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The coefficient of restitution $\epsilon$ for a head-on collision is defined as the ratio of the relative speed after the collision to the relative speed before. (a) What is e for a completely inelastic collision? (b) What is $\epsilon$ for an elastic collision? (c) A ball is dropped from a height $h$ onto a stationary surface and rebounds back to a height $H_{1}$ . Show that $e=\sqrt{H_{1}} / h .$ (d) A properly inflated basket-ball should have a coefficient of restitution of $0.85 .$ When dropped from a height of 1.2 $\mathrm{m}$ above a solid wood floor, to what height should a properly inflated basketball bounce? (e) The height of the first bounce is $H_{1}$ . If $\epsilon$ is constant, show that the height of the $n$ th bounce is $H_{n}=\epsilon^{2 n} h .(f)$ If $\epsilon$ is constant, what is the height of the eighth bounce of a properly inflated basketball dropped from 1.2 $\mathrm{m} ?$

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a. $\epsilon=0$b. $\epsilon=1$c. $v_{1}=\sqrt{2 g h}$$v_{2}=\sqrt{2 g H_{1}}$d. $=0.87 \mathrm{m}$e.$H_{n}=\varepsilon^{2 n} h$ f. $=0.089 \mathrm{m}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Moment, Impulse, and Collisions

University of Washington

Simon Fraser University

McMaster University

Lectures

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

03:30

In physics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Given a force, F, applied for a time, t, the resulting change in momentum, p, is equal to the impulse, I. Impulse applied to a mass, m, is also equal to the change in the object's kinetic energy, T, as a result of the force acting on it.

04:37

A ball is dropped from a h…

09:02

12:15

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01:26

Coeffictent of restitution…

05:25

05:15

A dramatic (and perhaps un…

06:17

Bouncing Balls A tennis ba…

02:07

03:45

Problem You drop a 0.5 kg …

06:26

Amplified Rebound Height T…

03:07

10:31

(II) A measure of inelasti…

05:37

The coefficient of restitu…

Ignore air resistance.…

03:39

11:20

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