WORK, ENERGY AND POWER
4.0
BB101 ENGINEERING SCIENCE
WORK, ENERGY AND POWER
By the end of this lesson, the students should be able to:
4.1
Define work, energy and power and their unit. List types of energy and their unit Solve the calculation problem using the formula work, energy and power.
Define Work, Energy And Power
Work Work done by a constant force is given by the product of the force and the distance moved in the direction of the force. The unit of Nm(Newton Nm(Newton metre) or J(Joule). Work is a scalar quantity.
Equation of Work
When the direction of force and motion are same, θ = 0°, therefore cosθ = 1 Work done, W = F × s
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WORK, ENERGY AND POWER
BB101 ENGINEERING SCIENCE
Example 1
A force of 50 N acts on the block at the angle shown in the diagram. 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 Example 2
Diagram above shows a 10N force is pulling a metal. If the distance travelled by the metal block is 2m, 2m, find the work done by the pulling force. Asnwer: The force is in the same direction of the motion. Work done by the pulling force, W = F × s = (10)(2) = 20J Example 3:
Diagram A:
W = 100 x 5 x cos0 = 500 J
Diagram B:
Diagram C:
W = 100x5 x cos30 = 433 J W = 147x5 x cos0 = 735 J
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WORK, ENERGY AND POWER
BB101 ENGINEERING SCIENCE
Work Done Against the Force of Gravity
Example 3 Ranjit runs up a staircase of 35 steps. Each steps is 15cm in height. Given that Ranjit's mass is 45kg, find the work done by Ranjit to reach the t op of the staircase. 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 Defination of Energy
Energy is defined as the capacity to do work. The SI unit of energy energy is the same as the unit of work, which is the Joule, (J). Energy has many different forms and can can be converted from one form to other. For example, an electrical motor converts electrical energy to kinetic energy. Work is done when energy energy is converted converted from one form to other. For example, example, chemical energy in petrol is converted to heat energy which in turn operates the engine to enable it to move. In some physics calculations, we also can state (supposing) (supposing) the amount of of energy is equal to work we have done :
Defination of Power Power is the time rate at which work which work is done or energy energy is transferred. Power is a measure of how quickly quickly work is done. The SI unit of power is the watt (W) or joule per second (J/s). One watt watt is equal about 1 joule per second. Horsepower is a unit of power in the British system of measurement. One horsepower is equal to about 746 W. Power is scalar scalar quantity. Power is defined as the rate at which work is done in a certain amount of time.
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WORK, ENERGY AND POWER
BB101 ENGINEERING SCIENCE
Example calculation: You’re riding a toboggan down an icy run to a frozen lake, and you accelerate the 80 kg combination of you and the toboggan from 1 m s-1 to 2 m s-1 in 2 s. How much power does that require? ,
,
Example calculation: A crane lifts a heavy bucket to a height of 2.5m from the ground in 3.5s. a) Calculate the power power generated by the crane in lifting the the bucket in 840kg. 840kg. b) Explain why the power generated by the crane is actually higher higher than the 2 value calculated calculated in (a). [Given g = 9.81m/s ] (a) Power,
P = mgh ,
Power =
840 x 9.81x 2.5 3.5
t = 5880 W
(b) This is because besides lifting the bucket, work also done to overcome frictional forces between the cable and the pulley and others part of crane. 4.2 Kinetic Energy & Potential Energy Kinetic Energy 1. Kinetic energy is the energy possessed by an object due to its motion. 2. All moving object possess possess kinetic energy 3. The kinetic enegy enegy of a moving moving object depends depends on its mass and speed. In symbols: EK = (½)mv2 Equation of Kinetic Energy
Example Calculation: How much kinetic energy does an object have if its mass is 5.0 kg and it is moving at a speed of 4.0 m/s? EK = (1/2)mv (1/2)mv
Formula Formula for kinetic kinetic energy. energy.
EK = (1/2)(5.0 kg)(4.0 m/s)2
Plug in values for mass and speed.
EK = 40 J
Kinetic Energy equals 40 J.
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WORK, ENERGY AND POWER
BB101 ENGINEERING SCIENCE
Potential Energy 1. Potential energy is the energy possessed by an object due to its position or state. 2. Potential energy can be classified classified into gravitational gravitational potential energy and elastic potential energy. 3. The gravitational potential potential energy of an object depends depends on its mass, mass, height and the gravitational field, Ep = mgh.
Example Calculation: What is the gravitational potential energy for a 4 kg object that is lifted 5 m? Ep = mgh
Formula for gravitational potential energy.
Ep = (4 kg)(9.8 m/s/s)(5 m)
Plug in values for mass, acceleration due to gravity, and height.
Ep = 196 J
Gravitational potential energy equals 196 Joules.
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WORK, ENERGY AND POWER
BB101 ENGINEERING SCIENCE
4.2 Principle Of Conservation Of Energy The principle of conservation of energy states energy states that energy can neither be created nor destroyed, but can be converted from one form to another. This principle implies that the total amount of energy in a closed system remain constant.:
Even though, some of the conservation of energy not only depends by using kinetic energy and potential energy formula only. It also can be use by variety of formula to calculate other energy using its own formula of energy. For example, if an object produce heat when in motion its can be calculate by using heat energy and kinetic energy formula by applying conservation of energy principle. But, in this topic s tudent just stu dy the kinetic energy and potential energy only.
Example: Diagram below shows a coconut is falling from a certain height to the ground.
P Q
R
At which position, P, Q or R, the coconut coconut has the highest gravitational gravitational potential energy? Example calculation: During a basketball game, a 1.0 kg ball gets thrown vertically in the air. It’s momentarily stationary at a height of 5.0 m and then falls back down. What is the ball’s speed when it hits the floor?
,
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WORK, ENERGY AND POWER
BB101 ENGINEERING SCIENCE
Examples Calculation: If you jump out of an airplane at 2000 m height and fall 1000 m before opening your parachute. What is your speed (neglecting air resistance) when you open your parachute? , ,
,
4.3 The efficiency Of Mechanical Mechanical System Efficiency is Efficiency is a comparison of the useful work energy provided by a machine or system to the work energy applied to the machine or system. 1. Machine are are devices devices that make our work easier. easier. 2. Machine require energy to work. This energy energy is called called the input. input. 3. A machine transforms this input into other forms of energy to perform useful works. 4. However, the useful useful work obtained is not equal to the input input as there is energy lost in this processs. This loss is mainly due to work done against frictional forces and takes the form of heat. Formula for efficiency is:
Efficiency =
P ou t
x100%
P in
Example calculation: A petrol engine has a work outpout of 96 kJ per minute. What is the power if the engine efficiency is 20%? Solution
Power output output = 96000 J/ 60 s = 1600 Watt Efficiency =
P out P in
x100%
20%
= (1600/Pin)x 100%
Power input, P in = 160000/20 = 8000 Watt
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WORK, ENERGY AND POWER
BB101 ENGINEERING SCIENCE
Example calculation: An electrical motor has an input power of 120W. 120W. it lifts a 20kg load to a vertical height of 1.5m in 5s. What is the efficiency of the electrical motor? Given g = 9.81m/s2 Solution
Input power = 120W Useful output power = P = mgh ,
Power
=
20 x 9.81x 1.5 5
t = 58.80W
Efficiency = Useful Output Power
X 100%
Input Power = 58.8 X
100%
120
= 49%
Tutorial 1 (work) a) How much work is done in raising a 2 kg book from the ground to a height of 1.8 m? b) In raising a 200 kg bronze statue 10 000 J of work work is performed. How height is it raised? c) You’re pushing an out-of-gas out -of-gas car down the road, applying a force of 800.0 N. How much work have you done in moving the car 10.0 m? d) You’re pulling a chest of drawers, applying a force of 60.0 N at an angle of 60.0°. How much work do you do pulling it over 10.0 m? e) You’re pushing a box of dishes across the kitchen floor, using 100.0 J to move it 10.0 m. If you apply the f orce at 60.0°, what is the force you used? Tutorial 2 (Energy) a) You’re ice skating and travelling travelling at 30 m s-1. If your mass is 65 kg, what is your kinetic energy? b) Determine the kinetic energy of a 1000 kg roller coaster car that is moving with a speed of 20.0 m s-1. c) A 1.5 kg book is held 60 cm above a desk whose whose top is 70 cm above the floor. Find the potential energy of the book: i. With respect above to the desk ii. With respect above to the floor d) How much much work must must be done to raise an 1100 kg car 2 m above the ground? ground? What is the car’s potential energy afterward? e) A 70 kg object is raised to a height of 40 m above the ground. i. How much work is done? ii. What is its potential potential energy? iii. If the object is dropped, what will its kinetic energy just before it strikes the ground? f) A 40 kg box of books books falls off a shelf shelf that’s 4 m above the ground. How fast is the box travelling when it hits the ground? g) A ball with mass 500g is falling from the top of the building. If the height height of the building is 250 m. What is t he final velocity before it reaches the ground? h) A metal block with mass 50 kg is being dropped onto a pile to build a tall building. The height of the metal block from the pile is 20 m. Calculate: (i) Weight of the metal block. (ii) Velocity of the metal block just before it hits the pile.
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WORK, ENERGY AND POWER
BB101 ENGINEERING SCIENCE
Tutorial 3 (Power & Efficiency) a) A 1000 kg car accelerates from 88 m s-1 to 100 m s -1 in 30 sec. How much power does that require? b) You’re driving a snowmobile that accelerates from 10 m/sec to 20 m/sec over a time interval of 10.0 sec. If you and the snowmobile together have a mass of 500 kg, how much power is used? c) A certain tractor is said to be capable of pulling with a steady force of 14 KN while moving at a speed of 3 m/s. How much power in kilowatts and in horse power is the tractor developing under these conditions? d) One hydraulic cylinder gives 2000 watt watt of power and a 550 N of force. Find the velocity of the piston in m/s. e) An inclined plane of length 10 m is used to raise a load of 500N by 1.0 m. If the force used to pull the load along the inclined plane is 100 N, calculate the effiency of the inclined plane.
Answer: 4.1.1 EXERCISES (work) a) W = 35.316 Joule Joule b) h = 5.10 m c) W = 8000 Joule Joule d) W = 300 Joule e) Force = 20.0 N 4.2.1 EXERCISES (energy) a) 29250 Joule b) 200 kJoule c) i) 8.829 Joule
ii) 10.30 Joule
d) Work = 21582 Joule, Potential energy = 21582 Joule e) Work done = 27468 Joule , Potential energy= 27468 Joule f) v= 8.86 ms-1 g) 70.8 m/s h) (i) 500N 4.2.2
(ii) 20 m/s
EXERCISES (Power & Efficiency)
a) 37600 Watt b) 7500 Watt c) 42000 Watt. 56.3 horsepower horsepower d) v= 3.64 ms-1 e) Efficiency = 50% Minimum requirement assessment task for this topic:
1 Theory Test & 1 End Of Chapter Specification of Theory Test : CLO1 - C1 & CLO3 – (C2, A1) Specification of End Of Chapter: CLO3 - (C2,A1) ****************************** ******************************************** ****************************** ****************************** **************************** **************** COURSE LEARNING OUTCOME (CLO) Upon completion of this topic, students should be able to: 1. 2.
Identify Identif y the basic concept of work, energy and power, (C1) Apply the concept of work, energy and power in real basic engineering problems. (C2,A1)
Compliance to PLO : PLO1 , LD1 (Knowledge) – Test 1 PLO4, LD4 (Critical Thinking and Problem Solving Skills) – Test 1, End Of Chapter 1
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BB101 ENGINEERING SCIENCE
5.
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