   Chapter 7, Problem 22P

Chapter
Section
Textbook Problem

A 40.0-kg child swings in a swing supported by two chains, each 3.00 m long. The tension in each chain at the lowest point is 350 N. Find (a) the child’s speed at the lowest point and (b) the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.)

(a)

To determine
The child’s speed at lowest point.

Explanation

Given Info: The length of the swing chain is 3.00m , the tension in each chain is 350N , mass of the child is 40.0kg , and acceleration due to gravity is 9.80m/s2 .

Explanation: At the lowest swing point, the net force acting on the child is equal to the centripetal force and it could be represented as Fy=mv2r or 2Tmg=mv2r and this expression is rearranged to the speed of the child at lowest point.

The formula for the speed of the child at the lowest point is,

v=r(2Tmg)

• v is the speed of the child at the lowest point
• m is mass of the child.
• T is tension in each chain.
• r is length of each chain.
• g is acceleration due to gravity.

Substitute 3

(b)

To determine
The force exerted by the seat on the child at the lowest point.

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