Simple Machines

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In all the above examples, a machine either multiplies or reduces the effect of the force that is applied.

A bicycle is a machine which is used to gain speed. We gain speed by exerting additional force. When we try to ride a bicycle up a steep hill, we soon realize that we gain speed by applying greater force. It is impossible to multiply both the force and gain the speed at the same time.

Machines are used to multiply or reduce the force or to change its direction of application.

We use a rope threaded through a pulley for flag hoisting on a pole. The pulley used here multiplies neither force nor speed. It helps in changing the direction of the downward force which we exert, into an upward force which raises the flag. A machine can be used to change the direction of a force.

There are five simple machines:

• The lever

• The pulley

• The wheel and axle

• The inclined plane, and

• The gear wheels

We will be discussing in detail only two of the above machines i.e., the levers, and the pulley systems. Before we go into the details, it is necessary to understand some of the terms used in connection with these machines. These are Effort, Load, Mechanical Advantage [M.A.], Velocity Radio [V.R.] and Efficiency.

Effort :

The effort is the force applied to the machine.

Load:

The load is the force against which the machine does the work.

Mechanical Advantage (M.A.)

This ratio is a measure of the advantage that one obtains by using the machine. If a load of 40 N is moved by applying an effort of 10 N on the machine then the mechanical advantage of the machine is given by

Velocity Ratio (V.R)

The 'corresponding distance' is the distance moved by the load in the same time as the distance moved by the effort.

The velocity ratio depends only on the design of the machine and is always same for a particular machine. The mechanical advantage on the other hand can vary for a particular machine as it depends on friction.

Efficiency

M.A., V.R. and efficiency have no units as they are ratios between similar quantities.

To summarize:

Effort: The force applied to the machine.

Load: The force against which the machine does the work.

Since the effort does the work on the machine and the load is worked upon by the machine, efficiency can also be expressed as

The efficiency is very often expressed as a percentage i.e.,

It should be noted that 100% efficiency is possible only for an ideal (imaginary) machine. Usually, for all practical purposes the efficiency of a machine is always less than 100%. This is because practical M.A. is always less than theoretical M.A. due to friction and the weight of the moving parts.

It is important to note that a machine does not enable to perform more work than the work done on it. The output energy can never be greater than the input energy. In fact in actual machines output energy is always smaller than the input energy.

Numericals :

1. In a certain simple machine with velocity ratio 5, an effort of 1000 N is needed to overcome a load of 4500 N. Calculate

(i) mechanical advantage

(ii) efficiency of the machine

Suggested answer :

V.R = 5

Effort = 1000 N

Load = 4500 N

(i) M.A

(ii) Efficiency

2. A pulley system has a V.R of 3 and efficiency 80%

(i) calculate the M.A of the system

(ii) Value of the effort required to raise a load of 300 N.

(iii) If the effort moves through a distance of 6m. Calculate the distance moved by the load.

Suggested answer :

(i) V.R = 3

efficiency = 80%

= efficiency

= 2.4

(ii) Load = 300 N, M.A = 2.4

=125 N

(iii) d_E = 6m, V.R = 3

= 2m

Distance moved by load = 2m.