NCERT Solutions for Chapter 7: Work, Energy and Simple Machines
This page contains answers are designed to help students understand the answers of ncert questions of class 9 science chapter 7.
Revise, Reflect, Refine (Exercise Questions)
Question 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.
False. In physics, work requires both a force and a displacement (movement) in the direction of that force.
(ii) Lifting a bucket vertically upward results in positive work done on the bucket.
True. Because both the upward force applied and the displacement of the bucket are in the same direction, the work done is positive.
(iii) The SI unit for both work and energy is joule (J).
True. Both work and energy are measured using the joule (J).
(iv) A motionless stretched rubber band has kinetic energy.
False. A motionless stretched rubber band possesses elastic potential energy, not kinetic energy.
(v) Energy can change from one form to another.
True. This is the fundamental principle of the Law of Conservation of Energy.
Question 2. Fill in the blanks.
(i) Work done = ………………… × ……………………. (in the direction of force).
Force, displacement.
(ii) 1 joule of work is done when a force of ………………… newton displaces an object by 1 metre in the direction of the force.
1.
(iii) The expression for kinetic energy of a body of mass m and velocity v is …………… .
1/2 mv².
(iv) The potential energy of an object of mass m at a small height h from the Earth's surface is ………………… .
mgh.
(v) Power is defined as the ………………….. at which work is done.
rate.
Question 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.
(iii) True: At the highest point, the velocity is 0, so Kinetic Energy (KE) is zero.
(iv) True: All kinetic energy has been converted, so Potential Energy (PE) is at its maximum.
(Note: Statements i and ii are false because gravity and acceleration (g) still act on the ball).
Question 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 firecracker, (vii) speaking into a microphone, (viii) a glowing electric bulb, and (ix) a solar panel.
(i) Truck moving uphill: Kinetic energy turns into Potential energy.
(ii) Unwinding watch spring: Elastic Potential energy turns into Kinetic energy.
(iii) Photosynthesis: Light energy turns into Chemical energy.
(iv) Water from a dam: Potential energy → Kinetic energy → Electrical energy.
(v) Burning matchstick: Chemical energy → Thermal (heat) and Light energy.
(vi) Firecracker explosion: Chemical energy → Kinetic, Sound, Light, and Heat energy.
(vii) Speaking into microphone: Sound energy turns into Electrical energy.
(viii) Glowing electric bulb: Electrical energy turns into Light and Thermal energy.
(ix) Solar panel: Light energy turns into Electrical energy.
Question 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 ms⁻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) Potential Energy = mgh = 50 x 10 x 72.5 = 36,250 J.
(ii) Since the height is the same, the gain is also 36,250 J.
(iii) Conclusion: Potential energy depends only on mass and the vertical height gained; it does not depend on the path taken.
Question 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.
Energy: Reaching the 20th floor (double height) requires double the energy (20mgd vs 10mgd).
Power: Since the time is also doubled, the power required remains the same (Power = Work / Time).
Question 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 Factors: Mass (m), height (h), and gravity (g).
Work Done: The speed does not change the total work done (W = mgh).
Power Change: If speed doubles, time is halved. Therefore, the power required doubles.
Question 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.
Day 1 Total Mass = 160 kg. Day 2 Total Mass = 200 kg.
Fuel consumption relates to Kinetic Energy (1/2 mv²).
Fuel Ratio = 160 : 200 = 4 : 5.
Question 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.
To balance the seesaw (Weight x Distance), the child must sit at twice the distance from the center (fulcrum) compared to the adult.
Question 10. A ball of mass 2 kg is thrown up with a velocity of 20 ms⁻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 ms⁻²).
(i) Work by gravity is negative while moving up (opposing motion) and positive while moving down (aiding motion).
(ii) Ideally, height should be 20 m. The missing energy is used by air resistance: -12 J.
Question 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) Speed at 0 m: 1/2 x 10 x v² = 180; v = 6 m/s.
(ii) Speed at 4 m: Total work (area under graph) = 150 J. Final KE = 180 + 150 = 330 J. Speed = approx 8.1 m/s.
The block does not have negative acceleration because the force remains positive.
Question 12. The gravitational attraction on the surface of the Moon (lunar surface) is about 1/6th 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 the Moon, gravity is 6 times weaker. With the same initial velocity, the ball will reach 6 times the height: 8 m x 6 = 48 m.
Question 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 car moves at a constant speed of 35 m/s.
(ii) Kinetic Energy at A = 612,500 J.
(iii) Work by brakes = -612,500 J (removes all kinetic energy).
(iv) Kinetic energy transforms into heat (thermal energy) and sound energy.
Question 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 ms⁻¹ and potential energy is 30 J. Calculate the velocity of the ball at P, Q and R.
Total mechanical energy = 30 J.
At P: PE = 20 J, KE = 10 J; Speed = approx 6.32 m/s.
At Q: PE = 30 J, KE = 0 J; Speed = 0 m/s.
At R: The ball cannot reach point R (PE = 40 J) because it exceeds the total available energy of 30 J.
Question 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 ms⁻²
(i) Velocity: sqrt(2 x 10 x 10) = approx 14.14 m/s.
(ii) Depth: Energy = 150 J. Depth = 150 / 3000 = 0.05 m = 5 cm.
In-Text Questions (Think It Over & Pause and Ponder)
Question 1. What will be the magnitude of velocity of the child at the bottom of the blue slide?
The velocity is calculated as v = sqrt(2gh), depending only on the height of the slide.
Question 2. Will two children of different masses reach the bottom of the same slide with the same velocity?
Yes. Mass does not affect the final velocity when neglecting friction.
Question 3. Which slide will result in the largest magnitude of velocity at the bottom?
The slide with the greatest vertical height (h).
Question 4. Is she [weight lifter] doing any work on the barbell while holding it steady?
No. Since there is no displacement (s = 0), the scientific work done is zero.
Question 5. Is the work done by friction on the stack of coins that travels on a rough surface positive, negative, or zero?
Negative, as friction acts opposite to the direction of motion.
Question 6. Two objects A and B of mass m and 4m have the same kinetic energy. What is the ratio of the magnitude of velocities of A and B?
The ratio of velocities vA : vB is 2 : 1.
Question 7. Explain why roads on hills are built to wind around in gentle slopes rather than going straight up.
A winding road acts as an inclined plane. Increasing the distance reduces the force (effort) required to climb the hill.