# Hooke's Law and Centripetal Motion

• CAG0625
In summary: You can use the first one to check your answer before trying the second one. If you use the second one you'll have to make sure you get the right answer. There are two answers.
CAG0625

## Homework Statement

A 0.20 kg mass hangs vertically from a spring and an elongation below the support point of the spring of 9.50 cm is recorded. With 1.00 kg hanging on the spring, a second elongation of 12.00 cm is recorded. Calculate the spring constant k in Newtons per meter. (Note the equilibrium position is not 0.) Then at the elongation of 9.50 cm, a frequency of 300 rev/min is recorded. Then at elongation of 12.00 cm, frequency of 400 rev/min is recorded. Calculate the effective mass of the system in kilograms. (convert to SI. w=f*2pi/60 switches from rev/min to rad/sec.)

W=mg
W=-kd

## The Attempt at a Solution

W=(0.20kg)(980.35 cm/s^2) = 196.07N
W=(1.00kg)(980.35cm/s^2)=980.35N
196.07N=-k(0.095m)=-2063.89N/m
980.35N=-k(0.12m) = -8169N/m
Is that all correct and I do not know where to go from here.

CAG0625 said:
W=(0.20kg)(980.35 cm/s^2) = 196.07N
kg cm/s^2 is not going to give Newtons. Better to convert the cm to m, not the other way around.
CAG0625 said:
196.07N=-k(0.095m)=-2063.89N/m
You are misreading the question. I'm not sure if it is misleading because it refers to 'elongation' when it means length, or maybe you are supposed to allow for the spring's own mass:
CAG0625 said:
(Note the equilibrium position is not 0.)

Your first two lines in 3 give you the force F for two different extensions x below the unweighted length.
You don't know x, but if you assume the unweighted length of the hanging spring is h then you have two values of x+h.
Using Hooke's Law you can get two independent equations in h and k. Then solve for h and k.

## What is Hooke's Law?

Hooke's Law states that the force required to stretch or compress a spring is directly proportional to the distance the spring is stretched or compressed.

## What is the equation for Hooke's Law?

The equation for Hooke's Law is F = -kx, where F is the force applied, k is the spring constant, and x is the distance the spring is stretched or compressed.

## What is centripetal force?

Centripetal force is the inward force that keeps an object moving in a circular path. It is always directed towards the center of the circle.

## What is the relationship between centripetal force and centripetal acceleration?

Centripetal force and centripetal acceleration are directly proportional to each other. This means that as the centripetal force increases, the centripetal acceleration also increases.

## How do you calculate the centripetal force?

The centripetal force can be calculated using the equation F = mv^2/r, where m is the mass of the object, v is the velocity, and r is the radius of the circular path.

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