Consider a ball on a fixed-length string being whirled in a vertical circular pa

Question

Consider a ball on a fixed-length string being whirled in a vertical circular path as shown in the diagram below.

(a) When the ball is at the top of the circle, what is the direction of the tension force in the string? Use the direction rosette to answer this question.
---Select--- 1 2 3 4 5 6 7 8 9

(b) When the ball is at the top of the circle, what is the direction of the gravitational force on the ball? Use the direction rosette to answer this question.
---Select--- 1 2 3 4 5 6 7 8 9

(c) When the ball is at the top of the circle, what is the direction of the centripetal force on the ball? Use the direction rosette to answer this question.
---Select--- 1 2 3 4 5 6 7 8 9

(d) When the ball is at the top of the circle, what is the expression for the centripetal force on the ball? Take the upward direction as positive and downward direction as negative when considering the sign of the forces. (Use the following as necessary: m, g, and T.)
Fc =   

(e) If the speed of the ball at the top of the circle is v what is the expression for the centripetal force on the ball in terms of its speed v and radius L? Take the upward direction as positive and downward direction as negative when considering the sign of the forces. (Use the following as necessary: m, v, and L.)
Fc =   

(f) Use your answers in parts (d) and (e) to get an expression for the tension in the string in terms of the speed of the ball and the length of the string. (Use the following as necessary: m, v, L, and g.)
T =   

(g) What minimum speed should the ball have at the top of the circle to continue in its circular motion? (Use the following as necessary: m, v, L, and g.)
vmin =  

Explanation / Answer

Here ,

a) at the top of the circle

as the string is pulling towrds the centre

the direction of force is 5

b)

at the top of the circle

the as the direction of gravitational force is always same

the direction of force on the ball is 5

c)

at the top of the circle

as the centrepetal force on the ball is towards the centre of circle

the direction of force on the ball is 5

d)

at the top of the circle

FC = m *g + T

where T is the tension of the circle

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