A spring has a spring constant of 259N/m. Find the magnitude of the force needed
(a) to stretch the spring by 3.54 10-2m from its unstrained length and
N
(b) to compress the spring by the same amount.
N
Force=k x
To find the magnitude of the force needed to stretch or compress a spring, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position.
Hooke's Law can be expressed as:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant (259 N/m in this case), and
x is the displacement from the spring's equilibrium position.
Now, let's calculate the force needed to stretch the spring by a displacement of 3.54 x 10^(-2) m:
(a) To stretch the spring:
F = k * x
F = 259 N/m * 3.54 x 10^(-2) m
F ≈ 9.17 N
Therefore, the force needed to stretch the spring by 3.54 x 10^(-2) m is approximately 9.17 N.
(b) To compress the spring:
The magnitude of the force needed to compress the spring would be the same as the force needed to stretch it, as per Hooke's Law. Therefore, the force required to compress the spring by the same displacement, 3.54 x 10^(-2) m, would also be approximately 9.17 N.