Equation of WorkWhen the direction of force and motion are same, θ = 0o, therefore cosθ = 1 Work done, W=F×s The unit of Nm(Newton metre) or J(Joule). Example 1 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 work done by the frictional force W = F × s × cos180o= (5)(2)(-1) = -10J Work Done Against the Force of Gravity Example 3 Ranjit runs up a staircase of 35 steps. Work done by the pulling force. Each steps is 15cm in height. find the work done by Ranjit to reach the top of the staircase.Example 2 Diagram above shows a 10N force is pulling a metal. W = F × s = (10)(2) = 20J (b) The force is not in the same direction of motion. find the work done by the pulling force the work done by the frictional force Asnwer: (a) The force is in the same direction of the motion. If the distance travelled by the metal block is 2m. The friction between the block and the floor is 5N. Given that Ranjit's mass is 45kg. . 5J Finding Work from Force-Displacement Graph In a Force-Displacement graph. h = 35 × 0. W = ? W = mgh = (45)(10)(35 × 0. Example 4 The graph above shows the force acting on a trolley of 5 kg mass over a distance of 10 m.Answer: In this case.15 Gravitational field strength. Ranjit does work to overcome the gravity. Find the work done by the force to move the trolley. . Ranjit's mass = 45kg Vertical height of the motion.15) = 2362. g = 10 ms-2 Work done. work done is equal to the area in between the graph and the horizontal axis. Formula: Example 1 A ball of 1kg mass is droppped from a height of 4m.. height).Answer: In a Force-Displacement graph. work done is equal to the area below the graph. work done Kinetic Energy Kinetic energy is the energy of motion. What is the maximum kinetic energy possessed by the ball before it reached the ground? . Work is done when energy is converted from one form to another.e. Therefore. Equation of Kinetic Energy Example 1 Energy Energy is defined as the capacity to do work. 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. find the energy stored in the spring.Answer According to the principle of conservation of energy.5kg. the amount of potential energy losses is equal to the amount of kinetic energy gain. The extention of the spring is 6cm. 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. Find the amount of work done by the machine and hence find the power of the electric motor. hence Power Power is the rate at which work is done. Answer: . kinetic energy is converted into heat energy due to the friction.5 m. What is the work done to overcome the friction? Answer: In this case. which means how fast a work is done. Its velocity at A is 4ms-1 and it stops at B after 4 seconds. Amount of Work Done = Amount of Energy Converted Example A trolley of 5 kg mass moving against friction of 5 N. Formula: Example 1 An electric motor takes 20 s to lift a box of mass 20kg to a height of 1. The work done to overcome the friction is equal to the amount of kinetic energy converted into heat energy.Relationship between Energy and Work Done During a conversing of energy. Defrost the refrigerator regularly. the input power is 100J/s. Choose the refrigerator with capacity suitable for the family size. the remaining power is lost as undisire output. Use a lamp with reflector so that more light is directed towards thr desirable place. Washing Machine Use front-loading washing machine rather than top-loading wahing machine because it uses less water and electricity. Fluorescent bulbs are much more efficient than incandescent bulbs. Close all the doors and windows of the room to avoid the cool air in the room from flowing out. Therefore. Buy the air conditioner with suitable capacity according to the room size. Example In the example above. the desire output power (useful energy) is only 75J/s. Refrigerator of large capacity is more efficient compare with refirgerator of small capacity.Efficiency The efficiency of a device is defined as the percentage of the energy input that is transformed into useful energy. Open the refrigerator only when necessarily. Always keep the cooling coil clean. Lamp or Light Bulb Use fluorecent bulb rather than incandescent bulb. Refrigerator Always remember to close the door of refrigerator. . the efficiency of this machine is 75/100 x 100% = 75% Air Conditioner Switch off the air conditioner when not in use. Graph of Forces Between 2 atoms . At the equilibrium distance d. If the 2 atoms are brought closer. the attractive force will dominate. Forces Between Atoms The intermolecular forces consist of an attractive force and a repulsive force. Try to avoid washing small amount of clothes. the attractive force equal to the repulsive force.Use washing machine only when you have sufficient clothes to be washed. the repulsive force will dominate. produces a net attractive force between the atoms. If the 2 atoms are brought furhter. produces a net repulsive force between the atoms. Elasticity Elasticity is the ability of a sub-stance to recover its original shape and size after distortion. we can derived that Spring Constant . the attractive force between the particles increases. 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. the attractive force will decreases. Equation derived from Hooke's Law From Hook's Law. x < x0. Hooke's Law Hooke's Law states that if a spring is not stretched beyond its elastic limit. If the distance x exceeds the elastic limit. the force that acts on it is directly proportional to the extension of the spring.x0 = Equilibrium Distance When the particles are compressed. Spring constant is defined as the ratio of the force applied on a spring to the extension of the spring. Graph of Streching Force . It is a measure of the stiffness of a spring or elastic object.Extension Gradient = Spring constant Area below the graph = Work done F-x graph and spring constant . For example. Spring Arrangement in series: Extension = x × number of spring Arrangement in parallel: Extension = x ÷ number of spring . the greater the spring constant and the harder (stiffer) spring. the stiffness of spring A is greater than spring B.The higher the gradient. Stiffness decreases Spring constant = k/number of spring Stiffness increases Spring constant = k × number of spring Factors Affecting the Stiffness of Spring Stiffer Less stiff Material type of spring (A steel spring is stiffer than a copper spring) Diameter of wire of spring (The greater the diameter of the wire. the stiffer the spring) Length of the string (Shorter spring is stiffer) . the stiffer the spring) Diameter of the spring (The smaller the diameter of spring.