   Chapter 7, Problem 54AP

Chapter
Section
Textbook Problem

A 0.400-kg pendulum bob passes through the lowest part of its path at a speed of 3.00 m/s. (a) What is the tension in the pendulum cable at this point if the pendulum is 80.0 cm long? (b) When the pendulum reaches its highest point, what angle does the cable make with the vertical? (c) What is the tension in the pendulum cable when the pendulum reaches its highest point?

(a)

To determine
The tension in the pendulum cable at the lowest part of its path.

Explanation

Given info: The mass of the pendulum is 0.400kg . At the lowest part of its path the speed of the pendulum is 3.00ms-1 . The length of the pendulum is 80.0cm .

Explanation:

At the lowest position of the pendulum the gravitational force is acting vertically downward and the tension in the string is acting vertically upward. Hence the centripetal force will be,

mv2r=Tmg

• v is the velocity at the lowest position
• m is the mass of the pendulum
• T is the tension in the string
• g is the free fall acceleration
• r is the length of the pendulum

On re-arrangement for the tension,

T=mv2r+mg=m(v2r+g)

Substitute 0.400kg for m , 3.00ms-1 for v , 80.0cm for r , 9

(b)

To determine
The angle made by the pendulum cable with the vertical when the pendulum reaches its maximum position.

c)

To determine
The tension in the pendulum cable at the highest point.

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