Question

In a lifting machine, the effort required to lift loads of 200N and 300N were 50N and 60N respectively. If the velocity ratio of the machine is 20 determine law of the machine.

(a) P = 1/10W +30

(b) P = 1/20W +30

(c) P = 1/30W +30

(d) P = 1/40W +30

The question was asked in an international level competition.

Question is taken from Relative Velocity of Two Bodies Moving in Straight Lines in chapter Velocity in Mechanisms of Machine Kinematics

Answer 1

Correct option is (a) P = 1/10W +30

For explanation I would say: Let the law of machine be P = mW + C

where P = effort applied, W = load lifted and m and C being constants.

when W = 200 N    P = 50 N

when W = 300 N    P = 60 N

Putting these values in the law of machine.

50 = 200m + C                                        …………(i)

60 = 300m + C                                        …………(ii)

Subtracting (i) and (ii), we get

1 = 10 m

or, m = 1/10

Putting this value in equation (i), we get

50 = 200 x 1/10 + C

C = 30

Hence, the machine follows the laws

P = 1/10W +30.