Question

A spring whose spring constant is 850 N/m is compressed 0.40 m. What is the maximum speed it can give to a 0.5 kg box? Assume there is no friction in the system.

Answer 1

The maximum speed, the box can attain is 16.5 m/s.

Explanation:

According to law of conservation of energy, energy can be transferred from one form to another. So here the spring force is converted to kinetic energy experienced by the box due to the spring.

As we know, that spring force is directly proportional to the square of the displacement and spring constant, the conservation of energy will be give

$\frac{kx^{2} }{2} =\frac{mv^{2} }{2}$

So, we know that spring constant k = 850 N/m, the displacement experienced by the spring due to compression is given as x = 0.4 m. The mass of the box is given as m = 0.5 kg and the velocity we have to find.

$v^{2} = \frac{kx^{2} }{m}$

$v^{2} = \frac{850 \times 0.4 \times 0.4}{0.5} =272 \\ \\v=\sqrt{272} =16.5\ m/s$

Thus, the maximum speed, the box can attain is 16.5 m/s.