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Physics For Scientists & Engineers
Found in: Page 282
Physics For Scientists & Engineers

Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

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Short Answer

A car of mass m traveling at speed v crashes into the rear of a truck of mass 2m that is at rest and in neutral at an intersection. If the collision is perfectly inelastic, what is the speed of the combined car and truck after the collision?

(a) v

(b)v2

(c) v3

(d) 2v

(e) None of those answers is correct.

The speed of the combined car and truck after the collision is v3, so option (c) is the correct answer.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Concept

The total momentum of an isolated system (no external forces) is conserved and doesn’t depend on the nature of the forces between the members of the system:

ΔP→tot=0

The system may be isolated in terms of momentum but Non-isolated in terms of energy, as in the case of inelastic collisions.

The linear momentum of a particle P→of mass m moving with a velocity v→ is,

P→=mv→

Where,

P→=The momentum of the particle

v→=Velocity of particle

role="math" localid="1663741365134" m= Mass of the particle

Step 2: Final velocity

A car of mass m traveling at speed v crashes into the rear of a truck of mass 2m that is at rest and in neutral at an intersection.

Assuming that the collision was head-on so that, after impact, the wreckage moves in the original direction of the car’s motion, conservation of momentum during the impact is the law we are going to use to solve the equation for final velocity as,

mc+mtvf=mcv0c+mtv0tmc+mtvf=mcv+mt0vf=mcmc+mtv

Here is mcthe mass of the car, mtis the mass of the truck.

Substitute the values in the above expression, and we get,

vf=mm+2mvvf=v3

The speed of the combined car and truck after the collision is v3 , so option (c) is the correct answer.

Most popular questions for Physics Textbooks

A small block of mass m1=0.500kg is released from rest at the top of a frictionless, curve-shaped wedge of mass m2=3.00kg, which sits on a frictionless, horizontalsurface as shown in Figure P9.80a. When theblock leaves the wedge, its velocity is measured to be 4.00 m/s to the right as shown in Figure P9.80b.(a) What is the velocity of the wedge after the block reaches the horizontal surface? (b) What is the height of the wedge?

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A basketball is tossed up into the air, falls freely, and bounces from the wooden floor. From the moment after the player releases it until the ball reaches the top of its bounce, what is the smallest system for which momentum is conserved?

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(b) the ball plus player

(c) the ball plus floor

(d) the ball plus the Earth

(e) momentum is not conserved for any system.

Question: (a) Three carts of masses, m1=4.00 kg, m2=10.0 kg and m3=3.00 kg move on a frictionless, horizontal track with speeds of v1=5.00 m/s to the right, v2=3.00 m/s to the right, and v3=4.00 m/s to the left as shown in Figure P9.34. Velcro couplers make the carts stick together after colliding. Find the final velocity of the train of three carts.

(b) What If? Does your answer in part (a) require that all the carts collide and stick together at the same moment? What if they collide in a different order?
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