Name (please print): Total Points: last) (first) [30 pts] An aluminum disk and a
ID: 3307664 • Letter: N
Question
Name (please print): Total Points: last) (first) [30 pts] An aluminum disk and a stcel ring are both wound with thread and hung from the ceiling. Alongside is a solid plastic sphere. The disk, the ring, and the sphere all have the same mass and radius. They are then all released at the same time from the same height. The ball falls freely, and both the disk and the ring unwind as they move downward a distance h where they will each hit the floor, not necessarily at the same time. System 1 contains the aluminum disk, thread, and the earth. System 2 contains the steel ring, thread and the earth. System 3 contains the plastic ball and the Earth. 1. 2-Explanation / Answer
(d) At the same time, when all the three bodies were released together, since system 1 and system 2 are both hunged from a ceiling with a thread, therefore, by the law of conservation of energy,
Energy Before = Energy After
mgh = 1/2 mv2 , but since it is being released from the ceiling the kinetic energy at the topmost point is zero and the potential energy will be mgh and when the body reach the ground the potential energy will be zero as height is zero and the kinetic energy will be 1/2 mv2.
Which will have greater kinetic energy, it will depend on the mass of the object, if the mass of the object will be greater it will have greater kinetic energy and so for the lower mass object, therefore, since mass of steel is greater than mass of aluminium which is greater than mass of plastic ball, therefore,
K.E.steel > K.E.aluminium> K.E.plastic ball .
(e) Following the above law, Energy Before = Energy After
mgh = 1/2 Iw2 therefore, the object having more moment of inertia will have greater rotational kinetic energy, in this case the moment of inertia of steel is more than the moment of inertia of aluminium since the mass of steel is more than the mass of aluminium which is more than the mass of the plastic ball, therefore,
Rotational K.E.steel > Rotational K.E.aluminium > Rotational K.E.plastic ball .
(f) Form newton's second equation of motion, h = ut + (1/2) at2 , where a is the acceleration, t is the time , u is the initial velocity of an object which is zero , therefore, for a time t = 0, since u = 0 , therefore, h = 0.
For the time t = t, u = 0,
h = ut + (1/2) at2
h = (1/2) at2 ,
t = (2h/a)1/2 , so an object having high acceleration, will take less time to hit the ground and the object having less acceleration, will take more time to hit the ground, therefore , the object having more mass will have more acceleration, hence the mass of steel is more than the mass of aluminium and the plastic ball, therefore, it will take less time to reach the ground, therefore, the ranking will be
(delta)t3 > (delta)t1 > (delta)t2 .
(g) Tension T = mg , where m is the mass of the object and g is the acceleration due to gravity, therefore, the object having more mass will have more tension as compared to the object having less mass, therefore, the mass of steel is more than the mass of aluminium, so the tension of system 2 will be greater than tension of system 1.
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