- #1
sharkNC
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Homework Statement
A ball of 10kg mass is suspended by a cable that passes through a hole in a floor. The ball rotates in a circular orbit, A, that is in a plane that is 3m below the floor. If the orbit has a radius of 1m, calculate;
a) Tension in the cable
b) speed va of the ball in orbit A
c) angular momentum about the vertical axis
The motor then draws in the cable until the ball rotates in orbit B. If the radius of orbit B is 0.5m, calculate;
d)The new speed vb of the ball
e) The angle between the cable and vertical axis
f) The height, h, gained by the ball
Homework Equations
θa - tan-1(1/3) = 18.43
The Attempt at a Solution
I am able to a-c by working out the tension as T = 10x9.81/cos18.43 = 103.4 N
the velocity √1x103.4xsin18.43/10 = 1.808 m/s
the angular momentum as L = r x mv = 1 x 10 x 1.808 = 18.08
When I attempted to do the rest of the question I got the new speed to be half of the original speed and angle B to be smaller. However in the question the image for angle B looks to be greater than angle A so I am not sure whether its just the question or if I am doing something wrong to calculate the angle. (I find the sum of the forces in the x and y direction and make them equal to each other and then find angle B). For part f I am using the conservation of energy however when I make h the subject I find that it comes out as 3 which doesn't make sense.
Can someone please help me. I have been stuck on this question for a long time and cannot seem to find where I have gone wrong.