9. A uniform sphere, cylinder, and hoop (each with the same mass M and radius R) are going to compete in a rolling race, but this time they will race up the hill instead of down the hill. The hill makes an angle 0 with the vertical as indicated in the diagram. The moment of inertia of each round object is I = BMR², where ß is different for each shape (Broop = 1, Beylinder = 0.5, ßgsphere = 0.2). Each object will be sent up the hill at the same time with the same translational speed, ī]. Each object will roll without slipping during the entire path. In answering each of the parts below, be certain to show all your work and justify your answers. a. Rank the objects in terms of how much initial translational kinetic energy each object has. If any of the quantities are the same, then state that. b. Rank the objects in terms of how much initial rotational kinetic energy each object has. If any of the quantities are the same, then state that. c. Using the work-energy theorem, find the distance (let's call it dmax) an object will travel up the ramp. Clearly state what constitutes your "system". The variables that can be in your answer are: M, R, B, Kroti, 0, g
9. A uniform sphere, cylinder, and hoop (each with the same mass M and radius R) are going to compete in a rolling race, but this time they will race up the hill instead of down the hill. The hill makes an angle 0 with the vertical as indicated in the diagram. The moment of inertia of each round object is I = BMR², where ß is different for each shape (Broop = 1, Beylinder = 0.5, ßgsphere = 0.2). Each object will be sent up the hill at the same time with the same translational speed, ī]. Each object will roll without slipping during the entire path. In answering each of the parts below, be certain to show all your work and justify your answers. a. Rank the objects in terms of how much initial translational kinetic energy each object has. If any of the quantities are the same, then state that. b. Rank the objects in terms of how much initial rotational kinetic energy each object has. If any of the quantities are the same, then state that. c. Using the work-energy theorem, find the distance (let's call it dmax) an object will travel up the ramp. Clearly state what constitutes your "system". The variables that can be in your answer are: M, R, B, Kroti, 0, g
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Transcribed Image Text:9. A uniform sphere, cylinder, and hoop (each with the same mass M and radius R) are going to compete
in a rolling race, but this time they will race up the hill
instead of down the hill. The hill makes an angle 8 with the
vertical as indicated in the diagram. The moment of inertia
of each round object is I = BMR², where ß is different for
each shape (Broop = 1, Beyinder = 0.5, Pgsphere = 0.2).
Each object will be sent up the hill at the same time with
the same translational speed, 7). Each object will roll without slipping during the entire path.
In answering each of the parts below, be certain to show all your work and justify your answers.
a. Rank the objects in terms of how much initial translational kinetic energy each object has. If
any of the quantities are the same, then state that.
b. Rank the objects in terms of how much initial rotational kinetic energy each object has. If any
of the quantities are the same, then state that.
c. Using the work-energy theorem, find the distance (let's call it dmax) an object will travel up the
ramp. Clearly state what constitutes your "system". The variables that can be in your answer
are: M, R, B, Kzогi, 6,g
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