/*! 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 60 When a body moves in a circle, t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 60

When a body moves in a circle, the work done by the centripetal force is always (A) \(>0\) (B) \(<0\) (C) Zero (D) None of these

Short Answer

Expert verified
The work done by the centripetal force on a body moving in a circle is always zero because the centripetal force is always perpendicular to the displacement vector. Thus, the angle between the force and displacement vectors is 90 degrees, and the cosine of 90 degrees is 0. Therefore, the correct answer is (C) Zero.

Step by step solution

01

Recalling the centripetal force formula

Centripetal force is calculated using the formula: \(F_c = \frac{mv^2}{r}\), where \(F_c\) is the centripetal force, \(m\) is the mass of the object, \(v\) is the velocity of the object, and \(r\) is the radius of the circle.
02

Understanding the direction of centripetal force

The direction of the centripetal force is always towards the center of the circular path. Hence, by definition, it is always perpendicular to the velocity vector of the object.
03

Calculating the work done by the centripetal force

To find the work done by the centripetal force, we need to calculate the dot product of the force vector and the displacement vector (remember that work done is equal to W = F * d * cos胃). Since the centripetal force is always directed towards the center of the circular path, it is always perpendicular to the velocity vector and the tangent of the path (which is the direction of the displacement vector). Thus, the angle between the centripetal force vector and the displacement vector is always 90 degrees. The cosine of 90 degrees is 0. Therefore, the work done by the centripetal force on a body moving in a circle is: \[W = F_c * d * \cos(90掳) = F_c * d * 0 = 0\]
04

Identifying the correct answer

The work done by the centripetal force on a body moving in a circle is always zero, which means the correct answer for this exercise is (C) Zero.

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 particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that (A) Its velocity is constant. (B) Its acceleration is constant. (C) Its kinetic energy is constant. (D) It moves in a straight line.

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time \(t\) is proportional to \([2003]\) (A) \(t^{3 / 4}\) (B) \(t^{3 / 2}\) (C) \(t^{1 / 4}\) (D) \(t^{1 / 2}\)

A block of mass \(0.5 \mathrm{~kg}\) is kept in an elevator moving down with an acceleration \(2 \mathrm{~m} / \mathrm{s}^{2}\). Find the magnitude work done (in Joule) by the normal contact force on the block in first second. Initially system is at rest \(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)\)

A bullet losses \(19 \%\) of its kinetic energy when passes through an obstacle. The percentage change in its speed is (A) Reduced by \(10 \%\) (B) Reduced by \(19 \%\) (C) Reduced by \(9.5 \%\) (D) Reduced by \(11 \%\)

This question has Statement 1 and Statement \(2 .\) Of the four choices given after the statements, choose the one that best describes the two statements. If two springs \(S_{1}\) and \(S_{2}\) of force constants \(k_{1}\) and \(k_{2}\), respectively, are stretched by the same force, it is found that more work is done on spring \(S_{1}\) than on spring \(S_{2}\) Statement 1: If stretched by the same amount, work done on \(S_{1}\) will be more than that on \(S_{2}\) Statement \(2: k_{1}
See all solutions

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Read Explanation

Rotational Dynamics

Read Explanation

Thermodynamics

Read Explanation

Particle Model of Matter

Read Explanation

Kinematics Physics

Read Explanation

Translational Dynamics

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.