# Mechanics ( one easy Questionw hich i cant solve ) A-Levels Sylabbus

1. Apr 5, 2006

### Szeki

1 a) A particle P of mass m is placed on a rough plane inclined at an angle tan-1 (5/12) to the horizontal.The coefficient of friction between the plane and P is 0.5. Prove that P will remain stationary.

1b ) A light inextensible string is fastened to P, passes up a line of greatest slope, over a frictionless pulley at the top of the plane, and to its other end is attached a particle Q of mass 2m , which hangs freely. Prove that the particles will move and find magnitude of their acceleration.

1c ) When Q has decended a distance h , it hits the floor and rebounds with 0.5 of its speed. Show that Q will hit the floor again before P comes to instantaneous rest.

I cant solve the problem of 1C ) Someone pleae help.
No diagram is included in the question orginally.
6b) a= 5g/13 = 3.846 ms-2
6c) T(Q) = 1.387(h)^0.5 Means Root h
T(P)=0.3396(h)^0.5 = 1.074(h/g)^0.5
So t(Q) < t(P)

2. Apr 5, 2006

### barob1n

The forces acting on Q are gravity and the tension force from being connected to that other mass (and is directed opposite to the gravitational force). The sum of those two forces is equal to the mass of Q (2m) times the acceleration. Solve for the acceleration. Knowing the acceleration and the height that Q falls you can find the speed at which it hits the ground.

The problem then tells you that it rebounds at one half that speed. Find the height that it will reboud to and the time it will take to get there (the mass P should not affect this since it is not pulling on Q). Then find the time it will take to fall from that rebound height (it will be the same time that it took to rebound to that height).

At some point you gotta find the time it takes for P to stop moving. To do this you calculate the time it will take for the fricional force plus the gravitational force (remembering it is on an inclined plane) to stop it from a velocity equal the velocity of Q right before it hit the ground for the FIRST time.