Physics 207 GH Exam 3

Dr. Min Xu

Apr 28, 2003
LAST NAME: ___________________________________________________________________________________________________ FIRST NAME: __________________________________________________________________________________________________ SS#: ________________________________________________________________________________________________________________

General Instruction

You have 1.5 hours to answer 4 questions on this exam. Work each problem only on the sheet provided for this problem, using the back if necessary. Please write the name and the last four digits of your SS# on each sheet at the top of the page.

You must indicate the reasoning and show all the steps.

If you are unable to obtain the answer to part of a problem and you need the answer to solve the subsequent parts, use an appropriate symbol for the answer to the previous part and solve in terms of that symbol.

1. (30 points) A 3.00m long, 240N uniform rod at the zoo is held in a horizontal position by two ropes at its ends. The left rope makes an angle of 150o with the rod and the right rope makes an angle h with the horizontal. A 90N howler monkey hangs motionless 0.5m from the right end of the rod as he carefully studies you.


(a) (5 points) Draw a free-body diagram for the rod.
(b) (5 points) Mark the lever arms of all nonzero torques in the above figure with respective to the right end of the rod.
(c) (10 points) Find the tension in the left rope.
(d) (10 points) Find the tension in the right rope.
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2. (30 points) A yo-yo is made by wrapping a string several times around a solid cylinder with mass M and radius R. You hold the end of the string stationary while releasing the cylinder with no initial motion. The string unwinds but does not slip or stretch as the cylinder drops and rotates. The moment of inertia of a solid cylinder about its symmetrical axis is 1 2MR2.


(a) (15 points) Use the energy considerations to find the speed v of the center of mass of the solid cylinder after it has dropped a distance h.
(b) (5 points) Find the acceleration a of the center of mass of the solid cylinder using the answer you obtained in (a).
(c) (10 points) The acceleration of the mass center of the solid cylinder in the previous problem can also be obtained by studying the forces and the torques acting on the solid cylinder. The torques are with respective to the mass center of the solid cylinder. Find the acceleration a of the mass center of the solid cylinder again using this method.

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3. (20 points) Three men were shot to the moon in a shell fired from a great cannon sunk in a novel. Neglect everything but the gravity of the earth. The earth’s radius RE = 6380km and its mass mE = 5.97 × 1024kg.


(a) (10 points) Find the muzzle speed needed to shoot the shell straight up to a height above the earth equal to the earth’s radius.
(b) (10 points) Find the escape speed, i.e., the muzzle speed that would allow the shell to escape from the earth completely.

4. (20/40 points) You are free to choose to answer either question (a) or (b). You are also welcome to solve both of them to get extra credits.


(a) (20 points) A large turntable rotates about a fixed vertical axis, making one revolution in 6s. The moment of inertia of the turntable about this axis is 1200kg.m2. A child of mass 40kg, initially standing at the center of the turntable, runs out along a radius. What is the angular speed of the turntable when the child is 2m from the center? Assume that the child can be treated as a particle.
(b) (20 points) A nodding bucket in a gift shop is shown in the figure below. The water continuously flows into the bucket. The bucket automatically dumps the water contained inside completely when the level of the water is nearly full by rotating anticlockwise. The bucket stands up again once the water is dumped. Please explain this phenomenon.
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