Acceleration of spring power cart

[ms. confused]

OK this problem is probably really easy, but I totally have no idea how to handle it. Please help! Here goes:

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

 

[PrudensOptimus]

You know mass, you know k, you know dx, you know F.

F = -kx = 1/2kx^2 = ma

a = -kx/m

 

[ms. confused]

One question: how come kx is negative?

 

[PrudensOptimus]

it is usually opposite to the direction of inertia

 

[ms. confused]

OK thanks for the help!

 

[Doc Al]

OK this problem is probably really easy, but I totally have no idea how to handle it. Please help! Here goes:

To find the acceleration of an object, use Newton's 2nd law. First find the net force on the cart. There are two (horizontal) forces on the cart: the spring, pushing out from the wall; and the applied force of 20 N pushing towards the wall. Find the net force and then calculate the acceleration a = F_{net}/m.

The force law for springs: F = -kx, tells you the force that the spring exerts for a given stretch or compression x (from equilibrium). The negative sign means that the force is in the opposite direction of the compression. For example: If the spring is pushed in, the force it exerts pushes out.