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.
Find the spring constant k if the spring
is stretched a distance 16 m by a suspended
weight of 96 N. The acceleration of gravity is
9.8 m/s^2
Answer in units of N/m.

Answer 1

Answer:

$K=6\ N/m$

Explanation:

Force Constant of a Spring

The force F applied to a spring produces a stretching distance x. These variables are linearly related as expressed by Hook's law:

$F=K.x$

If we could measure the distance a spring stretches when applying a known force, we'd be able to find the value of K. The experiment stated in the question places some mass of a known weight of 96 N that produced a stretching distance of 16 m. Knowing both variables, we can solve the above equation for K

$\displaystyle K= \frac{F}{x}=\frac{96\ N}{16\ m}=6\ N/m$

$\boxed{K=6\ N/m}$

Answer 2

The spring constant K should be 6 N/m.

Hook law:

When the force F should be applied at the spring so it generated the stretching distance

i.e.

F = k.x

F means the force

K means the constant

x means the stretching distance

Here the weight should be 96 N, the stretching distance is 16 km

Now the spring constant should be

K = f/x

= 96/16

= 6 N/m

Hence, The spring constant K should be 6 N/m.

Learn more about spring here: https://brainly.com/question/20288380