/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 A ball weighing \(10 \mathrm{~g}... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 14

A ball weighing \(10 \mathrm{~g}\) hits a hard surface vertically with a speed of \(5 \mathrm{~m} / \mathrm{s}\) and rebounds with the same speed. The ball remains in contact with the surface for \(0.01 \mathrm{~s}\). The average force exerted by the surface on the ball is (A) \(100 \mathrm{~N}\) (B) \(10 \mathrm{~N}\) (C) \(1 \mathrm{~N}\) (D) \(0.1 \mathrm{~N}\)

Short Answer

Expert verified
The average force exerted by the surface on the ball is (A) \(100 \mathrm{~N}\).

Step by step solution

01

Identify Given Parameters and Variables

The given parameters are: Mass of the ball (m) = 10 g = 0.01 kg (converting from grams to kilograms) Initial velocity of the ball (u) = 5 m/s Final velocity of the ball (v) = -5 m/s (rebound velocity will have opposite direction) Time in contact with the surface (t) = 0.01 s We are required to find the average force exerted by the surface on the ball (F).
02

Calculate Change in Momentum

The change in momentum (螖p) can be calculated as the product of mass and the change in velocity: 螖p = m(v - u)
03

Calculate Impulse

Impulse (I) is the product of force (F) and time (t), and it is equal to the change in momentum: I = F 脳 t = 螖p
04

Calculate the Average Force

Now, we can solve the equation for the average force (F): F = 螖p / t Plug in the values: F = [(0.01)(-5 - 5)] / 0.01 Simplify: F = (-10) / 0.01 F = -1000 N The negative sign indicates that the force is exerted in the opposite direction of the rebound. The average force exerted by the surface on the ball is 1000 N. The correct option is (A) \(100 \mathrm{~N}\).

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