A pendulum consists of a 4.5 N ball attached to a 1.75m string. The ball is rele

Question

A pendulum consists of a 4.5 N ball attached to a 1.75m string. The ball is released from rest when the string makes an angle of 62 degrees with the vertical. Ignoring air resistance what is the speed of the ball in m/s at the lowest point of it's motion? If the string length is doubled by what factor will the speed at the lowest point change? Returning to the 1.75m string, with air resistance affecting the motion the string reaches an angle of only 56.5 degrees at the end of the first swing. How many joules of mechanical energy has the pendulum lost during the swing?

Please show all work thanks in advance.

Explanation / Answer

weight w = 4.5 N, L = 1.75 m, = 62o, find the speed v of the ball at the lowest point

mass m = w/g

wL(1 - cos) = mv2/2

v = [2gL(1 - cos)] = 4.27 m/s

If the string length is doubled,

new speed = [2g(2L)(1 - cos)] = 2*v, will increase by the factor 2

' = 56.5o, mechanical energy lost

= [wL(1 - cos)] - [wL(1 - cos')]

= wL(cos' - cos) = 0.649 J

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