/*! 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 5 A volleyball is spiked so that i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 5

A volleyball is spiked so that its incoming velocity of \(+4.0 \mathrm{~m} / \mathrm{s}\) is changed to an outgoing velocity of \(-21 \mathrm{~m} / \mathrm{s}\). The mass of the volleyball is \(0.35 \mathrm{~kg}\). What impulse does the player apply to the ball?

Short Answer

Expert verified
The impulse applied to the ball is -8.75 Ns.

Step by step solution

01

Understanding Impulse

Impulse is the change in momentum of an object when a force is applied over a period of time. It is given by the formula: \( J = riangle p = m imes (v_f - v_i) \) where \( J \) is the impulse, \( m \) is the mass, \( v_f \) is the final velocity, and \( v_i \) is the initial velocity.
02

Substitute Values

Substitute the given values into the formula: mass \( m = 0.35 \) kg, final velocity \( v_f = -21 \) m/s, and initial velocity \( v_i = +4 \) m/s. This gives: \( J = 0.35 imes (-21 - 4) \).
03

Calculate the Velocity Change

Calculate the change in velocity: \( v_f - v_i = -21 - 4 = -25 \) m/s.
04

Calculate Impulse

Substitute the change in velocity into the impulse formula: \( J = 0.35 imes (-25) = -8.75 \) N路s.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Change in Momentum
Momentum is a fundamental concept in physics, essentially describing how much motion an object has. It is the product of the mass and velocity of an object. When an external force is applied to an object, its momentum changes. Such a change is precisely what we refer to as the 'Change in Momentum'.

When the volleyball is spiked, the player's action results in altering the ball's direction and speed, effectively changing its momentum.
  • For the volleyball, its initial momentum is given by multiplying its mass by its initial velocity: \( p_i = m \times v_i \) with \( m = 0.35 \text{ kg} \) and \( v_i = 4.0 \text{ m/s} \).
  • The final momentum then becomes: \( p_f = m \times v_f \) where \( v_f = -21 \text{ m/s} \).
  • The change in momentum is: \( \Delta p = p_f - p_i \).
Understanding the change in momentum is crucial for calculating the impulse, aiding us in analyzing the effects of forces over time.
Velocity Change Calculation
Velocity change is a key part of understanding how the volleyball's speed and direction transform under the action of force. The velocity change is derived from subtracting the initial velocity from the final velocity.

In mathematical terms:
  • The change in velocity \( \Delta v \) is computed as \( v_f - v_i \).
  • For the volleyball, this translates to \(-21 \text{ m/s} - 4 \text{ m/s} = -25 \text{ m/s} \).
The negative sign indicates a directional change, meaning the volleyball has been reversed and accelerated in the opposite direction after being hit.

This calculation is crucial as it indicates how rapidly the speed is altered; hence impacting how we assess the exerted force's effectiveness.
Impulse Formula
The impulse formula is a central piece in bridging the concepts of force and momentum. Impulse quantifies the overall effect of a force acting over a time period, exhibited by a change in an object's momentum.

The impulse \( J \) can be described by the formula:
  • \( J = \Delta p = m \times (v_f - v_i) \)
For the volleyball spike:
  • The mass \( m = 0.35 \text{ kg} \).
  • The calculated velocity change is \( -25 \text{ m/s} \).
  • Therefore, the impulse becomes: \( J = 0.35 \times (-25) = -8.75 \text{ N路s} \).
The negative impulse indicates the force was applied in the opposite direction to the initial motion, changing the volleyball's trajectory significantly.

Impulse is a powerful tool in physics, enabling us to understand the effects of forces in dynamic environments.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A person stands in a stationary canoe and throws a \(5.00-\mathrm{kg}\) stone with a velocity of 8.00 \(\mathrm{m} / \mathrm{s}\) at an angle of \(30.0^{\circ}\) above the horizontal. The person and canoe have a combined mass of \(105 \mathrm{~kg}\). Ignoring air resistance and effects of the water, find the horizontal recoil velocity (magnitude and direction) of the canoe.

An \(85-\mathrm{kg}\) jogger is heading due east at a speed of \(2.0 \mathrm{~m} / \mathrm{s}\). A \(55-\mathrm{kg}\) jogger is heading \(32^{\circ}\) north of east at a speed of \(3.0 \mathrm{~m} / \mathrm{s}\). Find the magnitude and direction of the sum of the momenta of the two joggers.

Batman (mass \(=91 \mathrm{~kg}\) ) jumps straight down from a bridge into a boat (mass \(=510 \mathrm{~kg}\) ) in which a criminal is fleeing. The velocity of the boat is initially +11 \(\mathrm{m} / \mathrm{s}\). What is the velocity of the boat after Batman lands in it?

During July 1994 the comet Shoemaker-Levy 9 smashed into Jupiter in a spectacular fashion. The comet actually consisted of 21 distinct pieces, the largest of which had a mass of approximately \(4.0 \times 10^{12} \mathrm{~kg}\) and a speed of \(6.0 \times 10^{4} \mathrm{~m} / \mathrm{s}\). Jupiter, the largest planet in the solar system, has a mass of \(1.9 \times 10^{27} \mathrm{~kg}\) and an orbital speed of \(1.3 \times 10^{4} \mathrm{~m} / \mathrm{s} .\) If this piece of the comet had hit Jupiter head-on, what would have been the change (magnitude only) in Jupiter's orbital speed (not its final speed)?

The earth and moon are separated by a center-to-center distance of \(3.85 \times 10^{8} \mathrm{~m}\). The mass of the earth is \(5.98 \times 10^{24} \mathrm{~kg}\) and that of the moon is \(7.35 \times 10^{22} \mathrm{~m}\). How far does the center of mass lie from the center of the earth?
See all solutions

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Read Explanation

Mechanics and Materials

Read Explanation

Medical Physics

Read Explanation

Linear Momentum

Read Explanation

Scientific Method Physics

Read Explanation

Electrostatics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.