Answer:
Explanation:
Hooke's Law states that the distance a spring stretches (or compresses) from its natural length varies directly as the applied force on the spring. Mathematically, this can be expressed as:
F = kx
Where F is the force applied, x is the distance the spring stretches (or compresses), and k is the spring constant.
To solve the given problem, we need to find the value of k first, using the given information:
265 N = k * 0.15 m
k = 265 N / 0.15 m
k = 1766.67 N/m
(a) To find the force that stretches the spring 0.2 meter, we can use Hooke's Law again:
F = kx
F = 1766.67 N/m * 0.2 m
F = 353.33 N
Therefore, a force of 353.33 N stretches the spring 0.2 meter.
(b) To find how far a force of 190 N stretches the spring, we can rearrange Hooke's Law:
x = F/k
x = 190 N / 1766.67 N/m
x = 0.11 m
Therefore, a force of 190 N stretches the spring 0.11 meter.