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Forces and Motion

2.12.5 Factors that Affect the Elasticity Springs

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Arrangement in series: Arrangement in parallel:
Extension = x × number of spring
Stiffness decreases
Spring constant = k/number of spring		 Extension = x ÷ number of spring
Stiffness increases
Spring constant = k × number of spring

Factors Affecting the Stiffness of Spring

Material type of spring

(A steel spring is stiffer than a copper spring)
Stiffer Less Stiff

Diameter of wire of spring

(The greater the diameter of the wire, the stiffer the spring)
Stiffer Less Stiff

Diameter of the spring

(The smaller the diameter of spring, the stiffer the spring)
Stiffer Less Stiff

Length of the string

(Shorter spring is stiffer)
Stiffer Less Stiff

 

2.12.4 Elastic Potential Energy

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Elastic Potential Energy

Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing.

Formula:


Example:


Diagram above shows a spring with a load of mass 0.5kg. The extention of the spring is 6cm, find the energy stored in the spring.

 Answer:
The energy stored in the spring is the elestic potential energy.


 

2.12.2 Hooke’s Law

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Hooke's Law states that if a spring is not stretched beyond its elastic limit, the force that acts on it is directly proportional to the extension of the spring.

Elastic Limit

The elastic limit of a spring is defined as the maximum force that can be applied to a spring such that the spring will be able to be restored to its original length when the force is removed.

Equation derived from Hooke's Law

From Hook's Law, we can derived that

Spring Constant

Spring constant is defined as the ratio of the force applied on a spring to the extension of the spring.

It is a measure of the stiffness of a spring or elastic object.

Graph of Streching Force - Extension

Gradient = Spring constant

Area below the graph = Work done

F-x graph and spring constant

The higher the gradient, the greater the spring constant and the harder (stiffer) spring.

For example, the stiffness of spring A is greater than spring B.

 

2.12.1 Elasticity

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Elasticity is the ability of a sub-stance to recover its original shape and size after distortion.

Forces Between Atoms

The intermolecular forces consist of an attractive force and a repulsive force.

  • At the equilibrium distance d, the attractive force equal to the repulsive force.
  • If the 2 atoms are brought closer, the repulsive force will dominate, produces a net repulsive force between the atoms.
  • If the 2 atoms are brought furhter, the attractive force will dominate, produces a net attractive force between the atoms.

Graph of Forces Between 2 atoms


x0 = Equilibrium Distance

When the particles are compressed, x < x0, the attractive force between the particles increases.

If the distance x exceeds the elastic limit, the attractive force will decreases.

 

2.11.7 Efficiency

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The efficiency of a device is defined as the percentage of the energy input that is transformed into useful energy.


Example:
In the example above, the input power is 100J/s, the desire output power (useful energy) is only 75J/s, the remaining power is lost as undisire output. Therefore, the efficiency of this machine is

Air Conditioner

  1. Switch off the air conditioner when not in use.
  2. Buy the air conditioner with suitable capacity according to the room size.
  3. Close all the doors and windows of the room to avoid the cool air in the room from flowing out.

Refrigerator

  1. Always remember to close the door of refrigerator.
  2. Open the refrigerator only when necessarily.
  3. Always keep the cooling coil clean.
  4. Defrost the refrigerator regularly.
  5. Choose the refrigerator with capacity suitable for the family size.
  6. Refrigerator of large capacity is more efficient compare with refirgerator of small capacity.

Lamp or Light Bulb

  1. Use fluorecent bulb rather than incandescent bulb. Fluorescent bulbs are much more efficient than incandescent bulbs.
  2. Use a lamp with reflector so that more light is directed towards thr desirable place.

Washing Machine

  1. Use front-loading washing machine rather than top-loading wahing machine because it uses less water and electricity.
  2. Use washing machine only when you have sufficient clothes to be washed. Try to avoid washing small amount of clothes.

 

2.11.6 Power

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Power is the rate at which work is done, which means how fast a work is done.

It is also a measure of how fast a form energy is converted to another form.

Formula:


Example:
An electric motor takes 20 s to lift a box of mass 20kg to a height of 1.5 m. Find the amount of work done by the machine and hence find the power of the electric motor.

 Answer:
Work done,
W = mgh = (20)(10)(1.5) = 300J

Power,


 

2.11.5 Conservation of Energy

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During a conversing of energy,

Amount of Work Done = Amount of Energy Converted

Example:
A trolley of 5 kg mass moving against friction of 5 N. Its velocity at A is 4ms-1 and it stops at B after 4 seconds. What is the work done to overcome the friction?

 Answer:
In this case, kinetic energy is converted into heat energy due to the friction. The work done to overcome the friction is equal to the amount of kinetic energy converted into heat energy, hence



 

2.11.4 Gravitational Potential Energy

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Gravitational potential energy is the energy stored in an object as the result of its vertical position (i.e., height).

Formula:


Example:
A ball of 1kg mass is droppped from a height of 4m. What is the maximum kinetic energy possessed by the ball before it reached the ground?

 Answer:
According to the principle of conservation of energy, the amount of potential energy losses is equal to the amount of kinetic energy gain.

Maximum kinetic energy
= Maximum potentila energy losses
= mgh = (1)(10)(4) = 40J

 

2.11.2 Energy

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  1. Energy is defined as the capacity to do work.
  2. Work is done when energy is converted from one form to another.
  3. The unit of is the same as the unit of work, which is Nm or Joule (J)
  4. In SPM, we need to know the calculation related to the kinetic energy and potential energy.