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YOUR STUDY SPACE · CBSE

Work, Energy, and Simple Machines — Class 9 Science

Exploration · Chapter 7

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Chapter summary

This chapter gives the scientific meanings of work, energy and power and links them through energy conservation, then introduces simple machines. In science, work is done only when a force moves an object along its direction: , measured in joules (J); no work is done if there is no displacement or if the force is perpendicular to the motion. Energy is the capacity to do work, also measured in joules. Kinetic energy is the energy of motion, , while gravitational potential energy is the energy of position, . The law of conservation of energy states that energy can neither be created nor destroyed but only transformed; for a freely falling or sliding body the sum of kinetic and potential energy stays constant, which is why two children of different masses reach the bottom of the same frictionless slide with the same speed. Power is the rate of doing work, , measured in watts (W); commercial electrical energy is sold in kilowatt-hours (units). Simple machines — the lever, pulley, inclined plane, wheel and axle, wedge and screw — do not create energy but make work easier by changing the size or direction of the effort needed, illustrating mechanical advantage in everyday tools.
Scientific meaning of workKinetic and potential energyConservation and transformation of energyPower and commercial energy (kWh)Simple machines and mechanical advantage

Key ideas & terms

Work
Done when a force moves an object along its own direction, ; measured in joules (J).
Kinetic energy
The energy possessed by a body because of its motion, .
Potential energy
The energy possessed by a body because of its position or configuration, e.g. gravitational .
Law of conservation of energy
Energy can neither be created nor destroyed, only changed from one form to another; the total stays constant.
Power
The rate of doing work or transferring energy, ; measured in watts (W).
Simple machine
A device such as a lever, pulley or inclined plane that makes work easier by changing the magnitude or direction of the effort.

Extra questions & answers

When is work said to be done in science?

Work is done only when an applied force produces a displacement of the object along the direction of the force; if there is no displacement, no work is done.

Write the formula for work and its SI unit.

Work , where F is force and s is displacement along the force; its SI unit is the joule (J).

Give an example where a force acts but no work is done.

A person holding a heavy bag while standing still applies an upward force, but since there is no displacement, the work done is zero.

Write the expressions for kinetic and potential energy.

Kinetic energy is (energy of motion) and gravitational potential energy is (energy of position at height h).

State the law of conservation of energy.

Energy can neither be created nor destroyed; it only changes from one form to another, and the total energy of an isolated system remains constant.

Why do two children of different masses reach the bottom of the same frictionless slide with the same speed?

Because all the potential energy converts to kinetic energy ; the mass cancels, giving , which is the same for both regardless of mass.

Define power and give its SI unit.

Power is the rate of doing work, ; its SI unit is the watt (W), where one watt is one joule per second.

What is a kilowatt-hour?

It is the commercial unit of electrical energy equal to the energy used by a 1 kilowatt appliance in 1 hour; .

Do simple machines reduce the total work needed?

No — they cannot create energy; they make a task easier by changing the size or direction of the effort, but the total work done (ignoring friction) is unchanged.

Name some simple machines and one use of a lever.

Lever, pulley, inclined plane, wheel and axle, wedge and screw; a lever such as a crowbar lets a small effort lift a heavy load by acting about a fixed pivot (fulcrum).

Think It Over

What will be the magnitude of velocity of the child at the bottom of the blue slide?

If friction is neglected the mechanical energy is conserved. Let be the vertical height of the top of the blue slide above the bottom. At the top and . At the bottom and . So and . The magnitude depends only on the vertical height and , not on the shape of the slide. Without a numerical value of the answer is given by this expression.

Will two children of different masses reach the bottom of the same slide with the same velocity?

Yes, if friction and air resistance are neglected. From the mass cancels to give . Both children start from the same height so they arrive with the same speed magnitude, although the heavier child has more kinetic energy . With friction the lighter child may be slowed a little more.

Which of the slides will result in the largest magnitude of velocity for the child at its bottom?

The slide with the greatest vertical height will give the largest speed at the bottom, because . For frictionless slides the shape, length or curvature does not matter, only the vertical drop. So the highest starting point produces the largest .

Pause and Ponder

1. In the previous chapter, a weightlifter is shown holding a barbell steady in her hands (Fig. 6.8). Is she doing any work on the barbell while holding it steady?

No work is done on the barbell in the scientific sense. Work requires displacement in the direction of the force, . Here the barbell is steady so , therefore . The weightlifter feels tired because her muscles use internal chemical energy to maintain the force, but no mechanical work is done on the barbell.

2. Is the work done by friction on the stack of coins that travels on a rough surface (Fig. 6.13c) — positive, negative or zero?

Negative. Friction acts opposite to the displacement of the coins. Since the force and the displacement are in opposite directions, the work with taken opposite to is negative, so friction removes kinetic energy from the coins.

Pause and Ponder

3. When you pedal a bicycle on a flat road, your muscles supply energy. In what forms does this muscular energy appear as you ride?

The chemical energy from muscles is transformed mainly into kinetic energy of the bicycle and rider, and work done against opposing forces. A large part becomes thermal energy due to friction in the chain, bearings, tyres and air resistance, and heat in the body, plus a small amount as sound energy. If you gain speed, kinetic energy increases; at steady speed the supplied energy continually replaces energy lost as heat and sound, so total mechanical energy does not accumulate.

Pause and Ponder

4. Two objects A and B of mass m and 4 m have the same kinetic energy. What is the ratio of the magnitude of velocities of A and B?

Let . Canceling gives so . Hence and . The lighter object must move twice as fast to have the same kinetic energy.

5. Does the kinetic energy of an object which moves with constant velocity change with its position?

No. Kinetic energy is and depends only on mass and speed magnitude. If is constant in magnitude and direction, remains constant, even though the position changes. Only if speed changes does change.

Pause and Ponder

6. Does the potential energy of an object near the surface of the Earth change if it moves with constant velocity in the horizontal direction? What if the object is gradually raised in the vertical direction?

Gravitational potential energy near the surface is where is vertical height. Moving horizontally at constant velocity leaves unchanged, so does not change. Raising the object vertically increases , so increases by . Work has to be done against gravity, which is stored as increased potential energy.

Pause and Ponder

7. For the situation depicted in Fig. 7.19, calculate the mechanical energy of the ball just before it hits the ground and show that even at this position, it is mgh.

At point A height , velocity : , , so . Let the ground be . Just before impact the velocity is where from . Then and . So total mechanical energy , same as at the top. Energy has been converted from potential to kinetic but total is conserved if air resistance is neglected.

8. You may have seen an exhibit like that in Fig. 7.22 in a science park, where a ball is released from the highest point. Describe how the kinetic energy and potential energy change at points A, B and C. Why do subsequent points, such as C, D and E, usually have lower heights compared to the previous ones? Could it have anything to do with the energy lost due to friction?

At A, the highest point, the ball has maximum and minimum speed, so is minimum, approximately zero if released from rest. As it rolls down to B, the lowest valley, decreases by and increases by the same amount, so is maximum at B. Climbing to C, is partly reconverted to , so decreases and increases, but not back to the value at A. Each successive peak C, D, E is lower because a part of mechanical energy is always lost as thermal energy and sound due to friction and air resistance. The work done against non-conservative forces is negative and reduces total mechanical energy, so the ball cannot rise to the original height again.

Pause and Ponder

9. Explain why roads on hills are built to wind around in gentle slopes rather than going straight up (Fig. 4.26)?

An inclined plane trades force for distance. To raise a load of weight to height the work needed is , independent of path if friction is neglected. Going straight up requires effort . On a gentle slope of length , the required effort along the slope is , which is smaller because . A winding road increases and decreases the slope angle, so vehicles need a much smaller tractive force, though they travel a longer distance. The mechanical advantage is .

10. To reach a higher floor, we find climbing an inclined ladder easier in comparison to climbing a vertical ladder (Fig. 7.30). Explain why.

The same reason as for an inclined plane. The vertical ladder requires lifting the body weight directly with a large force over a short distance . An inclined ladder of length lets you apply a smaller component of force along the ladder, , over the longer distance . The product is the same work, but the perceived effort at any instant is less, so it feels easier, even though total energy expended is essentially the same ignoring extra friction.

Pause and Ponder

11. Why is it easier to open the lid of a can by using a spoon as shown in Fig. 7.35?

The spoon acts as a lever of class I with the edge of the can as the fulcrum. The effort arm from the handle to the fulcrum is long, while the load arm at the lid edge is short. For a lever , so a small effort on the long arm creates a large force on the short arm to overcome the adhesion of the lid. The mechanical advantage makes it easier.

12. Why do you push an object closer to scissors (fulcrum) when you want to cut an object which is hard?

Scissors are a class I lever with fulcrum at the pivot. The effort is applied at the handles, load at the cutting point. Mechanical advantage is . Moving the hard object nearer the fulcrum reduces the load arm , so increases. The same hand force then produces a larger cutting force , sufficient to cut hard material.

13. Throughout history, many designs of perpetual machines (using wheels, weights or magnets) have been proposed but none actually work. Why do all real machines eventually slow down and stop? Explain in terms of work and energy.

In any real machine non-conservative forces like friction and air resistance do negative work. Mechanical energy is therefore not conserved; part of it is continuously converted into thermal energy and sound. Since machines cannot create energy, they cannot replace this loss without an external energy input. The total energy of the universe is conserved, but useful mechanical energy decreases. Eventually becomes zero and the machine stops. A perpetual motion machine would need to produce work without energy input, which violates the work-energy theorem and conservation of energy.

Revise, Reflect, Refine

1. State whether True or False. (i) Work is said to be done when a force is applied, even if the object does not move. (ii) Lifting a bucket vertically upward results in positive work done on the bucket. (iii) The SI unit for both work and energy is joule (J). (iv) A motionless stretched rubber band has kinetic energy. (v) Energy can change from one form to another.

(i) False. Work requires displacement in the direction of force, . If , . (ii) True. Applied upward force and upward displacement are in same direction, so work is positive. (iii) True. Both work and energy are measured in joule, . (iv) False. A motionless object has so ; a stretched band has potential energy, not kinetic. (v) True. Energy can be converted, e.g., electrical to light and heat, chemical to mechanical.

2. Fill in the blanks. (i) Work done = ______ × ______ (in the direction of force). (ii) 1 joule of work is done when a force of ______ newton displaces an object by 1 metre in the direction of the force. (iii) The expression for kinetic energy of a body of mass m and velocity v is ______. (iv) The potential energy of an object of mass m at a small height h from the Earth’s surface is ______. (v) Power is defined as the ______ at which work is done.

(i) Work done = force displacement in the direction of force, . (ii) 1 newton. . (iii) . (iv) . (v) Power is defined as the rate at which work is done, .

3. When a ball thrown upwards reaches its highest point, tick which of the following statement(s) are correct? (i) The force acting on the ball is zero. (ii) The acceleration of the ball is zero. (iii) Its kinetic energy is zero. (iv) Its potential energy is maximum.

(i) Incorrect. Gravity still acts downward. (ii) Incorrect. Acceleration is downward, about . (iii) Correct. At the top instantaneous velocity so . (iv) Correct. With maximum, is maximum. For the ideal frictionless case mechanical energy is still .

4. For each of the following situations, identify the energy transformation that takes place: (i) a truck moving uphill, (ii) unwinding of a watch spring, (iii) photosynthesis in green leaves, (iv) water flowing from a dam, (v) burning of a matchstick, (vi) explosion of a fire cracker, (vii) speaking into a microphone, (viii) a glowing electric bulb, and (ix) a solar panel.

(i) Chemical energy of fuel to kinetic energy plus increase in gravitational potential energy and heat due to friction. (ii) Elastic potential energy of wound spring to kinetic energy of hands and then to thermal and sound energy. (iii) Light energy to chemical energy stored in glucose. (iv) Gravitational potential energy of water to kinetic energy of flowing water to electrical energy in turbines. (v) Chemical energy in match head to thermal and light energy. (vi) Chemical energy of explosive to kinetic, thermal, light and sound energy. (vii) Sound energy to electrical energy plus small thermal loss. (viii) Electrical energy to light energy and thermal energy. (ix) Light energy to electrical energy and then typically to chemical energy in battery or electrical work.

5. A student is slowly lifted straight up in an elevator from the ground level to the top floor of a building. Later, the same student climbs the staircase, all the way to the top. Given that the height of the building is h = 72.5 m, acceleration due to gravity is g = 10 m s–2, and student’s mass is m = 50 kg. (i) Find the gain in the potential energy if the student is lifted straight up to the top. (ii) Find the gain in the potential energy when the student climbs the stairs to the same top. (iii) What do you conclude about the dependence of the potential energy on the path taken?

(i) . (ii) The same, . The stair path is longer, but vertical height gained is still , so gravitational potential energy change depends only on . (iii) Gravitational potential energy is path independent. It depends only on the initial and final vertical positions, not on the route taken. The extra distance on stairs means work is done over longer distance with smaller average force, and more energy is wasted as heat, but stored is identical.

6. A crane lifts a mass m to the 10th floor of a building in a certain time. It then raises the same mass to the 20th floor of the same building in double the time. How much more energy and power are required? Assume that the height of all floors is equal.

Let height per floor be . First lift height , energy . Second lift height , energy . So twice the energy is required in the second case. Let first time be , power . Second time , power . Thus energy doubles but average power is the same.

7. Which factors determine the energy required to raise a flag from the ground to the top of a tall flagpole using a pulley? Does raising the flag slowly or quickly change the amount of work done? If the speed at which the flag is raised is doubled, how does the power requirement change? Explain your answers.

Energy required is the increase in gravitational potential energy , so it depends on mass of flag , height of pole and . Ignoring friction, it is independent of speed. Work done is the same whether raised slowly or quickly if the final height is same and final kinetic energy is negligible. Power is . If speed is doubled, time halves for same , so doubles, because . A fixed pulley has mechanical advantage 1; it only changes direction, not energy required.

8. A man of mass 60 kg rides a scooter of mass 100 kg. He accelerates the scooter to a velocity v. The next day, his son with a mass of 40 kg joins him as a passenger. If the scooter reaches the same speed on both days in the same time interval, what is the ratio of the fuel of the tank used on the two days? Assume that the energy transfer to the scooter happens entirely due to fuel, and no other losses occur due to air resistance and friction.

Kinetic energy supplied equals fuel energy ideally. Day 1 total mass , . Day 2 total mass , . Ratio fuel used . So more fuel is used when son rides along. If ratio asked as day1:day2, it is .

9. On a seesaw with sliding seats, a child is sitting on one side and an adult on the other side. The adult weighs twice that of the child. The seesaw however is balanced. Draw a figure which depicts this situation showing the distances from the fulcrum where the child and the adult are seated.

For balance . Let child weight be , adult . Let child distance be and adult distance from fulcrum C. Then so . The child must sit twice as far from the pivot as the adult. For example, if adult is from C, child is on the opposite side. The figure would show a horizontal lever with fulcrum in middle, child on left at distance 2 units, adult on right at distance 1 unit, level balanced.

10. A ball of mass 2 kg is thrown up with a velocity of 20 m s–1. (i) Identify the sign of the work done by gravity on the ball during its upward motion and its downward motion. (ii) If the ball reaches a height of 19.4 m, how much work was done by air resistance (assume g = 10 m s–2).

(i) Gravity acts downward. On the way up displacement is upward, opposite to force, so work by gravity is negative: . On the way down displacement is downward, same as gravity, so work is positive: . (ii) Initial kinetic energy . Ideal maximum height without air resistance would be and ideal potential gain . Actual gain is . By work-energy theorem, change in mechanical energy equals work by air resistance: . About of energy is lost to air resistance on the way up.

11. A 10.0 kg block is moving on horizontal floor with negligible friction. As shown in the Fig. 7.37, a variable force is applied on the block in its direction of motion from its position at 0 m till 4 m. If the block had a kinetic energy of 180 J when it was at 0 m, find the block’s speed (i) at 0 m, and (ii) at 4 m. Does the block have negative acceleration in any portion of its motion?

(i) At , . So . (ii) Work done is area under graph. From the figure the force is about from to about then falls to zero and becomes negative? Estimated area up to is approximately the rectangular plus triangular area. Assuming typical triangular shape peaking at : work if triangular, or more if shape is rectangular for first 2 m. More generally . If , and . In any case . Negative acceleration would require net force opposite motion, i.e., negative . If the graph goes below zero after about , then in that interval is opposite or retarding and acceleration would be negative, so kinetic energy would decrease in that portion.

12. The gravitational attraction on the surface of the Moon (lunar surface) is about 1/6 th of that on the surface of the Earth. An astronaut can throw a ball up to a height of 8 m from the surface of the Earth. How far up will the ball thrown with the same upward velocity travel from the surface of the Moon?

On Earth . So . On Moon . With same , . The ball will rise about six times higher, about on the Moon, neglecting air resistance, which is absent on the Moon anyway.

13. A 1000 kg car is moving along a road at a constant speed. Suddenly, the driver notices some obstruction ahead and applies the brakes to come to a complete stop. The graphical representation of motion of the car starting from the instant the driver spots the traffic ahead is shown in Fig. 7.38. (i) Describe how the car moves between positions A and B. (ii) Calculate the kinetic energy of the car at A. (iii) State the work done by the brakes in bringing the car to a halt between B and C. (iv) What does the kinetic energy of the car transform into?

(i) Between A and B the speed-time graph is horizontal, so speed is constant. The car moves with uniform velocity, about , during the reaction time before brakes take effect. Distance covered is . (ii) At A , , . (iii) Between B and C speed drops to zero. Change in kinetic energy . By work-energy theorem work done by brakes equals , so . Negative sign indicates brakes do negative work, removing energy. (iv) The kinetic energy is transformed mainly into thermal energy in brake discs and tyres, plus sound energy and a small amount of heat due to air resistance.

14. The potential energy-displacement graph of a 0.5 kg ball moving along a frictionless track is shown in Fig. 7.39. At O, the velocity of the ball is 0 m s–1 and potential energy is 30 J. Calculate the velocity of the ball at P, Q and R.

Total mechanical energy is conserved and frictionless, so is constant. At O so and , hence everywhere. At P, Q, R read from graph: suppose , , as typical for such triangle. Then . So , . , . At R , , . If the graph values differ, use same formula with . Generally speed is largest where is smallest.

15. A coconut of mass 1.5 kg falls from the top of a coconut tree onto the wet sand on a beach. The height of the tree is 10 m. On impact, the coconut comes to rest by making a depression in the sand. (i) Calculate the velocity of the coconut just before it hits the sand. (ii) Assume that the average resistive force of sand is 3000 N and all of the coconut’s energy is used to create the depression in the sand. Calculate the depth of the depression the coconut makes in the sand. Assume g = 10 m s–2.

(i) Fall from height , using conservation so downward. (ii) Energy just before impact is or equivalently . Work done by sand to stop it is opposite displacement. By work-energy theorem . So . The depression is about deep.