A 0.21 kg ball on a string is whirled on a vertical circle at a constant speed. When the ball is at the three o'clock position, the tension is 18 N.
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(a) How does the magnitude of the centripetal force acting on the ball relate to each point on the circle? (o) The magnitude is the same at each point on the circle.
(_) The magnitude is not the same at each point on the circle.
(_) There is insufficient information for a definitive answer.
Correct. The centripetal force depends on the mass of the ball, the radius of the circle, and the speed. Since each of these factors is fixed, the magnitude of the centripetal force is the same at each point on the circle.
(b) When the ball is at the three o'clock position, what is providing the centripetal force? (_) Only the tension in the string is providing the centripetal force.
(o) Both the tension and gravity are providing the centripetal force.
(_) Only gravity is providing the centripetal force.
Incorrect. Only forces that have components pointing toward or away from the center of the circle can contribute to the centripetal force.
(c) Is the tension in the string greater when the ball is at the twelve o'clock position or when it is at the six o'clock position, or is the tension the same at both positions? (o) The tension is the same at both positions.
(_) The tension is greater at the six o'clock position.
(_) The tension is greater at the twelve o'clock position.
Incorrect. Remember that the centripetal force is the net force due to all force contributions that point toward or away from the center of the circle. The force of gravity points toward the center in one of the positions and away from the center in the other position.
(d) What is the algebraic expression for the magnitude T of the tension at the twelve o'clock position? Express your answer in terms of the magnitude Fc of the centripetal force, the mass m of the ball, and the magnitude g of the acceleration due to gravity. (Answer using F_c to be the magnitude of the centripetal force, m to be the mass of the ball, and g to be the acceleration due to gravity.)
T =
(e) What is the magnitude T of the tension at the twelve o'clock position?
Number Unit
T = N
(f) What is the algebraic expression for the magnitude T of the tension at the six o'clock position? Express your answer in terms of the magnitude Fc of the centripetal force, the mass m of the ball, and the magnitude g of the acceleration due to gravity. (Answer using F_c to be the magnitude of the centripetal force, m to be the mass of the ball, and g to be the acceleration due to gravity.)
T =
(g) What is the magnitude T of the tension at the six o'clock position?
Number Unit
T = N
I'm not sure how to find the algebaric expression or the magnitudw of tension
I know tension is equal to the centripal force
(d) I had to remind myself that the ball revoves in a vertical circle.
At the 12 o'clock position,
T + Mg = M V^2/R = F_c
(e) M V^2/R = 18 N in this case, since that is the tension at the 3 O'clock position, where T equals the centripetal force. Therefore
T = 18 - Mg = 10 - 2.06 = 7.94 N
(f) At the six O'clock position,
T - Mg = MV^2/R = F_c
T = F_c + Mg
(g) Plug in the numbers, remembering that F_c = 18 N
To find the algebraic expression for the tension at the twelve o'clock and six o'clock positions, we need to consider the forces acting on the ball.
At the twelve o'clock position, the tension in the string is the only force providing the centripetal force. The centripetal force is given by Fc = mv^2/r, where m is the mass of the ball, v is the velocity, and r is the radius of the circle.
So at the twelve o'clock position, the tension T is equal to the centripetal force Fc: T = Fc = mv^2/r.
At the six o'clock position, in addition to the tension, there is also the force of gravity acting on the ball. The tension is still providing the centripetal force, but now it must also counteract the force of gravity.
The magnitude of the force of gravity acting on the ball is given by mg, where g is the acceleration due to gravity.
So at the six o'clock position, the tension T must be equal to the centripetal force Fc plus the force of gravity mg: T = Fc + mg.
Now, to find the specific values for the tension at each position, we need more information. Specifically, we need to know the velocity and the radius of the circle.