Work of 5 Joules is done in stretching a spring from its natural length to 19 cm beyond its natural length. What is the force (in Newtons) that holds the spring stretched at the same distance (19 cm)? Don't forget to enter the correct units.

According to the question,

Work done in stretching the spring (x) be,

=

Given:

then,

→

By substituting the values, we get

→

hence,

The required force will be:

→

Thus the above answer is right.  

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Explanation:

Given that,

5J work is done by stretching a spring

e = 19cm = 0.19m

Assuming the spring is ideal, then we can apply Hooke's law

F = kx

To calculate k, we can apply the Workdone by a spring formula

W=∫F.dx

Since F=kx

W = ∫kx dx from x = 0 to x = 0.19

W = ½kx² from x = 0 to x = 0.19

W = ½k (0.19²-0²)

5 = ½k(0.0361-0)

5×2 = 0.0361k

Then, k = 10/0.0361

k = 277.008 N/m

The spring constant is 277.008N/m

Then, applying Hooke's law to find the applied force

F = kx

F = 277.008 × 0.19

F = 52.63 N

The applied force is 52.63N