Question

Use Hooke's Law, which states that the distance a spring stretches (or compresses) from its natural, or m, length varies directly as the applied force on the spring A force of 265 newtons stretches a spring 0.15 meter (a) What force stretches the spring 0.2 meter? (Round your answer to two decimal places.)_____N(b) How far does a force of 190 newtons stretch the spring? (Round your answer to tiwo decimal places.)_____ m

Answer 1

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.