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Work, Energy, and Simple Machines 129 2000000 J = (50000 + 50000) N × d d = 2000000 J = 2000000 N m = 20 m 100000 N 100000 N Thus, the minimum length of the ramp to be able to stop such a truck is 20 m. 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 . 8.  You may have seen an exhibit like that in A Fig. 7.22 in a science park, where a ball is E D C released from the highest point. Describe B 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 Fig. 7.22: Ball roller coaster in a to do with the energy lost due to friction? science park 7.5 Power Suppose you carry your bag up a flight of stairs to your classroom. Running up the stairs in one minute feels very different than walking up slowly in five minutes, even though the same work is done in both cases. This difference is described by a physical quantity called power. Threads of Power is defined as the rate at which work is done. Mathematically, the Curiosity average power P is the work done W, divided by the time taken t   i.e., W You may have P =  (7.11) heard about t another unit called To do more work in the same time interval, requires more power. To horsepower (hp) do the same amount of work but in a shorter time interval also requires used to measure power, especially more power. The SI unit of power is the watt (W),–1here 1 watt is equal to for car engines, 1 joule of work done per second, i.e., 1 W = 1 J s . Example 7.10: A weightlifter lifts a 75 kg mass by 2 m in 5 seconds. How or pumps used to lift water. One much power would she require for this task? horsepower is Answer: The work done would be equal to mgh = 75 kg × 10 m s × 2 m equal to 746 W. In the early days, = 1500 J when engines were 1500 J Thus, the power required will be 5 s = 300 W newly discovered, the powers of Example 7.11: A car of mass 1000 kg starts from rest and reaches a speed engines were of 72 km h in 10 seconds. Calculate the power of the engine required to compared to the achieve this start. power of actual horses which Answer: Final velocity, v = 72 km h –1= 72000 m = 20 ms −1 3600 s were used to drive while initial velocity u = 0 m s1 carriages.