Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 9, Problem 9.91AP

A 2.00-g particle moving at 8.00 m/s makes a perfectly elastic head-on collision with a resting 1.00-g object. (a) Find the speed of each particle after the collision. (b) Find the speed of each particle after the collision if the stationary particle has a mass of 10.0 g. (c) Find the final kinetic energy of the incident 2.00-g particle in the situations described in parts (a) and (b). In which case does the incident particle lose more kinetic energy?

(a)

Expert Solution
Check Mark
To determine

The velocity of each particle after collision.

Answer to Problem 9.91AP

The velocity of incident particle after collision is 2.67m/s and velocity of target particle after collision is 10.7m/s .

Explanation of Solution

Given info: The mass of incident particle is 2.00g , the initial velocity of the particle 8.00m/s and mass of target particle is 1.00g .

Write the condition for velocity of incident particle after collision.

v1f=(m1m2m1+m2)v1i+(2m2m1+m2)v2i

Here,

m1 is the mass of the incident particle.

m2 is the mass of the target particle.

v1f is the final velocity of the incident particle.

v1i is the initial velocity of incident particle.

v2f is the final velocity of target particle.

v2i is the initial velocity of target particle.

The initial velocity of the target particle is 0 .

Substitute 0 for v2i , 2.00g for m1 , 1.00g for m2 and 8.00m/s for v1i in above equation.

v1f=(2.00g1.00g2.00g+1.00g)(8.00m/s)+(2(1.00g)2.00g+1.00g)(0)=2.666m/s2.67m/s

Thus, the value of v1f is 2.67m/s .

Write the condition for velocity of target particle after collision.

v2f=(2m1m1+m2)v1i

Substitute 2.00g for m1 , 1.00g for m2 and 8.00m/s for v1i in above equation.

v2f=(2×2.00g(2.00g)+(1.00g))(8.00m/s)=10.666m/s10.7m/s

Thus, the value of v2f is 10.7m/s .

Conclusion:

Therefore, the velocity of incident particle after collision is 2.67m/s and velocity of target particle after collision is 10.7m/s .

(b)

Expert Solution
Check Mark
To determine

The velocity of each particle after collision.

Answer to Problem 9.91AP

The velocity of incident particle after collision is 5.33m/s and velocity of target particle after collision is 2.7m/s .

Explanation of Solution

Given info: The mass of incident particle is 2.00g , the initial velocity of the particle 8.00m/s and mass of target particle is 10.00g .

Write the condition for velocity of incident particle after collision.

v1f=(m1m2m1+m2)v1i+(2m2m1+m2)v2i

Here,

m1 is the mass of the incident particle.

m2 is the mass of the target particle.

v1f is the final velocity of the incident particle.

v1i is the initial velocity of incident particle.

v2f is the final velocity of target particle.

v2i is the initial velocity of target particle.

The initial velocity of the target particle is 0 .

Substitute 0 for v2i , 2.00g for m1 , 10.00g for m2 and 8.00m/s for v1i in above equation.

v1f=(2.00g10.00g2.00g+10.00g)(8.00m/s)+(2(1.00g)2.00g+1.00g)(0)=5.33m/s

Thus, the value of v1f is 5.33m/s .

Write the condition for velocity of target particle after collision.

v2f=(2m1m1+m2)v1i

Substitute 2.00g for m1 , 10.00g for m2 and 8.00m/s for v1i in above equation.

v2f=(2×2.00g(2.00g)+(10.00g))(8.00m/s)=2.666m/s2.7m/s

Thus, the value of v2f is 2.7m/s .

Conclusion:

Therefore, the velocity of incident particle after collision is 5.33m/s and velocity of target particle after collision is 2.7m/s .

(c)

Expert Solution
Check Mark
To determine

The kinetic energy of the incident particle in the situation described in part (a) and (b) and the case in which more kinetic energy is lost.

Answer to Problem 9.91AP

The kinetic energy of the incident particle in the situation described in part (a) is 7.11×103J and in part (b) is 2.84×102J and the incident particle loses more energy in case (a).

Explanation of Solution

Given info: The mass of incident particle is 2.00g , the initial velocity of the particle 8.00m/s and mass of target particle is 10.00g .

Case (a);

From part (a), the velocity of incident particle after collision is 2.67m/s .

Write the expression for final kinetic energy of incident particle for case (a).

KE1f=12m1v1f2

Here,

KE1f is the final kinetic energy of incident particle for case (a).

Substitute  2.00g for m1 and 2.67m/s for v1f in above equation.

KE1f=12×2.00g(103kg1g)×(2.67m/s)27.11×103J

Thus, the value of KE1f is 7.11×103J .

Case (b);

From part (b), the velocity of incident particle after collision is 5.33m/s .

Write the expression for final kinetic energy of incident particle case (b).

KE1f=12m1v1f2

Here,

KE1f is the final kinetic energy of incident particle for case (a).

Substitute  2.00g for m1 and 5.33m/s for v1f in above equation.

KE1f=12×2.00g(103kg1g)×(5.33m/s)2=2.84×102J

Thus, the value of KE1f is 2.84×102J .

Since, the incident kinetic energy is almost same in both cases.

The incident particle loses more kinetic energy in case (a) where the mass of the incident particle is 1.00g .

Conclusion:

Therefore, the kinetic energy of the incident particle in the situation described in part (a) is 7.11×103J and in part (b) is 2.84×102J and the incident particle loses more energy in case (a).

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Chapter 9 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

Ch. 9 - A massive tractor is rolling down a country road....Ch. 9 - A 2-kg object moving to the right with a speed of...Ch. 9 - A 5-kg cart moving to the right with a speed of 6...Ch. 9 - A 57.0-g tennis ball is traveling straight at a...Ch. 9 - The momentum of an object is increased by a factor...Ch. 9 - The kinetic energy of an object is increased by a...Ch. 9 - If two particles have equal momenta, are their...Ch. 9 - If two particles have equal kinetic energies, are...Ch. 9 - A 10.0-g bullet is fired into a 200-g block of...Ch. 9 - Two particles of different mass start from rest....Ch. 9 - Two particles of different mass start from rest....Ch. 9 - A basketball is tossed up into the air, falls...Ch. 9 - A 3-kg object moving to the right on a...Ch. 9 - A ball is suspended by a string that is tied to a...Ch. 9 - A car of mass m traveling at speed v crashes into...Ch. 9 - A head-on, elastic collision occurs between two...Ch. 9 - An airbag in an automobile inflates when a...Ch. 9 - In golf, novice players are often advised to be...Ch. 9 - An open box slides across a frictionless, icy...Ch. 9 - While in motion, a pitched baseball carries...Ch. 9 - Prob. 9.5CQCh. 9 - A sharpshooter fires a rifle while standing with...Ch. 9 - Two students hold a large bed sheet vertically...Ch. 9 - A juggler juggles three balls in a continuous...Ch. 9 - (a) Does the center of mass of a rocket in free...Ch. 9 - On the subject of the following positions, state...Ch. 9 - Prob. 9.11CQCh. 9 - Prob. 9.12CQCh. 9 - A bomb, initially at rest, explodes into several...Ch. 9 - A particle of mass m moves with momentum of...Ch. 9 - An object has a kinetic energy of 275 J and a...Ch. 9 - At one instant, a 17.5-kg sled is moving over a...Ch. 9 - A 3.00-kg particle has a velocity of...Ch. 9 - A baseball approaches home plate at a speed of...Ch. 9 - A 45.0-kg girl is standing on a 150-kg plank. Both...Ch. 9 - A girl of mass mg is standing on a plank of mass...Ch. 9 - A 65.0-kg boy and his 40.0-kg sister, both wearing...Ch. 9 - In research in cardiology and exercise physiology,...Ch. 9 - When you jump straight up as high as you can, what...Ch. 9 - Two blocks of masses m and 3m are placed on a...Ch. 9 - A man claims that he can hold onto a 12.0-kg child...Ch. 9 - An estimated force-time curve for a baseball...Ch. 9 - Review. After a 0.300-kg rubber ball is dropped...Ch. 9 - A glider of mass m is free to slide along a...Ch. 9 - In a slow-pitch softball game, a 0.200-kg softball...Ch. 9 - The front 1.20 m of a 1 400-kg car Ls designed as...Ch. 9 - A tennis player receives a shot with the ball...Ch. 9 - The magnitude of the net force exerted in the x...Ch. 9 - Review. A force platform is a tool used to analyze...Ch. 9 - Water falls without splashing at a rate of 0.250...Ch. 9 - A 1 200-kg car traveling initially at vCi = 25.0...Ch. 9 - A 10.0-g bullet is fired into a stationary block...Ch. 9 - A car of mass m moving at a speed v1 collides and...Ch. 9 - A railroad car of mass 2.50 104 kg is moving with...Ch. 9 - Four railroad cars, each of mass 2.50 104 kg, are...Ch. 9 - A neutron in a nuclear reactor makes an elastic,...Ch. 9 - A 7.00-g bullet, when fired from a gun into a...Ch. 9 - A tennis ball of mass 57.0 g is held just above a...Ch. 9 - As shown in Figure P9.30, a bullet of mass m and...Ch. 9 - A 12.0-g wad of sticky clay is hurled horizontally...Ch. 9 - A wad of sticky clay of mass m is hurled...Ch. 9 - Prob. 9.33PCh. 9 - (a) Three carts of masses m1 = 4.00 kg, m2 = 10.0...Ch. 9 - A 0.300-kg puck, initially at rest on a...Ch. 9 - Prob. 9.36PCh. 9 - An object of mass 3.00 kg, moving with an initial...Ch. 9 - Two shuffleboard disks of equal mass, one orange...Ch. 9 - Two shuffleboard disks of equal mass, one orange...Ch. 9 - A proton, moving with a velocity of vii, collides...Ch. 9 - A billiard ball moving at 5.00 m/s strikes a...Ch. 9 - A 90.0-kg fullback running east with a speed of...Ch. 9 - An unstable atomic nucleus of mass 17.0 10-27 kg...Ch. 9 - The mass of the blue puck in Figure P9.44 is 20.0%...Ch. 9 - Prob. 9.45PCh. 9 - The mass of the Earth is 5.97 1024 kg, and the...Ch. 9 - Explorers in the jungle find an ancient monument...Ch. 9 - A uniform piece of sheet metal is shaped as shown...Ch. 9 - A rod of length 30.0 cm has linear density (mass...Ch. 9 - A water molecule consists of an oxygen atom with...Ch. 9 - A 2.00-kg particle has a velocity (2.00. 3.00)...Ch. 9 - Consider a system of two particles in the xy...Ch. 9 - Romeo (77.0 kg) entertains Juliet (55.0 kg) by...Ch. 9 - The vector position of a 3.50-g particle moving in...Ch. 9 - A ball of mass 0.200 kg with a velocity of 1.50...Ch. 9 - Prob. 9.56PCh. 9 - A particle is suspended from a post on top of a...Ch. 9 - A 60.0-kg person bends his knees and then jumps...Ch. 9 - Figure P9.59a shows an overhead view of the...Ch. 9 - A model rocket engine has an average thrust of...Ch. 9 - A garden hose is held as shown in Figure P9.32....Ch. 9 - Review. The first stage of a Saturn V space...Ch. 9 - A rocket for use in deep space is to be capable of...Ch. 9 - A rocket has total mass Mi = 360 kg, including...Ch. 9 - Prob. 9.65APCh. 9 - An amateur skater of mass M is trapped in the...Ch. 9 - A 3.00-kg steel ball strikes a wall with a speed...Ch. 9 - (a) Figure P9.36 shows three points in the...Ch. 9 - Review. A 60.0-kg person running at an initial...Ch. 9 - A cannon is rigidly attached to a carriage, which...Ch. 9 - A 1.25-kg wooden block rests on a table over a...Ch. 9 - A wooden block of mass M rests on a table over a...Ch. 9 - Two particles with masses m and 3m are moving...Ch. 9 - Pursued by ferocious wolves, you are in a sleigh...Ch. 9 - Two gliders are set in motion on a horizontal air...Ch. 9 - Why is the following situation impossible? An...Ch. 9 - Two blocks of masses m1 = 2.00 kg and m2 = 4.00 kg...Ch. 9 - Prob. 9.78APCh. 9 - A 0.400-kg blue bead slides on a frictionless,...Ch. 9 - A small block of mass mt = 0.500 kg is released...Ch. 9 - Review. A bullet of mass m = 8.00 g is fired into...Ch. 9 - Review. A bullet of mass m is fired into a block...Ch. 9 - A 0.500-kg sphere moving with a velocity expressed...Ch. 9 - A 75.0-kg firefighter slides down a pole while a...Ch. 9 - George of the Jungle, will mass m, swings on a...Ch. 9 - Review. A student performs a ballistic pendulum...Ch. 9 - Review. A light spring of force constant 3.85 N/m...Ch. 9 - Prob. 9.88APCh. 9 - A 5.00-g bullet moving with an initial speed of i...Ch. 9 - Review. There are (one can say) three coequal...Ch. 9 - A 2.00-g particle moving at 8.00 m/s makes a...Ch. 9 - Prob. 9.92CPCh. 9 - Two particles with masses m and 3m are moving...Ch. 9 - Sand from a stationary hopper falls onto a moving...Ch. 9 - On a horizontal air track, a glider of mass m...Ch. 9 - Review. A chain of length L and total mass M is...
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