The maximum speed of the pendulum bob in a grandfather clock is 0.40m/s . If the

Question

The maximum speed of the pendulum bob in a grandfather clock is 0.40m/s .

If the pendulum makes a maximum angle of 6.1? with the vertical, what is the length of the pendulum?

Express your answer using two significant figures. L = ? m

Example of how to do the question. These arent my values !!!

Maximum kinetic energy = 0.5*m*v^2
= 0.5*m*0.16
= 0.08m J

Maximum gravitational potential energy = m * g * h
= 9.81*h*m
Let lowest point the pendulum can reach = 0m.

Therefore as KE=GPE
0.08m=9.81hm
0.008 meters = h

Length = L

When angle is 6.0 degrees, vertical length = L*cos(6.6)
= 0.9934L

Change in vertical length = L - 0.9945L
= 0.0066L
Therefore change in height = 0.008 m = 0.0066L
L=1.21m

Explanation / Answer

Maximum kinetic energy = 0.5*M*v^2

= 0.5*m*0.16

= 0.08M J

Maximum gravitational potential energy = M * g * h

= 9.81*h*M

Let lowest point the pendulum can reach = 0.

Therefore as KE = GPE

0.08*M = 9.81*h*M

0.008 meters = h

Length = L

When angle is 6.1 degrees,

vertical length = L*cos(6.1) = 0.9943 * L

Change in vertical length = L - 0.9943*L

h = 0.0057L

Therefore change in height
h = 0.008 = 0.0057*L

L = 1.4035 m

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