- #1
shepherd882
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Homework Statement
Two pucks are lying on ice where they can slide and rotate with almost no friction. A string is tied to both pucks but it is tied to the middle of the first puck and wrapped around the second puck. You pull on both strings with the same force, F. The first puck moves without rotating while the second puck moves and rotates.
a) The centres of both pucks will travel the same distance. Explain clearly why that is so.
b) Calculate the ratio of the total distance L that the end of the string attached to the second puck moved to the total distance d that the end of the string attached to the first puck moved. Beware that this is NOT a rolling without slipping problem and the relationship between angular speed and centre of mass speed may be different than in that case. There are at least two methods of solving this problem but they both require using the angular momentum principle. One method calculates the two types of kinetic energy and another method calculates the angle through which the second puck rotates.
Homework Equations
F=ma
Torque = I*w
I=0.5MR^2
Angular displacement = 0.5*a*t^2
The Attempt at a Solution
a) treat each puck as point-particle system. the external force (F) acting on the centre of mass for both pucks are the same. The centre of mass has a = F/m therefore distance traveled by both pucks is:
d=1/2*a*t^2
d= 1/2*F/M*t^2
b) for puck 2:
Divide angular displacement/distance:
R*angular displacement = 2D
(L=R*angular displacement)
Therefore, L=2D
not sure if this is right and for puck 1, how do you do it for slipping?
thanks for your help
