Call Now to Set Up Tutoring:

(888) 888-0446

AP Physics C: Mechanics : Understanding Elastic and Inelastic Collisions

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 Elastic And Inelastic Collisions

We have two balls. The first ball has mass 0.54kg and is traveling 7.1m/s to the right. It collides head-on elastically with a second ball of mass 0.95kg traveling 2.8m/s to the left. After the collision, what is the speed and direction of each ball?

1-d_collision

$v_1^{'}=final\ velocity\ of\ ball\ 1$

$v_2^{'}=final\ velocity\ of\ ball\ 2$

Possible Answers:

$v_1^{'}=-2.3\frac{m}{s}$ to the left, $v_2^{'}=-6.4\frac{m}{s}$ to the left

$v_1^{'}=5.5\frac{m}{s}$ to the right, $v_2^{'}=4.4\frac{m}{s}$ to the right

$v_1^{'}=-2.3\frac{m}{s}$ to the left, $v_2^{'}=6.4\frac{m}{s}$ to the right

$v_1^{'}=-2.3\frac{m}{s}$ to the left, $v_2^{'}=0.2\frac{m}{s}$ to the right

$v_1^{'}=-5.5\frac{m}{s}$ to the left, $v_2^{'}=4.4\frac{m}{s}$ to the right

Correct answer:

$v_1^{'}=-5.5\frac{m}{s}$ to the left, $v_2^{'}=4.4\frac{m}{s}$ to the right

Explanation:

We must use conservation of momentum to tackle this problem.

m_1v_1+m_2v_2=m_1v_1'+m_2v_2'

We are to find and , the velocities of the balls after the collision. We know the following for the first ball:

$m_1=0.54\ \text{kg}$

$v_1=7.1\ \frac{m}{s}$

and we know the following for the second ball:

$m_2=0.95\ \text{kg}$

$v_2=-2.8\ \frac{m}{s}$ .

After plugging these values into our conservation of momentum equation, it is clear that we can't use this equation alone to find and ; however, since we are dealing with an elastic collision, we can use the relation below.

v_1-v_2=v_2'-v_1'

This relation can be derived using conservation of momentum and conservation of kinetic energy equations. Remember that kinetic energy is only conserved if the collision is elastic. We can use this relation to eliminate either or in our conservation of momentum equation.

v_1'=v_2'-v_1+v_2

Plug this into our conservation of momentum equation.

m_1v_1+m_2v_2=m_1(v_2'-v_1+v_2)+m_2v_2'

So now is eliminated and we can solve for .

m_1v_1+m_2v_2=m_1v_2'-m_1v_1+m_1v_2+m_2v_2'

2m_1v_1+(m_2-m_1)v_2=(m_1+m_2)v_2'

$v_2'=\frac{2m_1v_1+(m_2-m_1)v_2}{m_1+m_2}$

$v_2'=\frac{2(0.54\ \text{kg})(7.1\ \frac{m}{s})+(0.95\ \text{kg}-0.54\ \text{kg})(-2.8\ \frac{m}{s})}{0.54\ \text{kg}+0.95\ \text{kg}}$

$v_2'=4.4\ \frac{m}{s}$

This is the speed of the second ball, and it is traveling to the right because of the positive value. Use this positive value to find by using the relation we found earlier.

v_1'=v_2'-v_1+v_2

$v_1'=4.4\ \frac{m}{s}-7.1\ \frac{m}{s}-2.8\ \frac{m}{s}$

$v_1'=-5.5\ \frac{m}{s}$

This is the speed of the first ball and it is traveling to the left due to the negative sign.

Report an Error

Example Question #2 : Understanding Elastic And Inelastic Collisions

A 30kg cart travels at 9m/s and it hits another cart of mass 46kg traveling at 4m/s in the opposite direction. After the collision, they stick together to form one cart. Find the speed of this cart

Possible Answers:

$v=1.57\frac{m}{s}$

$v=5.12\frac{m}{s}$

$v=2.32\frac{m}{s}$

$v=1.13\frac{m}{s}$

$v=0.04\frac{m}{s}$

Correct answer:

$v=1.13\frac{m}{s}$

Explanation:

For the 30 kg cart, we know

$m_1=30\ \text{kg}$

$v_1=9\ \frac{m}{s}$

and for the 46 g cart, we know

$m_2=46\ \text{kg}$

$v_2=-4\ \frac{m}{s}$ .

After the collision, we have v_1'=v_2'=v .

Use conservation of momentum to solve this problem.

m_1v_1+m_2v_2=m_1v_1'+m_2v_2'

m_1v_1+m_2v_2=m_1v+m_2v

m_1v_1+m_2v_2=(m_1+m_2)v

$v=\frac{m_1v_1+m_2v_2}{m_1+m_2}$

$v=\frac{(30\ \text{kg})(9\ \frac{m}{s})+(46\ \text{kg})(-4\ \frac{m}{s})}{30\ \text{kg}+46\ \text{kg}}$

$v=1.13\ \frac{m}{s}$

Report an Error

Example Question #3 : Understanding Elastic And Inelastic Collisions

There are two skaters. The male skater with mass 68kg travels 15m/s North. He approaches a 60kg female skater who is travel 12m/s East; they approach each other at right angles. When they meet, they hold on to each other. At what direction and speed do they move after they meet?

Possible Answers:

$v=9.8\frac{m}{s}$

$\theta=54.8^o$ from the female skater's direction

$v=13.4\frac{m}{s}$

$\theta=54.8^o$ from the female skater's direction

$v=10.0\frac{m}{s}$

$\theta=54.8^o$ from the female skater's direction

None of these

$v=8.7\frac{m}{s}$

$\theta=31.4^o$ from the female skater's direction

Correct answer:

$v=9.8\frac{m}{s}$

$\theta=54.8^o$ from the female skater's direction

Explanation:

This is a two-dimensional inelastic collision problem and we use conservation of momentum to solve. We know the following.

Male skater: $m_1=68\ \text{kg}$ , $v_{1y}=15\ \frac{m}{s}$

Female skater: $m_2=60\ \text{kg}$ , $v_{2x}=12\ \frac{m}{s}$

First, write down two equations representing conservation of momentum. One equation represents momentum in the x-direction (East-West direction), which is $m_2v_{2x}=(m_1+m_2)v\cos\theta$ ,and the other gives the momentum in the y-direction (North-South direction), $m_1v_{1y}=(m_1+m_2)v\sin\theta$ .

Take the y-direction of momentum and divide it by the x-direction momentum.

$\frac{m_1v_{1y}}{m_2v_{2x}}=\frac{(m_1+m_2)v\sin\theta}{(m_1+m_2)v\cos\theta}$

Simplify.

$\frac{m_1v_{1y}}{m_2v_{2x}}=\frac{\sin\theta}{\cos\theta}$

$\frac{m_1v_{1y}}{m_2v_{2x}}=\tan\theta$

Plug in the numbers to find the angle

$\frac{(68\ \text{kg})(15\ \frac{m}{s})}{(60\ \text{kg})(12\ \frac{m}{s})}=\tan\theta$

$\theta=54.8^o$

To find the speed at which they move at this angle we can use one of the momentum equations.

$m_2v_{2x}=(m_1+m_2)v\cos\theta$

Solve for v.

$v=\frac{m_2v_{2x}}{(m_1+m_2)\cos\theta}$

$v=\frac{(60\ \text{kg})(12\ \frac{m}{s})}{(68\ \text{kg}+60\ \text{kg})\cos(54.8)}$

$v=9.8\ \frac{m}{s}$

Report an Error

Example Question #5 : Momentum

Object A has mass $\small 1.0kg$ and initially moves to the right at $\small 6.0\frac{m}{s}$ . It then collides with object B, which has mass $\small 5.0kg$ and was initially moving to the right at $\small 4.0\frac{m}{s}$ . If the two objects stick together after the collision, what percentage of the initial kinetic energy has been dissipated?

Possible Answers:

$3.1\%$

$6.4\%$

$1.5\%$

$2.9\%$

$4.7\%$

Correct answer:

$2.9\%$

Explanation:

Relevant equations:

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

$\Delta K = K_f - K_i$

p_i = p_f

p = mv

Use conservation of momentum to determine the final velocity of the objects.

p_i = p_f

$m_Av_{A,i}+m_Bv_{B,i}=m_Av_{A,f}+m_Bv_{B,f}$

$m_Av_{A,i}+m_Bv_{B,i}=(m_A + m_B)v_f$

$(1kg)(6\frac{m}{s})+(5kg)(4\frac{m}{s})=(1kg+5kg)v_f$

$v_f=4.33\frac{m}{s}$

Calculate the total initial kinetic energy of the two objects.

$K_{A,i} = \frac{1}{2}(1kg)(6\frac{m}{s})^2=18J$

$K_{B,i}=\frac{1}{2}(5kg)(4\frac{m}{s})^2=40J$

$K_i = K_{A,i}+K_{B,i}=18J+40J=58J$

Calculate the total final kinetic energy of the two objects.

$K_{A,f}=\frac{1}{2}(1kg)(4.33\frac{m}{s})^2=9.39J$

$K_{B,f}=\frac{1}{2}(5kg)(4.33\frac{m}{s})^2=46.94J$

$K_f = K_{A,f}+K_{B,f}=9.39J+46.94J = 56.33J$

Find the difference in kinetic energy.

$\Delta K = K_f-K_i = 56.33J - 58J = -1.67J$

This is the amount of kinetic energy lost during the inelastic collision. Express this amount as a percentage of the initial kinetic energy.

$\frac{|\Delta K|}{K_i}*100\% = \frac{1.67}{58}*100\% \approx 2.9\%$

Report an Error

View Tutors

Roberto
Certified Tutor

Conservatorio Nacional de Musica, Bachelor in Arts, Music Performance. CUNY Hunter College, Master of Arts, Music Performance.

View Tutors

Shimelis
Certified Tutor

Alemaya Uniersity of Agriculture, Bachelor, Agricultural Engineering. Alemaya University, Master's/Graduate, Agricultural Eng...

View Tutors

Metaxia
Certified Tutor

Rutgers University-Camden, Bachelor in Arts, Digital Arts. Loyola University Maryland, Masters in Education, Special Education.

All AP Physics C: Mechanics Resources

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

Popular Subjects

GMAT Tutors in San Francisco-Bay Area, Algebra Tutors in San Francisco-Bay Area, Statistics Tutors in Philadelphia, Algebra Tutors in Chicago, French Tutors in New York City, MCAT Tutors in Seattle, GMAT Tutors in Dallas Fort Worth, Reading Tutors in Denver, ACT Tutors in Phoenix, English Tutors in Philadelphia

Popular Courses & Classes

Spanish Courses & Classes in New York City, LSAT Courses & Classes in Philadelphia, ACT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Houston, ACT Courses & Classes in New York City, SAT Courses & Classes in Phoenix, SAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Los Angeles, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Chicago

Popular Test Prep

SSAT Test Prep in Los Angeles, ACT Test Prep in Los Angeles, ISEE Test Prep in San Diego, SSAT Test Prep in Seattle, ISEE Test Prep in Chicago, GRE Test Prep in Atlanta, MCAT Test Prep in Chicago, MCAT Test Prep in Denver, GMAT Test Prep in Washington DC, GMAT Test Prep in Atlanta

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 Elastic and Inelastic Collisions

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

All AP Physics C: Mechanics Resources

Example Questions

Example Question #1 : Understanding Elastic And Inelastic Collisions

Example Question #2 : Understanding Elastic And Inelastic Collisions

Example Question #3 : Understanding Elastic And Inelastic Collisions

Example Question #5 : Momentum

All AP Physics C: Mechanics Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: