# 1. A crowbar of length 1.80m is used move a rock of mass 310kg. The fulcrum is 20cm from the load . Calculate (a) the VR neglecting the weight of crowbar, (b) MA ,(c) effort E and efficiency.2.In the above problem the weight of bar is not negligible.Its mass is 20kg.The torque exerted by this weight will reduce the efforts required .(a) Calculate this effort,equating torques ,the VR is the same as the dimensions remain the same as in problem 6.(b) Calculate the actual MA and (c) actual efficiency. (d)Explain briefly if the law of conservation of energy is violated.3.In the see-saw problem (problem no.2), the big brother lowers (swings) himself from the horizontal level by 50cm in 1 second , then comes back to the horizonal level in 1 second and then up above the horizontal level by 50cm in 1 second. Then he continues to swing up and down merrily. (a.) What is the maximum height (above the horizontal) to which the little brother goes up? (b.)What is the average speed of the little brother in one complete swing? (c.) What is the average velocity in one complete swing?

1.
It is assumed (i) The crow bar is weightless.
(ii) There is no friction at the fulcrum.
Length of the crowbar = 1.8 m
Length of load arm (d) = 0.2 m =20 cm
Length of effort arm (D)= (1.8 – 0.2) = 1.6 m.
(i) Velocity ratio(VR) = D/d =1.6/ 0.2 = 8
(ii)Mechanical advantage = L/E = V.R. = 8
(iii)Effort E ,
M.A = L/E
E = L/M.A
= 310 / 8
= 38.75 kg
Effieciency,η = M.A / V.R = 1 = 100%