Power
Power is the rate at which work is done, which means how fast a work is done.
Formula:
Example 1
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,
\[ P = \frac{W}{t} = \frac{{300}}{{20}} = 15J\]
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
\[\begin{array}{l}{\rm{Work Done}} \\{\rm{ = Kinetic Energy Loss}} \\= \frac{1}{2}mv_1^2 - \frac{1}{2}mv_2^2 \\{\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}(5)(4)^2 - \frac{1}{2}(5)(0)^2 \\= 40J \\\end{array}\]
Energy
Energy is defined as the capacity to do work. Work is done when energy is converted from one form to another.
Nm or Joule(J)
Gravitational Potential Energy
Gravitational potential energy is the energy stored in an object as the result of its vertical position (i.e., height).
Formula:
Example 1
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
Elastic Potential Energy
Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing.
Formula:
Example 2
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.
\[ E_P = \frac{1}{2}Fx \hfill \\ \]
\[ E_P = \frac{1}{2}(5)(0.06) = 0.15J \hfill \\ \]
Kinetic Energy
Kinetic energy is the energy of motion.
Equation of Kinetic Energy
Example 1
Determine the kinetic energy of a 2000-kg bus that is moving with a speed of 35.0 m/s.
Answer:
Kinetic Energy,
Work
When the direction of force and motion are same, θ = 0o, therefore cosθ = 1
Work done,
W = F × s
A force of 50 N acts on the block at the angle shown in the diagram. The block moves a horizontal distance of 3.0 m. Calculate the work being done by the force.
Answer:
Work done,
W = F × s × cos θ
W = 50 × 3.0 × cos30o = 129.9J
Diagram above shows a 10N force is pulling a metal. The friction between the block and the floor is 5N. If the distance travelled by the metal block is 2m, find
Asnwer:
(a) The force is in the same direction of the motion. Work done by the pulling force,
W = F × s = (10)(2) = 20J
(b) The force is not in the same direction of motion, work done by the frictional force
W = F × s × cos180o= (5)(2)(-1) = -10J
Answer:
In this case, Ranjit does work to overcome the gravity.
Ranjit's mass = 45kg
Vertical height of the motion, h = 35 × 0.15
Gravitational field strength, g = 10 ms-2
Work done, W = ?
W = mgh = (45)(10)(35 × 0.15) = 2362.5J
In a Force-Displacement graph, work done is equal to the area in between the graph and the horizontal axis.
The graph above shows the force acting on a trolley of 5 kg mass over a distance of 10 m. Find the work done by the force to move the trolley.
Answer:
In a Force-Displacement graph, work done is equal to the area below the graph. Therefore, work done
