Question

A spring has a k value of 100 N/m. A 100g mass is dropped from a height of 20 cm onto an uncompressed spring. How much will the spring compress?

A) 0.0098 m
B) 0.098 m
C) 0.98 m
D) 0.098 cm

Answer 1

The spring will compress by 0.098 m when a 100g mass is dropped from a height of 20cm, with the correct answer being option B) 0.098 m.

Step-by-step explanation:

The question asks how much a spring will compress when a 100g mass is dropped from a height of 20cm onto it. To solve this, we need to equate the gravitational potential energy at the height of 20cm to the elastic potential energy when the spring is compressed.

Gravitational potential energy (PEgrav) is given by mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s2), and h is the height. The elastic potential energy (PEelastic) stored in a compressed spring is ½kx2, where k is the spring constant and x is the compression.

Setting these two energies equal gives us mgh = ½kx2. Substituting the given values (m = 0.1 kg, g = 9.8 m/s2, h = 0.2 m, k = 100 N/m), we can solve for x, which is the compression of the spring:

0.1 kg * 9.8 m/s2 * 0.2 m = ½ * 100 N/m * x2

Solving for x gives x = √ (0.1 kg * 9.8 m/s2 * 0.2 m) / (0.5 * 100 N/m) = 0.098 m.

Therefore, the correct answer is B) 0.098 m, which is the amount the spring will compress when the mass is dropped onto it.