Figure above shows a wheel and axle. At one end of the axle, a wheel of a greater diameter is fixed. The axle and the wheel both rotate about the same axis. Ropes have been wound around both the wheel and the axle. The load can be lifted by pulling on the rope around the wheel once, so that the wheel and axle turn round once, then, effort force moves one circumference of the wheel =2πR
Load force moves one circumference of the axle =2πr
The mechanical advantage of this machine assuming there was no friction
Wheel and axle is like a rotating lever (shown in figure below).
Steering wheels, spanner, screw drivers and bicycle pedals all use the principle of wheel and axle.
Solved Examples:
Example 1 :
Figure below shows the use of a lever to lift a boulder of weight 3000 N by applying a suitable effort at C. If AB = 1 m and BC = 6 m, calculate the effort required to lift the boulder. State the class of lever to which it belongs.
Suggested Answer:
According to the principle of moments,
Load x Load arm = Effort x Effort arm
3000 x AB = Effort x BC
3000 x 1 = E x 6
The lever belongs to class I.
Example 2 :
A wheel barrow which is stationary has its C.G. at X (shown in figure below), the weight of wheel barrow is 50 N which holds 550 N of cement. Calculate the minimum force required to keep the leg just off the ground. What is the M.A. of this machine?
Suggested Answer:
Load x Load arm = Effort x Effort arm
600 x 0.5 = E x 1.5
= 3
Example 3 :
Figure below shows tongs used to lift a piece of coal of 3 kg. Calculate the effort required.
Suggested Answer:
Effort x Effort arm = Load x Load arm
E x 20 = 30 x 30
Example 4 :
A machine has a velocity ratio of 10. It is used to raise a load of 2000 N by 5 m using an effort of 250 N. Find (i) the work obtained from the machine, (ii) M.A., and (iii) efficiency of the machine.
Suggested Answer:
(i) Work obtained from machine
= Load x Distance moved
= 2000 x 5
= 10,000 J
(ii) Mechanical Advantage
(iii) Efficiency
= 80%
Example 5 :
A block and tackle having 2 pulleys in each block is used to raise a load of 60 N. The lower block weighs 12 N. Neglecting the frictions calculate the effort required to raise the load.
Suggested Answer:
Since there are two movable pulleys, 4 strings share the load. As a result the
V.R. = 4 and M.A. = 4.
Example 6 :
A block and tackle of 4 pulleys in each block has an efficiency of 80%. It is used to lift a load of 320 N. Calculate the following:
(i) V.R.
(ii) M.A
(iii) Effort
(iv) If the load is raised by 5 m, find the distance through which the effort acts.
(v) The work done in the machine.
Suggested Answer:
(i) V.R. = The total number of pulleys in the system = 8
(ii) 
(iii) 
(iv) 
Distance through which effort acts = V.R. x Distance moved by load
= 8 x 5 = 40 m
(v) Work done on the machine
= Effort x Distance through which it acts
= 50 x 40
= 2000 J
