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FORCE AND MOTION

2.10 : WORK, ENERGY, POWER AND EFFICIENCY. FORCE AND MOTION. WORK. Is defined as the product of the applied force and the distance moved in the direction of the force. Work = force x distance W = F x s SI unit is the Joule (J) Is a scalar quantity. No work done when:.

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FORCE AND MOTION

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  1. 2.10 : WORK, ENERGY, POWER AND EFFICIENCY FORCE AND MOTION

  2. WORK • Is defined as the product of the applied force and the distance moved in the direction of the force. • Work = force x distance • W = F x s • SI unit is the Joule (J) • Is a scalar quantity

  3. No work done when: • A force is applied but no displacement occurs. • An object undergoes a displacement with no applied force acting on it. • The direction of motion is perpendicular to the applied force.

  4. 3 SITUATION THAT INVOLVE WORK • Direction of force, F is same as the direction of displacement, s. W = F x s F F s

  5. Direction of force, F is not same as the direction of displacement, s. W = F cosθ x s W = F s cosθ F θ θ F F cos θ s

  6. Direction of force, F is perpendicular to the direction of displacement, s. W = F x s W = F cos 90° x s W = 0 F F s

  7. If a box is pushed with a force of 40 N and it moves steadily through a distance of 3m in the direction of the force, calculate the work done. Answer: W = 120 J Example 1

  8. A women pulls a suitcase with a force of 25 N at an angle of 60° with the horizontal. What is the work done by the women if the suitcase moves a distance of 8 m along the floor? Answer,: W = 100 J Example 2

  9. FORCE–DISTANCE GRAPH • Area under a force–distance graph = work done. Work = F x s = a x b Force, F a Distance, s b

  10. WORK DONE AGAINST THE FORCE OF GRAVITY • An upward force, F is applied to lift the object of weight, W to a height, h. • W = F x h • W = mgh F h W

  11. ENERGY • Is defined as potential or the ability to do work. • Form energy: • Gravitational potential energy • Kinetic energy • Heat energy • Sound energy • Electrical energy • SI unit in Joule, J and it scalar quantity. • Energy is transferred from 1 object to another when work is done.

  12. KINETIC ENERGY, Ek • Is a energy possessed by a moving object. • It scalar quantity. • SI unit in Joules, J. • Formula : • Ek = 1 mv2 2 • Ek = 1(mv2) – 1(mu2) 2 2 Object moving from initial velocity to final velocity

  13. POTENTIAL ENERGY, Ep • Defined as energy of an object due to its higher position in the gravitational field. • Depend on mass, gravitational field and height. • Formula: • Ep = mgh # m = mass # g = acceleration due to gravity # h = difference between height

  14. In a school sports event, a student of mass 40 kg runs past the finishing line with a velocity of 7 ms-1. Calculate his kinetic energy. Answer: Ek = 980 J Example 3

  15. Example 4 A durian fruit hanging from its branch has gravitational potential energy due to its higher position above the ground. The mass of the fruit is 2.5 kg and it hangs 3 m above the ground. What is the gravitational potential energy of the fruit? (g = 10 ms-2) Answer: Ep = 75 J

  16. PRINCIPLE OF CONSERVATION OF ENERGY • State that energy cannot be created or destroyed. • It can be transformed from one form to another. • The total energy in a system is constant. This means there is no energy gained or lost in a process. • Formula : mgh = 1mv2 2

  17. Example: • On winning a match, a tennis player hits a tennis ball vertically upward with an initial velocity of 25ms-1. What is the maximum height attained by the ball? (g = 10ms-2) • Answer ; • h = 31.25 m

  18. POWER • Is the rate at which work is done or rate at which energy is transformed. • Formula; Power, P = work done @ energy transformed time taken time taken P = W @ F x s @ F x s @ Fv t t t P = E t • SI unit is watt (W) or Js-1 • Is scalar quantity P ∞ W if t constant P ∞ 1 / t if work constant

  19. Example: • A weightlifter lifts 160kg of weights from the floor to a height of 2m above his head in a time of 0.8s. What is the power generated by the weightlifter during this time? (g = 10ms-2) • Answer : • P = 4000 W

  20. EFFICIENCY • The percentage of the input energy that is transformed to useful form of output energy. • Formula : efficiency = useful energy output x 100% energy input = Eo x 100% Ei

  21. Also can be calculated in terms of power. efficiency = useful power output x 100% power input = Po x 100% Pi

  22. Example: • An electric motor in a toy crane can lift a 0.12 kg weight through a height of 0.4m in 5s. During this time, the batteries supply 0.80 J of energy to the motor. Calculate • The useful energy output of the motor • The efficiency of the motor • Answer: • Eo = 0.48J • Efficiency = 60 %

  23. Exercise • A steel ball of mass 2 kg is released from a height of 8 m from the ground. On hitting the ground, the ball rebounds to a height of 3.2 m as shown in figure. If air resistance can be neglected and the acceleration due to gravity g = 10 ms-2, find • The kinetic energy of the ball before it reaches the ground. • The velocity of the ball on reaching the ground. • The kinetic energy of the ball as it leaves the ground on rebound. • The velocity of the ball on rebound. 8 m 3.2 m Ek =160 J v1 = 12.65 ms-1 Ek = 64 J v2 = 8 ms-1

  24. Exercise • A car moves at a constant velocity of 72 kmj-1. Find the power generated by the car if the force of friction that acts on it is 1500 N. • Answer : • P = 30000 W

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