3. Machines

Flashcards covering the technical terms, types of levers, and pulley systems based on the lecture notes on machines.

Machine

A device by which we can either obtain a gain in speed or overcome a large resistive force (load) by applying a small force (effort) at a convenient point and in a desired direction.

Force Multiplier

A machine that allows a user to lift a heavy load by applying less effort ($M.A. > 1$). Examples include a jack to lift a car or a wheel barrow to carry a load.

Gain in Speed

Obtained when a smaller movement of effort results in a greater movement of the load ($V.R. < 1$). Examples include a pair of scissors or the blade of a knife.

Load (L)

The resistive or opposing force to be overcome by a machine.

Effort (E)

The force applied on the machine to overcome the load.

Mechanical Advantage ($M.A.$ )

The ratio of the load to the effort ($M.A. = \frac{L}{E}$). It has no unit since it is the ratio of two similar quantities.

Velocity Ratio ($V.R.$ )

The ratio of the velocity of effort to the velocity of load; it is also defined as the ratio of the displacement of effort ($d_E$) to the displacement of load ($d_L$) in the same time ($V.R. = \frac{d_E}{d_L}$).

Work Input

The work done on the machine by the effort, calculated as $\text{Work input} = E \times d_E$.

Work Output

The work done by the machine on the load, calculated as $\text{Work output} = L \times d_L$.

Efficiency ($\eta$)

The ratio of work output to work input ($\eta = \frac{\text{Work output}}{\text{Work input}}$), usually expressed as a percentage.

Ideal Machine

A machine in which there is no loss of energy in any manner, making the work output equal to the work input and the efficiency equal to $100\%$.

Actual Machine

A machine where the output energy is always less than the input energy due to energy loss from friction and the weight of moving parts.

Relationship between $M.A.$, $V.R.$, and $\eta$

The mechanical advantage of a machine is equal to the product of its efficiency and its velocity ratio ($M.A. = V.R. \times \eta$).

Lever

A rigid, straight (or bent) bar which is capable of turning about a fixed axis called the fulcrum ($F$).

Effort Arm

The perpendicular distance from the fulcrum ($F$) to the point of application of effort ($E$).

Load Arm

The perpendicular distance from the fulcrum ($F$) to the point of application of load ($L$).

Law of Levers

In equilibrium, the clockwise moment of load about the fulcrum is equal to the anticlockwise moment of effort about the fulcrum ($\text{Load} \times \text{load arm} = \text{Effort} \times \text{effort arm}$).

Mechanical Advantage of a Lever

Defined as the ratio of the length of the effort arm to the length of the load arm ($M.A. = \frac{\text{Effort arm}}{\text{Load arm}}$).

Class I Lever

A lever where the fulcrum ($F$) is located between the effort ($E$) and the load ($L$). Examples include a seesaw, a pair of scissors, and the nodding action of the human head.

Class II Lever

A lever where the load ($L$) is located between the fulcrum ($F$) and the effort ($E$). These levers always act as force multipliers ($M.A. > 1$). Examples include a nut cracker and raising the weight of the human body on toes.

Class III Lever

A lever where the effort ($E$) is located between the fulcrum ($F$) and the load ($L$). These levers always provide a gain in speed ($M.A. < 1$). Examples include sugar tongs and the forearm raising a load.

Single Fixed Pulley

A pulley whose axis of rotation is stationary. It is used to change the direction of effort and has an ideal $M.A. = 1$ and $V.R. = 1$.

Single Movable Pulley

A pulley whose axis of rotation is not fixed. It acts as a force multiplier and has an ideal $M.A. = 2$ and $V.R. = 2$.

Block and Tackle System

A combination of several pulleys in two blocks (one fixed, one movable) where the total number of pulleys $n$ determines the mechanical advantage and velocity ratio ($M.A. = n$ and $V.R. = n$ in an ideal case).