}$$

Question 4

A 2 kg object is attached to a spring with spring constant $$k = 50\ 	ext{N/m}$$ and oscillates in simple harmonic motion. What is the period $$T of $$the oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{m}{k}}$$

Question 5

A 5 kg object is moving at 10 m/s and collides with a stationary 3 kg object. If the collision is perfectly inelastic, what is the final velocity $$v_f of $$the combined mass?

Accepted Answer

$$v_f = \dfrac{5 	imes 10}{5 + 3} = 6.25\ 	ext{m/s}$$

Question 6

Which of the following statements about conservative and non-conservative forces is correct?

Accepted Answer

Work done by a conservative force is independent of the path taken.

Question 7

A satellite orbits the Earth at a distance $$r$$ from the center of the Earth. What is the gravitational potential energy $$U_g of $$the satellite-Earth system?

Accepted Answer

$$U_g = -\dfrac{G M m}{r}$$

Question 8

A disk of mass $$M$$ and radius $$R$$ rotates about its center with angular velocity $$\omega. $$What is its rotational kinetic energy?

Accepted Answer

$$K = \dfrac{1}{2} I \$$omega^2$$ where I$$ = \dfrac{1}{2} M $$R^2$$

Question 9

A block is pulled across a rough surface with a constant velocity. If the coefficient of kinetic friction is $$\mu_k$$ and the normal force is $$N$$, what is the magnitude of the frictional force?

Accepted Answer

$$f_k = \mu_k N$$

Question 10

A ball is attached to a string and swung in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the centripetal acceleration $$a_c$$?

Accepted Answer

$$a_c = \dfrac{v^2$}{r}$$

Question 11

A force $$F is $$applied to a mass $$m$$ for a time $$\Delta t. $$What is the change in momentum $$\Delta p of $$the mass?

Accepted Answer

$$\Delta p = F \Delta t$$

Question 12

A 1 kg mass is attached to a spring and oscillates with amplitude $$A = 0.2 m. If $$the spring constant is $$k = 100 N/m$$, what is the maximum speed $$v_{max} of $$the mass?

Accepted Answer

$$v_{max} = A \sqrt{\dfrac{k}{m}}$$

Question 13

Which of the following is NOT a vector quantity?

Accepted Answer

Work

Question 14

A uniform rod of length $$L$$ and mass $$M is $$suspended horizontally and supported at its ends. Where is its center of mass located?

Accepted Answer

At the midpoint, $$\dfrac{L}{2}$$ from either end

Question 15

A planet orbits the Sun in an elliptical orbit. According to Kepler's second law, what happens to the planet's speed as it moves closer to the Sun?

Accepted Answer

The planet moves faster when it is closer to the Sun.

Question 16

A particle moves in a circle of radius $$r$$ with angular velocity $$\omega. $$What is its linear (tangential) speed $$v$$?

Accepted Answer

$$v = \omega r$$

Question 17

A spring is compressed by a distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \dfrac{1}{2} k x^2$

Question 18

A system is in static equilibrium. Which of the following must be true?

Accepted Answer

The net force and net torque on the system are both zero.

Question 19

A ball is dropped from a height $$h$$ and bounces back to a height $$h' \u003c h. $$Which of the following best explains why the ball does not return to its original height?

Accepted Answer

Some energy is lost due to non-conservative forces such as air resistance and deformation during the bounce.

PHYS4A Core Concepts: Vectors, Kinematics, Forces, Energy, Momentum, Rotation, and SHM

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