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:
[tex]U=mgh[/tex]
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:
[tex]U=(0.01 kg)(9.8 m/s^2)(22.0 m)=2.2 J[/tex]
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:
[tex]U=mgh[/tex]
and re-arranging it to find h, the maximum height reached by this new pebble. We find:
[tex]h=\frac{U}{mg}=\frac{2.2 J}{(0.025 kg)(9.8 m/s^2)}=9.0 m[/tex]
