Question

Captain Science, unmasker of fuzzy thinkers and proponent of cosmic truth, drops a 35 kg bowling ball on a stiff spring from a height of 1.0 m and finds that the spring compresses 2 cm.  If he drops the bowling ball from a height of 4.0 m, how much will the spring compress?

8 cm

1 cm

16 cm

2 cm

4 cm

Answer 1

SOLUTION:

From Law of conservation of energy, the initial gravitational potential energy of the ball is converted into spring potential energy.

That is:

Where we have:

Mass of the ball, m = 35 kg

Initial height of the ball, h = 1 m

Acceleration due to gravity, g = 9.8 m/s²

Compression of the spring, x = 2 cm = 0.02 m

Therefore, Spring constant (K) is given by:

Now, The ball is dropped from a height of, h = 4 m

Therefore, Compression of the spring is given by (use Law of conservation of energy as did earlier):

So the correct answer is option (5) 4 cm.