Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q. 57 (page 202)

A 60 g ball is tied to the end of a 50-cm-long string and swung in a vertical circle. The center of the circle, as shown in FIGURE P8.57, is 150 cm above the floor. The ball is swung at the
minimum speed necessary to make it over the top without the string going slack. If the string is released at the instant the ball is at the top of the loop, how far to the right does the ball hit the ground?

Short Answer

Expert verified

The ball will hit the ground at a distance of 1.41 meters.

Step by step solution

01

Given information

mass = 60 gm=0.06kg

length = 50 cm=0.5 m

Height of center of circle =1.5 m = 150 cm

02

Explanation

Lets draw a free body diagram as below and equate forces

Lets consider the top point, we have

Ttop=mv2r-mg

To find the minimum speed necessary to make it over the top we have, T=0,

0=mv2r-mgv=rg

Substitute values given, we get

v=(0.5m)(9.8m/s2)=2.21m/s

The height from which ball is falling =150 cm + 50cm=200 cm= 2m

Distance can be found by using the formula

s=ut+12at2

as u=0 and s= H , so

H=12gt2t=2Hg

Substitute the values we get

t=2(2m)(9.8m/s2)=0.639s

distance traveled in 0.639 sec with a velocity of 2.21 m/sec is

distance = (0.639 sec) x (2.21 m/sec) = 1.4121 meters.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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 heavy ball with a weight of 100N (m=10.2kg) is hung from the ceiling of a lecture hall on a 4.5-m-long rope. The ball is pulled to one side and released to swing as a pendulum, reaching a speed of 5.5m/s as it passes through the lowest point. What is the tension in the rope at that point?

Derive Equations 8.3 for the acceleration of a projectile subject to drag.

If a vertical cylinder of water (or any other liquid) rotates about its axis, as shown in FIGURE CP8.71, the surface forms a smooth curve. Assuming that the water rotates as a unit (i.e., all the water rotates with the same angular velocity), show that the shape of the surface is a parabola described by the equationz=ω22gr2

Hint: Each particle of water on the surface is subject to only two forces: gravity and the normal force due to the water underneath it. The normal force, as always, acts perpendicular to the surface.

Two wires are tied to the 300 g sphere shown in FIGURE P8.46. The sphere revolves in a horizontal circle at a constant speed of 7.5 m/s. What is the tension in each of the wires?

You can swing a ball on a string in a vertical circle if you swing it fast enough. But if you swing too slowly, the string goes slack as the ball nears the top. Explain why there’s a minimum speed to keep the ball moving in a circle.
See all solutions

Recommended explanations on Physics Textbooks

Force

Read Explanation

Electricity and Magnetism

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Astrophysics

Read Explanation

Translational Dynamics

Read Explanation

Magnetism

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.

Sign-up for free