Call Now to Set Up Tutoring:

(888) 888-0446

AP Physics C: Mechanics : Understanding Conservation of Energy

Study concepts, example questions & explanations for AP Physics C: Mechanics

Create An Account

All AP Physics C: Mechanics Resources

2 Diagnostic Tests 92 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Understanding Conservation Of Energy

A 0.8kg ball is dropped from rest from a cliff that is 150m high. Use conservation of energy to find the vertical velocity of the ball right before it hits the bottom of the cliff.

Possible Answers:

$32.8\frac{m}{s}$

$40.0\frac{m}{s}$

$92.3\frac{m}{s}$

$73.4\frac{m}{s}$

$54.2\frac{m}{s}$

Correct answer:

$54.2\frac{m}{s}$

Explanation:

The conservation of energy equation is K_1+U_1=K_2+U_2 .

The ball starts from rest so . It starts at a height of 150m, so . When the ball reaches the bottom, height is zero and thus, and $K_2=\frac{1}{2}mv^2$ . The conservation of energy equation can be adjusted below.

U_1=K_2

$mgh=\frac{1}{2}mv^2$

Solve for v.

$v=\sqrt{2gh}$

$v=\sqrt{2(9.8\ \frac{m}{s^2})(150\ m)}$

$v=54.2\ \frac{m}{s}$

Report an Error

Example Question #1 : Work, Energy, And Power

Starting from rest, a skateboarder travels down a 25^o incline that's 22m long. Using conservation of energy, calculate the skateboarder's speed when he reaches the bottom. Ignore friction.

Possible Answers:

$2.9\frac{m}{s}$

$21.8\frac{m}{s}$

$13.5 \frac{m}{s}$

$32.8\frac{m}{s}$

$6.3\frac{m}{s}$

Correct answer:

$13.5 \frac{m}{s}$

Explanation:

Conservation of energy states that K_1+U_1=K_2+U_2 .

The skateboarder starts from rest; thus, and . At the bottom of the incline, $K_2=\frac{1}{2}mv^2$ and .

U_1=K_2

$mgh=\frac{1}{2}mv^2$

Solve for v.

$v=\sqrt{2gh}$

Using trigonometry, $h=22\sin(25)$ .

$v=\sqrt{2(9.8\ \frac{m}{s^2})(22)(\sin(25))}$

$v=13.5\ \frac{m}{s}$

Report an Error

Example Question #1 : Understanding Conservation Of Energy

A $\small 5.0kg$ bowling ball is dropped from $\small 5.0m$ above the ground. What will its velocity be when it is $\small 1.0m$ above the ground?

Possible Answers:

$78.4\frac{m}{s}$

$10.8\frac{m}{s}$

$98.0\frac{m}{s}$

$9.9\frac{m}{s}$

$8.9\frac{m}{s}$

Correct answer:

$8.9\frac{m}{s}$

Explanation:

Relevant equations:

K_i+U_i=K_f+U_f

$K = \frac{1}{2}mv^2$

U = mgh

Determine initial kinetic and potential energies when the ball is dropped.

K_i = 0

$U_i = (5kg)(9.8\frac{m}{s^2})(5m)=245J$

Determine final kinetic and potential energies, when the ball has fallen to $\small 1.0m$ above the ground.

$K_f=\frac{1}{2}(5kg)v_f^2$

$U_f = (5kg)(9.8\frac{m}{s^2})(1m)=49J$

Use conservation of energy to equate initial and final energy sums.

$0 + 245J = \frac{1}{2}(5kg)v_f^2+49J$

Solve for the final velocity.

$0 + 245J = \frac{1}{2}(5kg)v_f^2+49J$

$v_f^2=\frac{245J-49J}{\frac{1}{2}(5kg)}=78.4\frac{m^2}{s^2}$

$v_f=8.85 \frac{m}{s} \approx 8.9\frac{m}{s}$

Report an Error

Example Question #11 : Work, Energy, And Power

A solid metal object with mass of $25\: kg$ is dropped from rest at the surface of a lake that is $20\:m$ deep. The water exerts a drag force on the object as it sinks. If the total work done by the drag force is - $3800\: J$ , what is the speed of the object when it hits the sand at the bottom of the lake?

Possible Answers:

$14.4\:m/s$

$9.38\:m/s$

$16.0\:m/s$

$11.7\:m/s$

$19.8\:m/s$

Correct answer:

$9.38\:m/s$

Explanation:

This is a conservation of energy problem. First we have to find the work done by gravity. This can be found using:

$W= F\cdot d, F = mg \\ W = 25\:kg \cdot 9.8\:m/s^2 \cdot 20\:m = 4900\:J$

It is given to us that the work done by the drag force is $-3800\:J$ which means that work is done in the opposite direction. We take the net work by adding the two works together we get, $1100\:J$ of net work done on the block.

Since this is a conservation of energy problem, we set the net work equal to the kinetic energy equation:

$W = \frac{1}{2}mv^2$

is the mass of the block and we are trying to solve for .

$v = \sqrt{\frac{2 \cdot 1100}{25}} = 9.38\:m/s$

Report an Error

Example Question #1 : Energy

If a roller coaster car is traveling at $15\: m/s$ when it is $24\: m$ above the ground, how fast is it going when $10\: m$ above the ground?

Possible Answers:

$21.5\:m/s$

$18.3\:m/s$

$19.5\:m/s$

$22.3\:m/s$

$20.5\:m/s$

Correct answer:

$22.3\:m/s$

Explanation:

This is a classic conservation of energy problem. We know that potential energy and kinetic energy both have to conserve. So we use the following equation:

$\frac{1}{2}mv_o^2+mgh_1 = \frac{1}{2}mv_f^2 + mgh_2$

What this equations says is, the sum of kinetic and potential energy is same at varying heights and velocities.

We can simplify this equation by cancelling out all the m terms.

$\frac{1}{2}v_o^2+gh_1 = \frac{1}{2}v_f^2 + gh_2$

We know all the terms except for v_f , which is the final speed we are trying to solve for h_1 , which is $24\:m$ , h_2 is $10\:m$ and v_o is $15\:m/s$ .

If we plug in all the numbers and solve for v_f , we get $22.3\:m/s$ .

Report an Error

View Tutors

Richard
Certified Tutor

Rutgers University-Newark, Bachelor of Science, Chemistry. Rutgers University-Newark, Doctor of Science, Chemistry.

View Tutors

Chandrika
Certified Tutor

University of Western Ontario, Master's/Graduate, Computer Science .

View Tutors

Laura Jeanne
Certified Tutor

Texas Tech University, Bachelor in Arts, Music Teacher Education. Asbury Theological Seminary, Master of Divinity, Music Teac...

All AP Physics C: Mechanics Resources

2 Diagnostic Tests 92 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Denver, Spanish Tutors in Houston, Physics Tutors in Atlanta, Calculus Tutors in Seattle, English Tutors in Denver, Spanish Tutors in Boston, GRE Tutors in Miami, Spanish Tutors in Denver, MCAT Tutors in Chicago, SAT Tutors in Atlanta

Popular Courses & Classes

ACT Courses & Classes in Atlanta, Spanish Courses & Classes in Phoenix, SSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Miami, GMAT Courses & Classes in Los Angeles, GRE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in San Diego, MCAT Courses & Classes in Houston, ISEE Courses & Classes in Boston, Spanish Courses & Classes in Houston

Popular Test Prep

ISEE Test Prep in Miami, GMAT Test Prep in Phoenix, ACT Test Prep in Atlanta, GMAT Test Prep in Boston, LSAT Test Prep in Phoenix, SAT Test Prep in Philadelphia, ACT Test Prep in Seattle, ACT Test Prep in Denver, SAT Test Prep in Miami, ISEE Test Prep in Los Angeles

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

AP Physics C: Mechanics : Understanding Conservation of Energy

Study concepts, example questions & explanations for AP Physics C: Mechanics

All AP Physics C: Mechanics Resources

Example Questions

Example Question #1 : Understanding Conservation Of Energy

Example Question #1 : Work, Energy, And Power

Example Question #1 : Understanding Conservation Of Energy

Example Question #11 : Work, Energy, And Power

Example Question #1 : Energy

All AP Physics C: Mechanics Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: