a jack in the box is built around with a spring constant of 70N/m. How much hard does the spring push when you compress it from 40 cm long down to 15 cm long?

Answer: 17.5N

Explanation:

Given that,

spring constant (k) = 70N/m

Original length (lo) = 40 cm

New length (ln) = 15 cm

extension of spring (e) = new length - original length

i. e e = ln - lo

e = 15 cm - 40 cm

e = - 25cm (the negative sign is negligible, just the same magnitude matters)

So, convert 25cm to metres

If 100cm = 1m

25cm = 25/100 = 0.25m

(Note that how hard the spring push refers to the Force, hence, find force.)

Now, apply the Hooke law (F = ke)

Force = spring constant x extension

F = 70N/m x 0.25m

F = 17.5N

Thus, the spring push with a force of 17.5N when compressed.