# Centripetal

CENTRIPETAL FORCE ON A PENDULUM
OBJECTIVE
To measure centripetal force exerted on a pendulum using the force sensor bob and in so doing compare this value determined by force calculations based on the height of the pendulum.
THEORY
Newton’s laws of motion are the basis for this experiment. Newton’s first law of motion states that a body in motion will remain in motion unless acted upon by an external force. Newton’s second law of motion states that the rate of momentum of a body is dependent on the product of its mass and acceleration. Where rate of change of momentum is given by
ma =mdvdt = Fnet
A pendulum bob follows a circular path and is therefore acted upon by centripetal force. In this experiment the tension in the string causes the bob to follow a circular path. From Newton’s second law of motion above it is related to the experiment as shown
F = T- mg =ma = Fc
Where T is the tension in the string
m is the mass of the pendulum
g is acceleration due to gravity
Fc is the centripetal force
The force measured by the force sensor when the pendulum passes through the lowest point of the swing is equal to centripetal force. This is because the force sensor is zeroed when the pendulum is at rest in its equilibrium position, where T= mg.
Centripetal force can also be found from the relationship below using the speed, v, when the bob passes through the lowest point
Fc   = mv2r
Where
r is the radius of the circular path (for the experiment it is equal to the length of the         pendulum)
It can also be found from the relationship of the height of the bob at the top of the swing
Fc = 2mghr
Where h is the maximum height of the bob
g is the acceleration due to gravity

APPARATUS
* Passport force sensor