Q: A car speeds up from rest with a constant acceleration of $$5\,\mathrm{m/s^2$}. $$How far will the car travel in $$10$$ seconds?

$$\Delta x = \frac{1}{2} a t^2$ = \frac{1}{2} \times 5 \times 10^2$ = 250\,\mathrm{m}$$

Q: A force of $$10\,\mathrm{N} is $$applied perpendicular to a wrench $$0.3\,\mathrm{m}$$ long. What is the torque produced?

$$\tau = 10 \times 0.3 = 3\,\mathrm{Nm}$$

Q: A $$2\,\mathrm{kg}$$ object moves in a circle of radius $$4\,\mathrm{m} at a $$speed of $$3\,\mathrm{m/s}. $$What is the magnitude of the centripetal force?

$$F_c = \frac{mv^2$}{r} = \frac{2 \times 9}{4} = 4.5\,\mathrm{N}$$

Q: Which of the following is the correct expression for the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

$$\vec{A} \cdot \vec{B} = AB \cos\theta$$

Q: A $$5\,\mathrm{kg}$$ mass is attached to a spring with a spring constant $$k = 200\,\mathrm{N/m}. $$What is the elastic potential energy when the spring is stretched $$0.1\,\mathrm{m}$$ from equilibrium?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\,\mathrm{J}$$

Q: A $$3\,\mathrm{kg}$$ object is moving at $$4\,\mathrm{m/s}. $$What is its linear momentum?

$$p = mv = 3 \times 4 = 12\,\mathrm{kg\cdot m/s}$$

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

$$KE = mgh = 0.5 \times 9.8 \times 10 = 49\,\mathrm{J}$$

Question 1

A ball is thrown at an angle of $$30^\circ$$ off the horizontal with an initial velocity of $$28\,\mathrm{m/s}. $$What is the vertical component of the initial velocity?

Accepted Answer

$$v_{0y} = 28 \sin(30^\circ)$$

Question 2

Which of the following correctly expresses the work done by a force $$\vec{F}$$ acting over a displacement $$\vec{d} at an $$angle $$	heta$$?

Accepted Answer

$$W = Fd \cos	heta$$

Question 3

A car speeds up from rest with a constant acceleration of $$5\,\mathrm{m/s^2$}. $$How far will the car travel in $$10$$ seconds?

Accepted Answer

$$\Delta x = \frac{1}{2} a t^2$ = \frac{1}{2} 	imes 5 	imes 10^2$ = 250\,\mathrm{m}$$

Question 4

Which of the following is the correct formula for the kinetic energy of a rotating rigid body?

Accepted Answer

$$KE = \frac{1}{2} I \$$omega^2$$

Question 5

A block slides down a frictionless incline of height $$h. $$What is its speed at the bottom if it starts from rest?

Accepted Answer

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

Question 6

Which of the following statements about the conservation of angular momentum is correct?

Accepted Answer

Angular momentum is conserved if the net external torque is zero.

Question 7

A force of $$10\,\mathrm{N} is $$applied perpendicular to a wrench $$0.3\,\mathrm{m}$$ long. What is the torque produced?

Accepted Answer

$$	au = 10 	imes 0.3 = 3\,\mathrm{Nm}$$

Question 8

Which equation correctly relates impulse to change in momentum?

Accepted Answer

$$J = \Delta p$$

Question 9

A $$2\,\mathrm{kg}$$ object moves in a circle of radius $$4\,\mathrm{m} at a $$speed of $$3\,\mathrm{m/s}. $$What is the magnitude of the centripetal force?

Accepted Answer

$$F_c = \frac{mv^2$}{r} = \frac{2 	imes 9}{4} = 4.5\,\mathrm{N}$$

Question 10

Which of the following is the correct expression for the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A} \cdot \vec{B} = AB \cos	heta$$

Question 11

A $$5\,\mathrm{kg}$$ mass is attached to a spring with a spring constant $$k = 200\,\mathrm{N/m}. $$What is the elastic potential energy when the spring is stretched $$0.1\,\mathrm{m}$$ from equilibrium?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\,\mathrm{J}$$

Question 12

Which of the following is the correct formula for the position of the center of mass for a system of two particles with masses $$m_1$$ and $$m_2 at $$positions $$x_1$$ and $$x_2$$?

Accepted Answer

$$x_{cm} = \frac{m_1$ x_1$ + m_2$ x_2$}{m_1$ + m_2$}$$

Question 13

A $$3\,\mathrm{kg}$$ object is moving at $$4\,\mathrm{m/s}. $$What is its linear momentum?

Accepted Answer

$$p = mv = 3 	imes 4 = 12\,\mathrm{kg\cdot m/s}$$

Question 14

Which of the following is the correct formula for the angular acceleration $$\alpha in $$terms of torque $$	au$$ and moment of inertia $$I$$?

Accepted Answer

$$\alpha = \frac{	au}{I}$$

Question 15

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

Accepted Answer

$$KE = mgh = 0.5 	imes 9.8 	imes 10 = 49\,\mathrm{J}$$

Question 16

Which of the following is the correct formula for the average velocity over a time interval $$\Delta t$$?

Accepted Answer

$$v_{avg} = \frac{\Delta x}{\Delta t}$$

Question 17

A $$2\,\mathrm{kg}$$ object is moving in a circle of radius $$0.5\,\mathrm{m}$$ with an angular velocity of $$4\,\mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} I \$$omega^2$$ = \frac{1}{2} (2 	imes 0.5^2$) 	imes 4^2$ = 4\,\mathrm{J}$$

Question 18

Which of the following is the correct formula for the vector (cross) product of $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A} 	imes \vec{B} = AB \sin	heta$$

Comprehensive Study Notes for Introductory Physics (PHY 161)

Study Guide - Practice Questions

Study Guide - Flashcards