Calculating Speed of Dropped Tennis Ball: Explaining Conservation of Energy

[RachelT]

Homework Statement

Using the formulae for potential energy and kinetic energy, find the speed that a tennis ball hits the ground when dropped from a height of 20m.

With reference to the principle of conservation of energy, explain why you could use these equations and what assumptions you have made.

Homework Equations

KE = 1/2mv^2
PE = mgh

The Attempt at a Solution

The first part I think I'm ok with. The tennis ball is dropped therefore no KE only PE.
PE = 9.8 x 20 = 196 Joules.

It is the second part that I don't really understand. What is it asking me? Can somebody maybe re-frase this part of the question. Thank you.

 

[RachelT]

sorry. I forgot to turn that PE into KE by making 196 = 1/2v^2
This would give 19.79m/s

 

[NascentOxygen]

Homework Statement

Using the formulae for potential energy and kinetic energy, find the speed that a tennis ball hits the ground when dropped from a height of 20m.

With reference to the principle of conservation of energy, explain why you could use these equations and what assumptions you have made.

Homework Equations

KE = 1/2mv^2
PE = mgh

The Attempt at a Solution

The first part I think I'm ok with. The tennis ball is dropped therefore no KE only PE.
PE = 9.8 x 20 = 196 Joules.

You can't just drop mass from your equation because the ball's mass is not stated. :yuck:
Keep mass where it belongs, but represent it by the symbol m.
PE = m x 9.8 x 20 = 196m Joules

 

[CWatters]

Also best to avoid plugging in the number until the end.


PE = mgh
KE = 0.5mv²

0.5mv² = mgh

Mass cancels.

Rearrange to give

v = SQRT(2gh)

Then put the numbers in.

As for part 2...

You need to explain why the KE the ball has when it hits the ground will be equal to the PE it had when dropped. What assumptions does that statement rely on?

Hint: Why would it be more reasonable to make that ssumption on the moon than on earth?

Make sure your answer mentions conservation of energy.

 

[Nickie]

I can explain the concept of conservation of energy in relation to the problem at hand. The principle of conservation of energy states that energy cannot be created or destroyed, it can only be transferred or converted from one form to another. This means that the total energy of a system remains constant. In this case, the system is the tennis ball and the Earth.

When the tennis ball is dropped from a height of 20m, it has a certain amount of potential energy due to its position above the ground. As it falls, this potential energy is converted into kinetic energy, which is the energy an object possesses due to its motion. This is represented by the equations for potential energy and kinetic energy, where PE = mgh and KE = 1/2mv^2.

By using these equations, we are assuming that there are no other external forces acting on the ball, such as air resistance or friction. This is because the principle of conservation of energy only applies in a closed system where there are no external forces. In reality, there will always be some loss of energy due to these external forces, but for the purposes of this calculation, we can assume that they are negligible.

Therefore, by using the equations for potential and kinetic energy, we can calculate the speed of the tennis ball when it hits the ground. This is because the total energy of the system (PE + KE) remains constant, and we can equate the initial potential energy (PE) to the final kinetic energy (KE) at the moment of impact. This is a direct application of the principle of conservation of energy.