A young boy of mass m = 25 kg sits on a coiled spring that has been compressed to a length 0.4 m shorter than its uncompressed length and then held at this length. Suddenly the spring is released, and the boy flies vertically into the air. He reaches a maximum distance 0.5 m above his initial position. The spring is ideal and massless and we ignore the air friction.

What is the spring constant k of the spring?

What is the speed of the boy when he is 0.4 meters above his starting position?

Question

A young boy of mass m = 25 kg sits on a coiled spring that has been compressed to a length 0.4 m shorter than its uncompressed length and then held at this length. Suddenly the spring is released, and the boy flies vertically into the air. He reaches a maximum distance 0.5 m above his initial position. The spring is ideal and massless and we ignore the air friction.

What is the spring constant k of the spring?

What is the speed of the boy when he is 0.4 meters above his starting position?

mani_jha · Answer

When the spring is compressed, it increases its elastsic potential energy, which gets stored inside it. When it is released, all the spring potential energy gets converted to kinetic energy of the boy. Again, this kinetic energy gets converted to the potential energy of the boy as he reaches the height.
$$kx ^{2}/2=mgh$$
Now, can you do this?