Question

Use Hooke's Law and Newton's 2nd Law to derive a formula for the acceleration of an object of mass m on a frictionless surface which is attached to a spring with a constant k which is stretched a distance L. The acceleration should be in terms of m, k, and L.

Answer 1

a = kL/m

Step-by-step explanation:

Here we can use Hooke's Law to find out the force applied on the system. Hooke's Law states that when a spring is stretched by some force, the force applied is directly proportional to the displacement of spring. The formula is given as:

F = kL

Now, the Newton's Second Law of motion states that whenever an unbalanced force is applied to a body it produces an acceleration in the body, in its own direction. So, the force is given by the formula:

F = ma

Comparing both the forces, we get:

kL = ma

a = kL/m