Question

A slingshot will shoot a 10-g pebble 22.0 m straight up.Part AHow much potential energy is stored in the slingshot's rubber band?Express your answer using two significant figures.Part BWith the same potential energy stored in the rubber band, how high can the slingshot shoot a 25- pebble?Express your answer using two significant figures.Part CWhat physical effects did you ignore in solving this problem?Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

Answer 1

A) 2.2 J

Explanation:

The problem can be solved by using conservation of energy. In fact, the initial elastic potential energy stored in the rubber band is entirely converted into gravitational potential energy of the pebble. We can write therefore the equation:

$U=mgh$

where

U is the potential energy initially stored in the rubber band

m = 10 g = 0.01 kg is the mass of the pebble

g = 9.8 m/s^2 is the acceleration due to gravity

h = 22.0 m is the maximum height reached by the pebble

Substituting the numbers into the formula, we find:

$U=(0.01 kg)(9.8 m/s^2)(22.0 m)=2.2 J$

B) 9.0 m

Explanation:

Now we know the potential energy stored in the rubber band initially, U=2.2 J. We also know that this time, the mass of the pebble is m = 25.0 g = 0.025 kg. So we can use again the same equation:

$U=mgh$

and re-arranging it to find h, the maximum height reached by this new pebble. We find:

$h=\frac{U}{mg}=\frac{2.2 J}{(0.025 kg)(9.8 m/s^2)}=9.0 m$