Connected Particles (Movable Pulleys)?

Question

A light inextensible string is fastened at one end to a point on the ceiling. It then passes under a smooth movable pulley P of mass 4kg, then over a smooth, light fixed pulley. a second particle Q, of mass 6kg, hangs freely from the other end of the string. All parts of the string which are not in contact with the pulleys are vertical.
If P moves up a distance x metres while Q moves down a distance y, explain why y=2x. - ?? why ???
Hence show that the acceleration of Q is twice that of P. - ??? . Find the acceleration of each mass and the tension in the string ...... I don't understand these movable pulley questions at all !

Answer 1

When the pulley P moves upward there is a displacement of string which is twice the distance moved. This is because there is string on both sides of the pulley.

Therefore the y=2x since Q is attached to the string. It really is that simple.

Under a constant acceleration of p, p will follow the equation of x(t)=x0+vi*t+.5*a*t^2

set x0=0 and vi=o
x(t)=.5*a*t^2

since x(t) = y(t)/2 since the string sets this constraint
then
y(t)=a*t^2

j

Answer 2

Movable A movable or class 2 pulley has a free axle. That is, the axle is "free" to move in space. A movable pulley is used to transform forces. A movable pulley has a mechanical advantage of 2. That is, if one end of the rope is anchored, pulling on the other end of the rope will apply a doubled force to the object attached to the pulley.