COLLEGE PHYSICS-CONNECT ACCESS
COLLEGE PHYSICS-CONNECT ACCESS
5th Edition
ISBN: 9781260486834
Author: GIAMBATTISTA
Publisher: MCG
bartleby

Videos

Question
Book Icon
Chapter 7, Problem 86P
To determine

The average force exerted on the ball.

Expert Solution & Answer
Check Mark

Answer to Problem 86P

The average force exerted on the ball is 34N.

Explanation of Solution

Write the expression for velocity of the ball before bounce.

  u=uxcosθi^uysinθj^        (I)

Here, u is the initial velocity of the ball before bounce, ux is the velocity of the ball strikes the ground below the horizontal position, uy is the velocity of the ball strikes the ground in vertical position, and θ is the angle with respect to ground below the horizontal position.

Write the expression for velocity of the ball after bounce.

  v=vxcosϕi^+vysinϕj^        (II)

Here, v is the final velocity of the ball after bounce, vx is the velocity of the ball strikes the ground above the horizontal position, vy is the velocity of the ball strikes the ground in vertical position, and ϕ is the angle with respect to ground above the horizontal position.

Write the expression for the change in momentum of the ball.

  Δp=pfpi        (III)

Here, Δp is the change in momentum of the ball, pf is the final momentum of the ball, and pi is the initial momentum of the ball.

The expression for initial momentum of the ball is,

  pi=mu        (IV)

Here, m is the mass of the tennis ball.

The expression for final momentum of the ball is,

  pf=mv        (V)

Write the expression from the relation between force and rate of change of momentum.

  Favg=ΔpΔt        (VI)

Here, Favg is the average force exerted on the ball and Δt is the interaction time period of the ball with ground.

Conclusion:

Substitute the equation (IV) and (V) in equation (III).

  Δp=mvmu=m(vu)        (VII)

Substitute 54m/s for ux and uy, 22° for θ in equation (I) to find u.

  u=(54m/s)cos(22°)i^(54m/s)sin(22°)j^=(50.1m/s)i^(20.2m/s)j^

Substitute 53m/s for vx and vy, 18° for ϕ in equation (II) to find v.

  v=(53m/s)cos(18°)i^+(53m/s)sin(18°)j^=(50.4m/s)i^+(16.4m/s)j^

Substitute (50.1m/s)i^(20.2m/s)j^ for u, (50.4m/s)i^+(16.4m/s)j^ for v, and 0.060kg for m in equation (VII) to find Δp.

  Δp=(0.060kg)[(50.4m/s)i^+(16.4m/s)j^(50.1m/s)i^+(20.2m/s)j^]=(0.018kgm/s)i^+(2.196kgm/s)j^

Substitute (0.018kgm/s)i^+(2.196kgm/s)j^ for Δp and 0.065s for Δt in equation (VI) to find average force.

  Favg=(0.018kgm/s)i^+(2.196kgm/s)j^0.065s=(0.277N)i^+(33.8N)j^

The magnitude of the average force exerted on the ball is,

  Favg=(0.277N)2+(33.8N)2=33.8N34N

Therefore, the average force exerted on the ball is 34N.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 7 Solutions

COLLEGE PHYSICS-CONNECT ACCESS

Ch. 7.7 - Prob. 7.7ACPCh. 7.7 - Prob. 7.7BCPCh. 7.7 - Instead of colliding elastically, suppose the two...Ch. 7.8 - Prob. 7.11PPCh. 7 - Prob. 1CQCh. 7 - Prob. 2CQCh. 7 - Prob. 3CQCh. 7 - Prob. 4CQCh. 7 - Prob. 5CQCh. 7 - Which would be more effective: a hammer that...Ch. 7 - Prob. 8CQCh. 7 - Prob. 10CQCh. 7 - Prob. 11CQCh. 7 - Prob. 1MCQCh. 7 - Prob. 2MCQCh. 7 - Prob. 3MCQCh. 7 - Prob. 4MCQCh. 7 - Prob. 5MCQCh. 7 - Prob. 6MCQCh. 7 - Prob. 7MCQCh. 7 - Prob. 8MCQCh. 7 - Prob. 9MCQCh. 7 - Prob. 10MCQCh. 7 - Prob. 11MCQCh. 7 - Prob. 12MCQCh. 7 - Prob. 1PCh. 7 - Prob. 2PCh. 7 - Prob. 3PCh. 7 - Prob. 4PCh. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - A ball of mass 5.0 kg moving with a speed of 2.0...Ch. 7 - Prob. 10PCh. 7 - Prob. 11PCh. 7 - Prob. 12PCh. 7 - Prob. 13PCh. 7 - Prob. 14PCh. 7 - Prob. 15PCh. 7 - Prob. 16PCh. 7 - Prob. 17PCh. 7 - Prob. 18PCh. 7 - Prob. 19PCh. 7 - Prob. 20PCh. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - Prob. 23PCh. 7 - Prob. 24PCh. 7 - Prob. 25PCh. 7 - Prob. 26PCh. 7 - Prob. 27PCh. 7 - Prob. 28PCh. 7 - Prob. 29PCh. 7 - Prob. 30PCh. 7 - Prob. 31PCh. 7 - Prob. 32PCh. 7 - Prob. 34PCh. 7 - Prob. 35PCh. 7 - Prob. 36PCh. 7 - Prob. 37PCh. 7 - Prob. 38PCh. 7 - Prob. 39PCh. 7 - Prob. 40PCh. 7 - Prob. 41PCh. 7 - Prob. 42PCh. 7 - Prob. 43PCh. 7 - Prob. 44PCh. 7 - Prob. 45PCh. 7 - Prob. 46PCh. 7 - Prob. 47PCh. 7 - Prob. 48PCh. 7 - Prob. 49PCh. 7 - Prob. 50PCh. 7 - Prob. 51PCh. 7 - Prob. 52PCh. 7 - Prob. 53PCh. 7 - Prob. 54PCh. 7 - Prob. 55PCh. 7 - Prob. 56PCh. 7 - Prob. 57PCh. 7 - Prob. 58PCh. 7 - Prob. 59PCh. 7 - Prob. 61PCh. 7 - Prob. 62PCh. 7 - Prob. 63PCh. 7 - Prob. 64PCh. 7 - Prob. 65PCh. 7 - Prob. 66PCh. 7 - Prob. 67PCh. 7 - Prob. 68PCh. 7 - Prob. 69PCh. 7 - Prob. 70PCh. 7 - Prob. 71PCh. 7 - Prob. 72PCh. 7 - Prob. 73PCh. 7 - Prob. 74PCh. 7 - Prob. 75PCh. 7 - Prob. 76PCh. 7 - Prob. 77PCh. 7 - Prob. 78PCh. 7 - Prob. 79PCh. 7 - Prob. 80PCh. 7 - Prob. 81PCh. 7 - Prob. 82PCh. 7 - Prob. 83PCh. 7 - Prob. 84PCh. 7 - Prob. 85PCh. 7 - Prob. 86PCh. 7 - Prob. 87PCh. 7 - Prob. 88PCh. 7 - Prob. 89PCh. 7 - Prob. 90PCh. 7 - Prob. 91PCh. 7 - Prob. 92PCh. 7 - Prob. 93PCh. 7 - Prob. 94PCh. 7 - Prob. 95PCh. 7 - Prob. 96PCh. 7 - Prob. 97PCh. 7 - Prob. 98PCh. 7 - Prob. 99PCh. 7 - Prob. 100PCh. 7 - Prob. 101PCh. 7 - Prob. 102PCh. 7 - Prob. 103PCh. 7 - Prob. 104PCh. 7 - Prob. 105PCh. 7 - Prob. 106PCh. 7 - Prob. 107PCh. 7 - Prob. 109PCh. 7 - Prob. 110PCh. 7 - Prob. 111P
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Text book image
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
Text book image
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
Elastic and Inelastic Collisions; Author: Professor Dave Explains;https://www.youtube.com/watch?v=M2xnGcaaAi4;License: Standard YouTube License, CC-BY