Question

A force of 16 N is required to stretch a spring a distance of 40 cm from its rest position. What force (in Newtons) is required to stretch the same spring …
a. … twice the distance?
b. … three times the distance?
c. … one-half the distance?

Answer 1

Answer:

  a. 32 N

  b. 48 N

  c. 8 N

Explanation:

Given 16 N is required to stretch a spring 40 cm from rest, you want the forces required for ...

  a. twice the distance
  b. three times the distance
  c. one-half the distance

Proportional

The force required to stretch the (ideal) spring is proportional to the distance. The constant of proportionality is called the "spring constant." It is the ratio of force to distance:

  k = (16 N)/(0.40 m) = 40 N/m

The force can be found using the formula ...

  F = kd

Or, we can simply take advantage of the proportionality.

a. Twice the distance

This will require twice the force: 2·16 N = 32 N.

b. Three times the distance

This will require three times the force: 3·16 N = 48 N.

c. One-half the distance

This will require one-half the force: 1/2·16 N = 8 N.