Question

It requires a force of 100 N to stretch a spring of negligible mass by a distance of 0.1 m. If the spring instead stretches a distance of 0.25 m, how much force was applied to it?
answer choices
1. 200 N
2. 300 N
3. 250 N
4. 100 N
5. 175 N
6. 325 N
7. 150 N
8. 225 N
9. 275 N

Answer 1

by the formula of spring force we know that

$F = kx$

here we know that

$F = 100 N$

$x = 0.1 m$

now we will have

$100 = k \times 0.1$

$k = 1000 N/m$

now by similar way if the stretch in spring is 0.25 m

force is given by

$F = kx$

$F = 1000 \times 0.25$

$F = 250 N$

so it will require F = 250 N force

Answer 2

Answer: The force applied on the spring is 250 N

Explanation:

To calculate the spring constant, we use the equation:

$F=kx$       ......(1)

where,

F = force exerted on the spring = 100 N

k = spring constant = ?

x = length of the spring = 0.1 m

Putting values in equation 1, we get:

$100N=k\times 0.1m\\\\k=\frac{100N}{0.1m}=1000N/m$

Now, calculating the force exerted on the spring, we use equation 1:

We are given:

$k=1000N/m\\x=0.25m$

Putting values in above equation, we get:

$F=1000N/m\times 0.25m\\\\F=250N$

Hence, the force applied on the spring is 250 N