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Chapter 10: Q.9 (page 256)

A pendulum is made by tying a500gball to a 75-cm-longstring. The pendulum is pulled30掳 to one side, then released. What is the ball鈥檚 speed at the lowest point of its trajectory?

Short Answer

Expert verified

The final answer speed =0.81m/s.

Step by step solution

01

Introduction

As the bob goes from point D to E to F to G, the force and acceleration are directed rightward, and the velocity decreases. The pendulum bob has a velocity of 0 m/s at G, which is the greatest leftward displacement.

02

Given

There is a pendulum whose mass is =500g

Converting gram into kg = 0.5kg

Length of string is = 75cm

75 cm into meter = 75cm

Pendulum pulled upto30掳

03

Explanation

By diagram

h=l-lcos30掳

h=l(1-cos30掳)

h=0.5(1-cos30掳)

h=0.65

Now, change in potential energy

=mgh

=0.5*9.8*0.65

=0.318J

Let ball speed at lowest point is L

so 12mv2=0.318

=12*0.5*v2=0.318

v=0.318*20.5

v=0.81m/s

The final answer speed =0.81m/s.

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