how do i work out the velocity ratio for a simple pulley system?

Question

ive been given a problem, and one part to the problem is i have to find the velocity ratio of 3 pulleys lifting a block of mass 500kg, using one rope. the effort, E, is given as E=(0.4W+0.5)kN, where W is the weight in kN of the block. how is this question possible?

Answer 1

The trick is that the effort work equals the resistance work, which means that the effort power equals the resistance power. Power is force times velocity. So if V is the effort velocity and R is the resulting velocity of the weight, you need to use the relationship EV = RW (products of force and velocity are equal, meaning powers are equal) to get an expression for R/V, the ratio of resultant velocity to effort velocity. Note that a 500 kg object has a weight of W = (500 kg)(9.8 m/s^2) = 4900 N.

EV = RW ==> (0.4W + 0.5)V = RW ==> R/V = (0.4W + 0.5) / W = 0.4 + (0.5 / W). You know W, so you can compute the exact numerical value of the ratio.