A 0.20 kg mass is whirled round in a vertical circle on the end of a light string of length 0.90 m. At the top point of the circle the speed of the mass is 8.2 m/s. What is the tension in the string at this point?
A diagram would be very beneficial for this problem. We can draw a free body force diagram of the mass. At the top of the circle the two forces acting on it are its weight and tension from the string. Both are acting vertically downwards.
This problem is an example of circular motion, so the equation to use will be:
F = (mv2) / r
where F is the centripetal force (acting towards the centre of the circle), m is mass, v is velocity and r is radius
Therefore we can calculate what the centripetal force will be:
F = (0.28.22) / 0.9
F = 14.94222...N
As we said earlier, there are two forces acting on the mass towards the centre of the circle: its weight and the tension. We can calculate the weight from the body's mass using W = mg
W = 0.29.81
Then F = weight + tension
tension = F - weight
tension = 14.942 - 0.2*9.81
tension = 13.0N
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