A simple pendulum has a length of 0.75 m and a bob of mass 0.6 kg. When the string is at 30º to the vertical, the bob has a speed of 2 m/s.
(a) What is the maximum speed of the bob?
(b) What is the maximum angle to the vertical?
A clearly written formula (with labels) to solve these questions would be enough, no need to fully solve the answers, i can calculate it using your help!
(a) What is the maximum speed of the bob?
(b) What is the maximum angle to the vertical?
A clearly written formula (with labels) to solve these questions would be enough, no need to fully solve the answers, i can calculate it using your help!
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PE at start + KE at start = KE at bottom of swing
PE at start = m g h where h is the height above the bottom of the swing, draw a picture to show that this distance is 0.75(1-cos30) meters
then you have
m g h + 1/2 m(2)^2 = 1/2 m V^2 where V is the max speed at bottom of the swing
cancel common factors and solve for V
once you have this value of V, use conservation of energy again to find the height H, the bob rises to on the other side:
1/2 m V^2 = m g H => H = V^2/2g
and this value of H = L(1-cos(Theta)) where L = 0.75m and theta is the max angle when the bob is at its greatest height
PE at start = m g h where h is the height above the bottom of the swing, draw a picture to show that this distance is 0.75(1-cos30) meters
then you have
m g h + 1/2 m(2)^2 = 1/2 m V^2 where V is the max speed at bottom of the swing
cancel common factors and solve for V
once you have this value of V, use conservation of energy again to find the height H, the bob rises to on the other side:
1/2 m V^2 = m g H => H = V^2/2g
and this value of H = L(1-cos(Theta)) where L = 0.75m and theta is the max angle when the bob is at its greatest height