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.

 

[asteriatic]

I would like to clarify that the equation W=Fcosθd is not applicable in this scenario. This equation is used to calculate work, which is defined as the product of force and displacement in the direction of the force. In this case, we are trying to calculate the average force exerted on the child swing, which is a different concept.

To calculate the average force exerted by the parent, we need to use the equation F=ma, where F is the force, m is the mass of the child, and a is the acceleration. Since the swing is moving in a circular motion, the acceleration can be calculated using the formula a=v^2/r, where v is the velocity and r is the radius of the swing.

1. To determine when the child will attain her maximum speed, we can use the conservation of energy principle. At the highest point of the swing, all of the potential energy is converted into kinetic energy. Therefore, we can equate the potential energy at the highest point to the kinetic energy at the lowest point. This would give us the equation mgh=1/2mv^2, where m is the mass of the child, g is the acceleration due to gravity, h is the maximum height, and v is the maximum velocity. Solving for v, we get v=√(2gh). This means that the child will attain her maximum speed at the lowest point of the swing.

2. The maximum speed through the subsequent swing can be calculated using the same equation as in question 1. However, we need to take into account the fact that there will be some energy loss due to friction and air resistance. This means that the maximum velocity will be slightly less than the calculated value in question 1.

3. To calculate the average force exerted by the parent, we can use the equation F=ma. Since we know the mass of the child and the acceleration, we can calculate the force. However, we also need to take into account the distance over which the force was applied. As the child swings, the distance between the parent's hand and the child changes. Therefore, we need to calculate the average distance over which the force was applied. This can be done by taking the average of the initial and final distances between the parent's hand and the child. Once we have the average force and distance, we can use the equation W=Fd to calculate the work done by the parent