Question

4. A 20 kg cart on wheels has been pushed up against a wall with a spring (k = 244 N/m) between the wall and the cart. If the spring is compressed a distance of 0.1m and a force of 20 N is continued to be applied toward the wall, what will the acceleration of the object be?

Answer 1

from hooke's law,

Force exerted by spring on cart will be,

Fs = -k*x

given, k = spring constant = 244 N/m

x = compression in spring = -0.1 m

So, Fs = -244*(-0.1) = 24.4 N (pushing out from wall)

now, from newton's law,

Fnet = m*a

Fs - F = m*a

given, F = 20 N (pushing towards the wall)

m = mass of cart = 20 kg

a = acceleration of cart = ??

So, a = (Fs - F)/m

a = (24.4 - 20)/20

a = 0.22 m/s^2 (cart will accelerate away from the wall)

Let me know if you have any query.