Simple machines

Simple machines. A simple machine is a device that work with one movement and change the size and direction of force.

Examples of simple machines

  • Lever system
  • Wheel and Axle machine
  • Gear system
  • Pulley system
  • Screws
  • Inclined planes
  • Wedges

(𝐚) 𝐋𝐄𝐕𝐄𝐑 π’π˜π’π“π„πŒ:
A lever is a rigid bar, which is free to move about a fixed point called fulcrum or pivot.
It works on the principle of moments.

Classes of levers;

image 268

NOTE: -Load arm is the distance of the load from pivot.
-Effort arm is the distance of effort from pivot.

image 269

Hence, a lever system is more efficient compared to other machines.

image 270

(𝐛) 𝐖𝐇𝐄𝐄𝐋 𝐀𝐍𝐃 𝐀𝐗𝐋𝐄 πŒπ€π‚π‡πˆππ„βˆΆ
This consists of two wheels of different radii on the same axis. The axle has the same attachment on the wheel.
The effort is applied to the wheel and a string attached to the axle raises the load.

image 271
For a complete turn or rotation;

The effort moves through a distance equal to the circumference of the wheel.𝐂=πŸπ›‘π‘, R= radius of wheel.

The load moves through a distance equal to the circumference of the axle. 𝐂=πŸπ›‘π«, r= radius of axle.

Thus from;

image 272

Example1:
The figure below shows a wheel land axle system, which uses an effort of 300N to raise a load of 900N using an axle of radius 10cm.

image 273

Calculate the; (i) velocity ratio
(ii) Efficiency of the system

Solution:

image 274

Example2:
A wheel and axle machine is constructed from a wheel of diameter 20cm and mounted on an axle of diameter 4cm.

(a) Calculate the;
(i) Velocity ratio of the machine
(ii) Greatest possible value of mechanical advantage.
(b) Explain why the mechanical advantage is likely to be less than this value.

image 275

(a)(ii)
For the greatest (or maximum) mechanical advantage, the system is 100% efficient.
Hence M.A=V.R= 5

(b) The M.A is likely to be less than 5 because work needs to be done against friction

Example3:
A common windlass is used to raise a load of 480N by application of an effort 200N at right angles to the handle. If the crank is33cm from the axis and the radius of the axle is 11cm, calculate the;
(i) Velocity ratio. (Ans: V.R=3)
(ii) Efficiency of the windlass. (Ans: Ξ· =80%)

(𝐜) 𝐆𝐄𝐀𝐑 π’π˜π’π“π„πŒ:

A gear is device consisting of toothed wheels.
These are rigidly fixed to the axis and turn with their axis.

image 20

They change direction and speed of rotation when the effort applied is not changed.
The direction of the driven gear is opposite to that of the driving gear.
The number of rotations of the gear wheels depends on the ratio of number of teeth and the radii of the wheels.

The effort and the load are applied on the shafts connected to the gear wheels. A large V.R is obtained only when the effort is applied on a small gear so that it drives the large gear.

image 21

Example 1:

Two gearwheels A and B with 20 and 40 teeth respectively lock into each other. They are fastened on axles of equal diameters such that a weight of 400N attached to a string wound around one-axle, raises a load of 600N attached to a string wound around the other axle.

Calculate the:
(a) Velocity ratio of the system when; (i) A drives B
(ii) B drives A
(b) Efficiency when; (i) A drives B
(ii) B drives A

Solution:
(a) N=40cm, n=20cm
L=600N, E=400N

image 22
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Example 2:

image 24
Two gear wheels P and Q with 80 and 20 teeth respectively, lock each other. They are fastened on axles of equal diameters such that a weight of 150 N attached to a string wound around one-axle raises a load of 450N attached to a string wound around the other axle. Calculate the;
(i) Velocity ratio of the gear system. (Ans: V.R=4)
(ii) Efficiency of the system. (Ans: Ξ· =75%)

Example: 3
Two gear wheels P and Q with 25 and 50teeth respectively lock into each other. They are fastened on axles of equal diameters such that a weight of 400N attached to the string wound around one axle raises a load of 600N attached to a string wound around the other axle. Calculate the:
(i) Velocity ratio and efficiency when Q drives P.
[Ans: V.R = 0.5, Efficiency = 300%]
(ii) Velocity ratio and efficiency when P drives Q.
[Ans: V.R = 2, Efficiency = 75%]

(𝐝) 𝐒𝐂𝐑𝐄𝐖 πŒπ€π‚π‡πˆππ„βˆΆ

A screw is a nail or bolt with threadlike windings.
It is like a spiral stair case.
It is an essential feature of machines like the vice and the screw jack.

image 25

The distance between any two successive threads of a screw is called a Pitch.
An effort is applied on a handle like in a vice or in a car jack.
For a complete turn (or rotation) of the effort, the load moves through a distance equal to 1pitch while the effort moves a distance equal to the circumference of the handle

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Example 1:
In a screw jack, the length of the handle is 56cm and a pitch of 2.5mm. It is used to raise a load of 2000N. Calculate the;
(i) Effort required to raise the load. (Ans: E = 1.42N).
(ii) V.R (Ans: V.R = 1408).
(iii) Efficiency of the screw, hence explain the significance of your value of efficiency. (Ans: Ξ· =100%)

Example 2:
A load of 800N is raised using a screw jack whose lever arm is 49cm has a pitch of 2.5cm.If it is 40% efficient, Find the
(i) V.R
(ii) M.A

Example 3:
A certain screw machine has a pitch of 3.5mm. The effort is applied using a handle, which is 44cm long. Calculate its velocity ratio. (Ans: V.R = 3.95)

Example 4:
A screw jack with a lever arm of 56 cm, has threads which are 2.5mm apart is used to raise a load of 800N. If its 25% efficient, find the;

(i) Velocity ratio (Ans: V.R = 1408)
(ii) Mechanical advantage (Ans: M.A = 352)
Solution:
(a) Radius (lever arm),l =56cm, Pitch of a screw =2.510 = 0.25cm
L= 800N.

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(𝐞) πˆππ‚π‹πˆππ„πƒ 𝐏𝐋𝐀𝐍𝐄

An inclined plane is a slope, which allows a load to be raised more gradually by using a smaller effort than when lifting vertically upwards.

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Example:
A load of 400N is pulled along an inclined plane as shown below.

image 29
Calculate the;
Solution:
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Practice Question:

  1. A wooden plank, 3m long is used to raise a load of 1200N through a vertical height of 60cm. If the friction between the load and the plane is40N, calculate the:
    (i) effort required [Ans: E = 280N]
    (ii) Mechanical advantage [Ans: M.A = 4.29]
  2. In the gear system in figure 3 below N1 and N2 are the number of teeth on the wheels. The efficiency of the gear system is 60%.
image 32

Find the;
(i) Velocity Ratio.
(ii) Load that can be raised by an effort of 200N.
(iii) Explain why its preferred to use a longer ladder to a shorter ladder when climbing a tree.