/*! 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} Q78P Question: The solid wood door of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q78P (page 1)

Question: The solid wood door of a gymnasium is 1.00 m wide and 2.00 m high, has total mass 35.0 kg, and is hinged along one side. The door is open and at rest when a stray basketball hits the center of the door head-on, applying an average force of 1500 N to the door for 8.00 ms. Find the angular speed of the door after the impact. (Hint: Integrating Eq. (10.29) yields \(\Delta {L_Z} = \int_{t1}^{t2} {\left( {\sum {\tau _z}} \right)} dt = {\left( {\sum {\tau _z}} \right)_{av}}\Delta t.\)The quantity \(\int_{t1}^{t2} {\left( {\sum {\tau _z}} \right)} dt\) is called the angular impulse.)

Short Answer

Expert verified

1.03 rad/s

Step by step solution

01

Given Data

\(\begin{array}{c}{\rm{mass}}\;(m) = 35\;{\rm{kg}}\\{\rm{force}}\;(F) = 1500\;{\rm{N}}\\t = 8\;{\rm{ms}} = 8 \times {10^{ - 3}}\;{\rm{s}}\\L = 1\;{\rm{m}}\\H = 2\;{\rm{m}}\end{array}\)

02

Concept

The rate of change of angular displacement is known as angular speed.

03

Find the angular speed

Moment of inertia,

\(\begin{array}{c}I = \frac{1}{3}m{L^2}\\ = \frac{1}{3} \times 35 \times {1^2}\\ = 11.7\;{\rm{kg}} \cdot {{\rm{m}}^{\rm{2}}}\end{array}\)

Using second law of motion,

Change in angular momentum = torque impulse applied

\(\begin{array}{c}I\omega = FL\Delta t\\11.7\omega = 1500 \times 1 \times 8 \times {10^{ - 3}}\\\omega = 1.03\;{\rm{rad/s}}\end{array}\)

Hence, the angular speed is 1.03 rad/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!

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 car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of20m/s2, and the car has an acceleration of3.40m/s2. The car overtakes the truck after the truck has moved60.0m. (a) How much time does it take the car to overtake the truck? (b) How far was the car behind the truck initially? (c) What is the speed of each when they are abreast? (d) On a single graph, sketch the position of each vehicle as a function of time. Takex=0at the initial location of the truck.

You decide to visit Santa Claus at the north pole to put in a good word about your splendid behavior throughout the year. While there, you notice that the elf Sneezy, when hanging from a rope, produces a tension of 395.0鈥�Nin the rope. If Sneezy hangs from a similar rope while delivering presents at the earth鈥檚 equator, what will the tension in it be? (Recall that the earth is rotating about an axis through its north and south poles.) Consult Appendix F and start with a free-body diagram of Sneezy at the equator.

Your uncle is in the below-deck galley of his boat while you are spear fishing in the water nearby. An errant spear makes a small hole in the boat鈥檚 hull, and water starts to leak into the galley. (a) If the hole is 0.09 m below the water surface and has area 1.20 cm2, how long does it take 10.0 L of water to leak into the boat? (b) Do you need to take into consideration the fact that the boat sinks lower into the water as water leaks in?

Planet Vulcan.Suppose that a planet were discovered between the sun and Mercury, with a circular orbit of radius equal to 2/3 of the average orbit radius of Mercury. What would be the orbital period of such a planet? (Such a planet was once postulated, in part to explain the precession of Mercury鈥檚 orbit. It was even given the name Vulcan, although we now have no evidence that it actually exists. Mercury鈥檚 precession has been explained by general relativity.)

Question: Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in 1.00 mile and (b) feet in 1.00 km.
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Quantum Physics

Read Explanation

Thermodynamics

Read Explanation

Astrophysics

Read Explanation

Wave Optics

Read Explanation

Fundamentals of Physics

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.