Circular motion in the vertical plane
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Circular motion in the vertical plane

[From: ] [author: ] [Date: 12-02-14] [Hit: ]
v²= 2gh = 2 x 9.8 x 2= 39.2m²/s²(we need v²,At the lowest position, the centripetal force = mv²/ r = 4 x 39.2 / 2 = 78.......
a wire of length 2m supports a bowling bowl of mass 4kg in a vertical position at point X (the bottom of the circle). The ball is moved to point Z (90 degrees anti clockwise from X) and reeleased. calculate the tension in the wire as the ball moves through point X.

thanks for your help! :)

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Kinetic energy gained at lowest position = gravitational potential energy lost
½mv² = mgh
v² = 2gh = 2 x 9.8 x 2 = 39.2m²/s² (we need v², not v in the next step)

At the lowest position, the centripetal force = mv²/ r = 4 x 39.2 / 2 = 78.4N

Remember, in circular motion, the centripetal force is just another name for the total force towards the centre.
And for circular motion take positive as towards the centre.

Resultant force on ball = tension - weight = T - mg. This is the centripetal force.
T - (4x9.8) = 78.4
T = 117.6N
= 120N to 2 significant figures.

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You have selected a best answer and have no email, this is the only way I can add information; I'm not sure if you get notified of it.
You have misunderstood centripetal force. It is not some sort of separate force. It is the resultant of weight (W) and tension (T). T and W are the ONLY forces.

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