Question

Suppose a spring compresses by 5cm if you put a 250 gram weight on top of it. How
much potential energy is contained in the compressed spring?

a) 49 J

b) 2.45 J

c) 122 J

d) 0.061 J

e) I cannot tell from the information given.

Answer 1

Answer:

Option D. 0.061 J

Explanation:

We'll begin by converting 5 cm to m. This can be obtained as follow:

100 cm = 1 m

Therefore,

5 cm = 5 cm × 1 m / 100 cm

5 cm = 0.05 m

Next, we shall convert 250 g to Kg. This can be obtained as follow:

1000 g = 1 Kg

Therefore,

250 g = 250 × 1 Kg / 1000

250 g = 0.25 Kg

Next, we shall determine the weight of the object. This can be obtained as follow:

Mass (m) = 0.25 Kg

Acceleration due to gravity (g) = 9.8 m/s²

Weight (W) =?

W = m × g

W = 0.25 × 9.8

W = 2.45 N

Next, we shall determine the spring constant. This can be obtained as follow:

Compression (e) = 0.05 m

Weight = Force (F) = 2.45 N

Spring constant (K) =?

F = Ke

2.45 = K × 0.05

Divide both side by 0.05

K = 2.45 / 0.05

K = 49 N/m

Finally, we shall determine the potential energy contained in the compressed spring. This can be obtained as follow:

Compression (e) = 0.05 m

Spring constant (K) = 49 N/m

Energy (E) =?

E = ½Ke²

E = ½ × 49 × (0.05)²

E = 24.5 × 0.0025

E = 0.061 J

Therefore, the potential energy contained in the compressed spring is 0.061 J