   Chapter 5, Problem 44P

Chapter
Section
Textbook Problem

A 25.0-kg child on a 2.00-m-long swing is released from rest when the ropes of the swing make an angle of 30.0° with the vertical. (a) Neglecting friction, find the child’s speed at the lowest position. (b) If the actual speed of the child at the lowest position is 2.00 m/s, what is the mechanical energy lost due to friction?

(a)

To determine
The speed of the child at the lowest position.

Explanation

Given Info:

The mass of the child is 25.0kg .

Swing length is 2.0m .

The angle made by the rope with the vertical is 30.0° .

Since the motion is frictionless, according to the conservation of mechanical energy,

KEf+PEg,f=KEi+PEg,i

Thus,

12mvf2+0=0+mgyi

On re-arranging,

vf=2gyi       (I)

Since,

yi=l(1cosθ)       (II)

• l is the swing length
• ;

(b)

To determine
The mechanical energy lost due to friction if the actual speed of the child is 2.0m/s .

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