Answer:
1. 10 N/m
2. 40 N
Explanation:
1. Determination of the spring constant.
We'll begin by converting 20 cm to m. This can be obtained as follow:
100 cm = 1 m
Therefore,
20 cm = 20 cm × 1 m / 100 cm
20 cm = 0.2 m
Finally, we shall determine the spring constant. This can be obtained as follow:
Extention (e) = 0.2 m
Force (F) = 2 N
Spring constant (K) =?
F = Ke
2 = K × 0.2
Divide both side by 0.2
K = 2/0.2
K = 10 N/m
Thus, the spring constant is 10 N/m
2. Determination of the force.
Initial extention (e₁) = 5 cm
Initial force (F₁) = 20 N
Final extension (e₂) = 10 cm
Final force (F₂) =?
F = Ke
Divide both side by e
K = F /e
Therefore,
F₁ /e₁ = F₂/e₂
20/5 = F₂/10
4 = F₂/10
Cross multiply
F₂ = 4 × 10
F₂ = 40 N
Thus, a force of 40 N is needed to stretch the spring by 10 cm.
