Help working out height of bounce

[irish_bhoy08]

1. A man is working in a building when he drops a screwdriver from the top, mass 400 grams, from a height of 40metres. Assuming g = 10N/kg

a)If the screwdriver loses 95% of its kinetic energy as heat and sound when it hits the ground, what will be the height of its first bounce?




2. KE = 1/2 x m x v2
gpe = m X g x h
v= √2gh



3. I have worked out the kinetic energy at as it hits the ground, the GPE and the velocity but i have no idea how to figure out what the height of the first bounce would be. Any hint to put in the right direction would be fantastic

 

[dotman]

Hello!

Well, when it is dropped, as you see, it starts out with all of its energy as potential energy, and no kinetic energy. As it falls, all of its potential energy becomes kinetic energy. When it hits the ground, by the problem statement its going to lose 95% of this energy, but then bounce off, back up again.

At this point, it will begin rising again, its kinetic energy becoming potential energy, until it reaches zero velocity, ie, its kinetic energy is zero. All of its energy will once again have become potential energy.

Because you know how much energy it started with, and you can calculate how much energy it loses on impact (95%, by problem definition), you can calculate how high the first bounce will be, by applying your potential energy formula (mgh).

Hope this helps! Of course, it will then again begin to fall, and the whole process repeats.

 

[arithmetix]

yes dotman!
work=energy=force x distance, and the quick answer is that the screwdriver bounces to 1/20 of the original height. (Of course the energy is not really 'lost', it is converted into heat... ultimately.)