High speed circular motion!
A ball of mass 1kg is hung with a massless rope of length 1m and is hit with a bat such that it attains a velocity of 100m/s in no time. Find the tension in the rope when the ball is at an angle of 60° with the topmost position attained by the ball(as shown in the diagram).
Details and Assumptions
• Take value of g as 10m/s² .
• Assume that as soon as the ball is hit, it attains a velocity of 100m/s (or in no time).
• Enter answer in Newton .
The answer is 9965.
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1 solution
Kinetic energy at bottommost point= 2 1 ×1×100²=5000J
At 60°
P.E.=1×10×(1+1sin30°)=15J
P.E.+K.E.=5000 (Law of conservation of energy)
15+1/2×1×v²=5000
v²=9970m²/s²
Centripetal force applied by rope - Weight applied by ball on rope at 60°= Tension in string
1 1 × 9 9 7 0 -10cos60°=T
9965N=T