A wheel (radius = 0.30 m) is mounted on a frictionless, horizontal axis. A light

Question

A wheel (radius = 0.30 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object. When released from rest the object falls with a downward acceleration of 5.0 m/sec^2. 17. Find the tension on the cord. 18. Find the angular acceleration of the wheel. 19. Find the moment of inertia of the wheel. A solid disk (M = 10 kg and R = 70 cm) is rotating at 300 rpm initially. Then a smaller ring (m = 3.0 kg and r = 40 cm) is dropped concentrically onto the disk and they rotate together with a new angular velocity. 20. find the final angular velocity of the system in rpm. 21. find the change in rotational kinetic energy of the system. 22. find the percent of energy loss during this collision between the solid disk and the ring. A hollow spherical ball is let go from the top of a track and goes around a circular loop (R = 60 cm). 23. What must be the minimum height of the track so that the ball will not fall off the track at the topmost point of the loop? 24. When the above condition is met. what is the tangential speed of the ball when it reaches the topmost point?

Explanation / Answer

17.

for the object's motion we have from Newton's 2nd law;

mg - T = ma

or, T = m(g-a) = (0.5 kg)(9.8 m/s2 - 5 m/s2)

or, T = 2.4 N

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18.

angular acceleration of the wheel is = a/R = (5 m/s2)/(0.3 m)

or = 16.67 rad/s2

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19.

Let the moment of intertia be I,

Torque on wheel is Tq = T.R = (2.4 N)(0.3 m) = 0.72 N-m

Now, Tq = I

or, I = Tq/ = (0.72 N-m)/(16.67 rad/s2)

or, I = 4.32X10-2 kg-m2

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This concludes the answers. Check the answer and let me know if it's correct. If you need any more clarification or correction, feel free to ask.....

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