Q.11. (a) State the relationship between mechanical advantage, velocity ratio and efficiency.
(b) Name the term that will not change for a machine of a given design.
Ans. Mechanical advantage is equal to the product of velocity ratio and efficiency.
For a machine of a given design, the velocity ratio does not change.
Q.12. Derive a relationship between mechanical advantage, velocity ratio and efficiency of a machine.
Ans. Let a machine overcome a load L by the application of an effort E. In time t, let the displacement of effort be dE and the displacement of load be dL.
Work input = Effort X displacement of effort
= E X dE
Work output = Load X displacement of load
= L X dL
Thus, mechanical advantage of a machine is equal to the product of its efficiency and velocity ratio.
Q.13. How is the mechanical advantage related with the velocity ratio of an actual machine? State whether the efficiency of such a machine is equal to 1, less than 1 or more than 1.
Ans. The mechanical advantage for an actual machine is equal to the product of its efficiency and velocity ratio.
The efficiency of such a machine is always less than 1, i.e. h<1. This is because there is always some loss in energy in form of friction etc. Q.14. State one reason why is mechanical advantage less then the velocity ratio for an actual machine. Ans. This is because the output work is always less than the input work, so the efficiency is always less than 1 because of energy loss due to friction.
Q.15. What is a lever ? State its principle.
Ans. A lever is a rigid, straight or bent bar which is capable of turning about a fixed axis.
Principle: A lever works on the principle of moments. For an ideal lever, it is assumed that the lever is weightless and frictionless. In the equilibrium position of the lever, by the principle of moments,
Moment of load about the fulcrum=Moment of the effort about the fulcrum.