Physics question please help!!

Question

If a cart with a mass of 0.253kg has a spring attached to the end of it and gets pushed against a wall making the spring shorten by 1cm and exerts a force in which makes the cart go 0.5m in 1.028 seconds what is the spring constant?

Answer 1

I suggest working this as an energy conservation problem, with the potential energy of the compressed spring converted to kinetic energy of the cart.  I am assuming the travel distance and time of the cart were measured after the cart/spring lost contact with the wall.

 

m = mass of car = 0.253 kg

x = compression of spring = 0.01 m

d = distance car travels = 0.5 m

t = time of travel = 1.028 s 

 

v = final speed of car = d/t = 0.5/1.028 m/s ≅ 0.4864 m/s

 

kx²/2 = mv²/2 ⇒

 

k = m(v/x)² = (0.253 kg)[(0.4864 m/s) / (0.01 m)]² ≅ 598.6 N/m