Calculating Average Force Exerted on Child Swing

[gbaby370]

I was given this question in a practice assignment;


A 31.0 kg child on a swing reaches a maximum height of 1.92 m above her rest position. Assuming no loss of energy:

1.At what point during the swing will she attain her maximum speed?
2.What will be her maximum speed through the subsequent swing?
3.Assuming this maximum height was the result of one push from her parent, what was the average force exerted by the parent if s/he pushed over a distance of 152 cm?

I got the first 2 questions no problem.

But for question 3, Can I simply use the equation W=Fcosθd. Where W would be equal to the gravitational potential so I would have mgh=fd, rearrange and solve, or am I missing something?

 

[HallsofIvy]

You can't use "W= F cos(\theta)d" because you don't know "d", the length of the swing. Instead just use W= Fh where "h" is the height to which the swing rises- and you are told that that is 1.92 m.

 

[rcgldr]

The total energy = m g h = m g 1.92 m. So what force x 1.52 meters would it take to result in the total amount of energy?

 

[gbaby370]

Figured it out!

It was simpler than I thought.

I was able to use W=Fd. The question wanted to know how much force was applied if it was pushed forward over a distance of 1.52m to have the string reach a 1.92m height. So I assumed the total work done would be the Etotal, which in this circumstance Et=Eg. So I had the equation mgh=fd, rearranged - and my instructor advised me the answer was correct.

Thanks for the pointers, greatly appreciated.