Question

A common technique used to measure the

force constant k of a spring is the following:
Hang the spring vertically, then allow a
mass m to stretch it a distance d from the
equilibrium position under the action of the
“load” m g.
61 m
63 N
Find the spring constant k if the spring
is stretched a distance 61 m by a suspended
weight of 63 N. The acceleration of gravity is
9.8 m/s
2
.
Answer in units of N/m.

Answer 1

Answer: 1.02 N/m

Step-by-step explanation:

To find the spring constant k, we can use Hooke's Law, which states that the force exerted by a spring (F) is proportional to the displacement from its equilibrium position (x). The equation for Hooke's Law is:

F = kx

In this case, the force exerted by the spring (F) is equal to the weight of the mass (mg). The problem provides the weight (63 N) and the displacement (61 m). We can rearrange the equation to solve for k:

k = F/x

Now, we can plug in the given values:

k = (63 N) / (61 m)

k ≈ 1.032 N/m

Rounded to two decimal places, the spring constant k is approximately 1.02 N/m.