Chapter 7 Solutions — Work, Energy and Simple Machines

Revise, Reflect, Refine

1. 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.
2. 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)…
3. 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.
4. 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.
5. 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…
6. 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.
7. 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.
8. 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…
9. 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.
10. 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).
11. 11.
    A 10.0 kg block is moving on a horizontal floor with negligible friction. As shown in 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? [Fig. 7.37…
12. 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?
13. 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. [Fig. 7.38: Speed-time graph. Speed (m s⁻¹) on y-axis, Time (s) on x-axis. Point A is at (0 s, 35 m…
14. 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. [Fig. 7.39: Potential Energy (J) on y-axis (0, 10, 20, 30, 40) vs Displacement (m) on x-axis. Starting from O on the left at PE = 30 J, the curve dips into a deep…
15. 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…