Question

b3 - sct100: ball whirled in vertical circle - net force on ball
a ball with a weight of 2 n is attached to the end of a cord of length 2 m. the ball is whirled in a vertical circle counterclockwise. the tension in the cord at the top of the circle is 7 n, and at the bottom it is 15 n. (the speed of the ball is not the same at these points.)
(a) three students discuss the net force on the ball at the top.
angelica: \the net force on the ball at the top position is 7 n since the net force is the same as the tension.\
bo: \the net force on the ball at the to position is 9 n. both the tension and the weight are acting downward so you have to add them.\
charles:
o, you are both wrong. you need to figure out the centripetal force (m v²/r) and include it in the net force.\
with which, if any, of these students do you agree?
angelica __ bo charles none of them __
explain your reasoning.
(b) now the students discuss the net force on the ball at the bottom.
angelica: \the net force on the ball at the bottom position is 15 n since the net force is the same as the tension.\
bo: \the net force on the ball at the bottom position is 17 n, since you need to add the weight of 2 n to the tension of 15 n.\
charles: \the net force on the ball at the bottom position is 13 n. i agree that you need to take into account both the weight and the tension, but they are in different directions so they will subtract.\
with which, if any, of these students do you agree?
angelica __ bo charles none of them __
explain your reasoning.

Explanation:

(a)

• At the top of the vertical circle, the net force \(F_{net}\) is the centripetal force \(F_c\). The forces acting on the ball are the tension \(T\) (downward) and the weight \(W\) (downward). According to Newton's second law for circular motion \(F_{net}=F_c = T + W\).
• Angelica is wrong because she only considers tension. Charles is wrong because centripetal force is the net force (not an additional force to be included). Bo is correct as \(F_{net}=T + W=7N + 2N=9N\)

• At the bottom of the vertical circle, the net force \(F_{net}\) is the centripetal force \(F_c\). The forces acting on the ball are the tension \(T\) (upward) and the weight \(W\) (downward). According to Newton's second law for circular motion \(F_{net}=F_c=T - W\)
• Angelica is wrong because she only considers tension. Bo is wrong because he adds the forces (they act in opposite directions). Charles is wrong with his calculation. The correct net force \(F_{net}=T - W = 15N-2N = 13N\), but none of the students have the correct reasoning.

Answer:

Bo

(b)