It takes 1900 J of work to stretch a spring from its natural length of 1 m to a length of 6 m . Find the force constant of the spring.
The spring’s force constant is .
(Type an integer or a simplified fraction.)

Ask by Montgomery Estrada. in the United States

Mar 13,2025

Question

It takes 1900 J of work to stretch a spring from its natural length of 1 m to a length of 6 m . Find the force constant of the spring.
The spring’s force constant is .
(Type an integer or a simplified fraction.)

Ask by Montgomery Estrada. in the United States

Mar 13,2025

UpStudy AI · Accepted Answer

The work done in stretching a spring by a displacement $$ x $$ from its natural length is given by

$$
W = \frac{1}{2} k x^2.
$$

1. The spring is stretched from 1 m to 6 m, so the displacement is

$$
x = 6 - 1 = 5 \text{ m}.
$$

2. Substitute the given work $$ W = 1900 $$ J and $$ x = 5 $$ m into the work formula:

$$
1900 = \frac{1}{2} k (5)^2.
$$

3. Simplify the equation:

$$
1900 = \frac{1}{2} k \cdot 25,
$$
$$
1900 = \frac{25}{2} k.
$$

4. Solve for $$ k $$ by multiplying both sides by $$\frac{2}{25}$$:

$$
k = \frac{1900 \cdot 2}{25} = \frac{3800}{25}.
$$

5. Simplify the fraction:

$$
k = 152.
$$

Thus, the spring's force constant is $$152 \text{ N/m}$$.
The spring's force constant is $$152 \text{ N/m}$$.