Explanation Given data: A ball is dropped from a height of 2 m. It bounces on a hard floor and rebounds to a height of 1.5 m. Mass of the ball ( m ) is 200 g, which is written as 0.2 Kg. Formula used: Write the expression for impulse in y -direction (vertical direction) from the impulse-momentum theorem. J y = Δ ( p y ) (1) Here, Δ ( p y ) is the change in momentum in the y -direction. Write the expression for change in momentum of the ball in terms of velocity and mass for the given system. Δ ( p y ) = m [ ( v y ) f − ( v y ) i ] (2) Here, m is the mass of the ball, ( v y ) f is the final velocity of the ball (speed of the ball just after hitting the floor), and ( v y ) i is the initial velocity of the ball (speed of the ball just before hitting the floor). Write the expression for impulse in terms of force and time period. J y = F avg Δ t (3) Here, F avg is the force experienced by the particle in a particular interval of time period, and Δ t is the time interval. Write the expression to find area of the triangle shaped curve. A = 1 2 b h (4) Here, b is the base of the triangle, and h is the height of the triangle. Explanation: Refer to Figure P9.49 in the textbook. From equation (3), the impulse exerted by the hard floor on the ball is the area under the force curve in Figure P9.49. From the figure, the base of the triangle shaped force curve is 5 ms and the height is F max . Modify the expression in equation (4) to find the impulse as follows. J y = 1 2 b h Substitute 5 ms for b , and F max for h , J y = 1 2 ( 5 ms ) ( F max ) = 1 2 ( 5 × 10 − 3 s ) ( F max ) = ( 2.5 × 10 − 3 s ) F max Rewrite the expression as follows. F max = J y 2.5 × 10 − 3 s (5) Calculation of initial velocity of the ball ( v y ) i : Consider the initial velocity of the ball is the speed of the ball just before hitting the hard floor. Write the expression to find initial velocity of the ball in terms of acceleration. ( v y ) i = v 0 y 2 + 2 a y ( y 1 − y 0 ) (6) Here, v 0 y is the speed of the ball when it is dropped from the height of 2.0 m, which is 0 m s since no speed is applied, a y is the acceleration, which is ( − 9.8 ) m s 2 for the given condition of the ball, y 1 is the position of the ball when it hit the floor, which is 0 m from the floors, and y 0 is the initial position of the ball before drop, which is 2.0 m from the floor. Substitute 0 m s for v 0 y , ( − 9.8 ) m s 2 for a y , 0 m for y 1 , and 2.0 m for y 0 in equation (6), ( v y ) i = ( 0 m s ) 2 + 2 ( − 9.8 m s 2 ) ( 0 m − 2.0 m ) = 0 m 2 s 2 + 39.20 m 2 s 2 = ± 6.2609 m s ≅ − 6.26 m s Calculation of final velocity of the ball ( v y ) f : Consider the final velocity of the ball is the speed of the ball just after hitting the hard floor

College Physics: A Strategic Approach (4th Edition)

4th Edition

ISBN: 9780134609034

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Question

Chapter 9, Problem 49GP

To determine

To find: The maximum force that exerted by the hard floor on the ball.

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Chapter 9, Problem 48GP

Chapter 9, Problem 50GP

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Chapter 9 Solutions

College Physics: A Strategic Approach (4th Edition)

Ch. 9 - Prob. 1CQ Ch. 9 - Prob. 2CQ Ch. 9 - Two pucks, of mass m and 4m, lie on a frictionless...Ch. 9 - Prob. 4CQ Ch. 9 - Prob. 5CQ Ch. 9 - Prob. 6CQ Ch. 9 - Prob. 7CQ Ch. 9 - Two students stand at rest, facing each other on...Ch. 9 - A 2 kg cart rolling to the right at 3 m/s runs...Ch. 9 - Automobiles are designed with crumple zones...

Ch. 9 - You probably know that it feels better to catch a...Ch. 9 - In the early days of rocketry, some people claimed...Ch. 9 - Two ice skaters, Megan and Jason, push off from...Ch. 9 - Suppose a rubber ball and a steel ball collide....Ch. 9 - While standing still on a basketball court, you...Ch. 9 - To win a prize at the county fair, youre trying to...Ch. 9 - Monica stands at the edge of a circular platform...Ch. 9 - If the earth warms significantly, the polar ice...Ch. 9 - Prob. 21CQ Ch. 9 - Prob. 23MCQ Ch. 9 - Curling is a sport played with 20 kg stones that...Ch. 9 - Prob. 25MCQ Ch. 9 - Prob. 26MCQ Ch. 9 - Prob. 27MCQ Ch. 9 - A 4.0-m-diameter playground merry-go-round, with a...Ch. 9 - A disk rotates freely on a vertical axis with an...Ch. 9 - At what speed do a bicycle and its rider, with a...Ch. 9 - Prob. 2P Ch. 9 - A 57 g tennis ball is served at 45 m/s. If the...Ch. 9 - Prob. 4P Ch. 9 - A student throws a 120 g snowball at 7.5 m/s at...Ch. 9 - Prob. 6P Ch. 9 - Prob. 7P Ch. 9 - Prob. 8P Ch. 9 - Use the impulse-momentum theorem to find how long...Ch. 9 - Prob. 10P Ch. 9 - Prob. 11P Ch. 9 - Prob. 12P Ch. 9 - A child is sliding on a sled at 1.5 m/s to the...Ch. 9 - Prob. 14P Ch. 9 - As part of a safety investigation, two 1400 kg...Ch. 9 - In a Little League baseball game, the 145 g ball...Ch. 9 - Prob. 18P Ch. 9 - A small, 100 g cart is moving at 1.20 m/s on a...Ch. 9 - Prob. 20P Ch. 9 - A 2.7 kg block of wood sits on a frictionless...Ch. 9 - Prob. 22P Ch. 9 - A 10,000 kg railroad car is rolling at 2.00 m/s...Ch. 9 - Prob. 24P Ch. 9 - A 55 kg hunter, standing on frictionless ice,...Ch. 9 - Prob. 26P Ch. 9 - Prob. 27P Ch. 9 - Prob. 28P Ch. 9 - A 71 kg baseball player jumps straight up to catch...Ch. 9 - Prob. 30P Ch. 9 - A kid at the junior high cafeteria wants to propel...Ch. 9 - The parking brake on a 2000 kg Cadillac has...Ch. 9 - A 2.0 kg block slides along a frictionless surface...Ch. 9 - Erica (36 kg) and Danny (47 kg) are bouncing on a...Ch. 9 - A 20 g ball of clay traveling east at 3.0 m/s...Ch. 9 - Prob. 37P Ch. 9 - A 20 g ball of clay traveling east at 2.0 m/s...Ch. 9 - A firecracker in a coconut blows the coconut into...Ch. 9 - Prob. 40P Ch. 9 - Prob. 41P Ch. 9 - Divers change their body position in midair while...Ch. 9 - Prob. 43P Ch. 9 - What is the angular momentum of the moon around...Ch. 9 - Prob. 46GP Ch. 9 - Prob. 47GP Ch. 9 - Prob. 48GP Ch. 9 - Prob. 49GP Ch. 9 - Prob. 50GP Ch. 9 - Prob. 51GP Ch. 9 - A 140 g baseball is moving horizontally to the...Ch. 9 - A tennis player swings her 1000 g racket with a...Ch. 9 - A 20 g ball of clay is thrown horizontally at 30...Ch. 9 - Dan is gliding on his skateboard at 4.0 m/s. He...Ch. 9 - Ethan, whose mass is 80 kg, stands at one end of a...Ch. 9 - Three identical train cars, coupled together, are...Ch. 9 - A 110 kg linebacker running at 2.0 m/s and an 82...Ch. 9 - Most geologists believe that the dinosaurs became...Ch. 9 - Two ice skaters, with masses of 75 kg and 55 kg,...Ch. 9 - Prob. 62GP Ch. 9 - One billiard ball is shot east at 2.00 m/s. A...Ch. 9 - A 10 g bullet is fired into a 10 kg wood block...Ch. 9 - A typical raindrop is much more massive than a...Ch. 9 - A 15 g bullet is fired at 610 m/s into a 4.0 kg...Ch. 9 - Prob. 67GP Ch. 9 - Two 500 g blocks of wood are 2.0 m apart on a...Ch. 9 - A spaceship of mass 2.0 106 kg is cruising at a...Ch. 9 - At the county fair, Chris throws a 0.15 kg...Ch. 9 - Prob. 73GP Ch. 9 - The carbon isotope 14C is used for carbon dating...Ch. 9 - Prob. 75GP Ch. 9 - A 2.0 kg, 20-cm-diameter turntable rotates at 100...Ch. 9 - Prob. 77GP Ch. 9 - A 3.0-m-diameter merry-go-round with a mass of 250...Ch. 9 - Disk A, with a mass of 2.0 kg and a radius of 40...Ch. 9 - Consider a golf club hitting a golf ball. To a...Ch. 9 - Consider a golf club hitting a golf ball. To a...Ch. 9 - Consider a golf club hitting a golf ball. To a...Ch. 9 - Consider a golf club hitting a golf ball. To a...

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