A pendulum consists of a 3.22 kg mass on the end of a 0.769 m string. The mass i

Question

A pendulum consists of a 3.22 kg mass on the end of a 0.769 m string. The mass is pulled aside so the string makes an initial angle with the vertical of 12.5o. The mass is then released with initial speed of 1.1 m/s upward and perpendicular to the rope. Assume:
- There is no friction anywhere.
- The rope remains taut at all times.

a) When the mass reaches the bottom of its arc, find:
- the speed of the mass: 1 m/s
- the magnitude of the tension in the string: 2 N

b) Find the maximum angle between the string and the vertical: 3o

Explanation / Answer

a)Conserving energy between initial position and bottom of its arc,

0.5mu2+mgl(1-Cos)=0.5mv2

Solving for v,

v2=u2+2gl(1-Cos)

v=1.252m/s

b)T=mv2/l+mg=38.1N

c)Let the maximum angle be and conserving energy between bottom and topmost position.

0.5mv2=mgl(1-Cos)

=26.4 degrees

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