For the Pre - Lab Derive the Predicted Period of the Motion: Derive an equation
ID: 581866 • Letter: F
Question
For the Pre
-
Lab Derive the Predicted Period of the Motion:
Derive an equation to predict the period of the ball, based on the length of the string, the mass of
the ball, and the mass of the hanger.
You will use this to compare with the measured period of
the ball.
Your expression should be give the
period of motion,
T
, based on only the variables
m
1
,
m
2
, L, g
and
2
?
:
Here are some hints on how to derive the equation:
1.
Find an expression for the velocity of the ball based on the radius of the circle and
the
ball’s period.
2.
Write an expression for the centripetal force on the ball in terms of its mass, velocity, and
radius.
3.
Write another expression for the centripetal force on the ball, this time in terms of the
weight of the hanging mass. Remember that the
hanging mass provides the tension on the
string.
Derive your equation for T as function of
m
1
, m
2
, L, g
and
2
?
T =
Explanation / Answer
The entripetal force is given by
F = mv^2 /L
As the mass 2 is stationary
M2g -Ft = 0
Hence , Ft = M2g
We can see that Ft is the only force in the horizontal direction
'Hence it will provide the centripetl force need to keep rotating in a circular path
Ft = Mv^2 / L
M2g = M1 V^2/L
V= sqrt(M2*g*L/M1)
Period of rotaion = 2*pi*L/ V = 2*pi* L/sqrt(M2*g*L/M1)
T = 2*pi* sqrt (L*M1/M2*g)