2. Calculate the minimum speed of the ball at A if the string is to stay taut.

1. Name the forces acting on the ball.

A ball is tied to some string and swung at a steady speed which just keeps the string taut at the top.

The mass of the ball is 0.10 kg

The string length is 1.25 m

A

B

C

Vertical circular motion

3. Draw the free body force diagram at A, B and C.A

A ball is tied to some string and swung at a steady speed which just keeps the string taut at the top.

The mass of the ball is 0.10 kg

The string length is 1.25 m

A

B

CAt point A the minimum speed is when the centripetal force is equal to gravity only.

2. Calculate the minimum speed of the ball at A if the string is to stay taut.

Vertical circular motion

E

A ball is tied to some string and swung at a steady speed which just keeps the string taut at the top.

The mass of the ball is 0.10 kg

The string length is 1.25 m

A

B

C

A

B C

Fc = Fg = 0.98 N

Fg = 0.98 N

Fc = 0.98 N

Fg = 0.98 N

Fc = 2Fg = 2.0 N

3 Draw the free body force diagram at A, B and C.

Vertical circular motion

A

E

M

clothoid

The picture shows a clothoid similar to the one at Rainbows End in Auckland.

The radius changes around the loop.

At the top the radius is 12 m

Energy conservation

The person will feel weightless when the speed is such that the reaction force is zero.

Fg = Fc

Free body diagram

1. Calculate the speed at the top of the clothoid that makes the person (P) with her arms raised in the picture feel weightless.

2. Draw the free body diagram of the person when she is at point P as shown in the picture.

P

3. Draw the free body diagram of the person when she is at point P as shown in the picture.

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M

E