Wheel and Axle

Definition of Wheel and Axle

A wheel and axle is really two machines in one because it consists of a wheel mounted rigidly upon an axle or drum of smaller diameter, the wheel and the axle having the same axis.

The wheel & axle device is similar to the lever simple machine. The wheel acts as the lever and the axle acts as a fulcrum. The lever applies force to the fulcrum, causing something to move.

If a rope is fixed onto the wheel and wound round it, leaving a free end where an effort E is to be applied, the rope attached to the axle is wound round in the opposite direction and the load attached to the free end,  For each complete rotation of the wheel, there is one complete rotation of the axle.

Let a and b be the radii of the wheel and axle respectively. Then

Velocity Ratio =Distance moved by EffortDistance moved by Load=2πa2πb=ab

Applications of the Wheel and Axle

Applications of the wheel and axle are:

1. Steering wheel of an automobile
2. Doorknob
3. Treadmill
4. Windmill
5. Waterwheel

Gear

Definition of Gear

A gear is a toothed wheel or cylinder used to transmit rotary or reciprocating motion from one part of a machine to another. Two or more gears, transmitting motion from one shaft to another, constitute a gear train.

Gears work on the wheel and axle principle. If  toothed wheel A drives wheel B resulting in turning forces,

Velocity Ratio =Number of teeth on the driven gear Number of teeth on the driving gear

GENERAL EVALUATION

A screw jack whose pitch is 4.4mm is used to raise a body of mass 8000kg through a height of 20cm. The length of the tommy bar of the jack is 70cm. If the efficiency of the jack is 80%, calculate the:

1. velocity ratio of the jack.
2. Mechanical advantage of the jack
3. Effort required in raising  the body.
4. Work done by the effort in raising the body (g = 10m/s², π = 22/7)