The spring, initially at rest, was compressed by the blue box by 0.15 m. The spring constant of the spring is 300 N/m. The mass of the box was 0.2 kg. What is the max height of the box when it comes to rest on the ramp

1.72m

Explanation:

Step 1:

Data obtained from the question.

Displacement (x) = 0.15 m

Spring constant (K) = 300 N/m

Mass (m) = 0.2 kg

Height (h) =?

Step 2:

Determination of the energy in the spring.

The energy is a spring can be obtained by the following equation:

E = 1/2 kx^2

E = 1/2 x 300 x 0.15^2

E = 150 x 0.0225

E = 3.375J

Step 3:

Determination of the maximum height.

At maximum height, the energy stored is the spring is equal to the potential energy i.e

Energy stored in the string = potential energy

E = P.E

Recall:

Potential energy = mgh

Where:

m is the mass = 0.2kg

g is the acceleration due to gravity = 9.8m/s2

h is the height. =?

Potential energy (P.E) = 3.375J

PE = mgh

3.375 = 0.2 x 9.8 x h

Divide both side by 0.2 x 9.8

h = 3.375/ (0.2 x 9.8)

h = 1.72m

Therefore, the maximum height of the box is 1.72m