One horsepower (hp) is the amount of power required to lift a 75-kg mass a vertical distance of 1 m in 1 s. What is 2 hp equivalent to in watts (W)?

Question

One horsepower (hp) is the amount of power required to lift a 75-kg mass a vertical distance of 1 m in 1 s.  What is 2 hp equivalent to in watts (W)?

Quizplus · Accepted Answer

11ecba2d_12ff_79d0_a3bf_75bb880b3991_MD0008_00 Mechanical power P is the amount of work W done per unit time t: 11ecba2d_12ff_79d1_a3bf_d5c0e8afa997_MD0008_00 From the work-energy theorem, the change in the potential energy (PE) of an object is equal to the amount of work done in the vertical direction. Gravitational potential energy is due to an object's position relative to Earth's gravitational field, and it is the product of mass m, gravitational acceleration g, and the height h. Therefore, the work done is equal to the change in PE, which depends on the change in height Δh: 11ecba2d_12ff_79d2_a3bf_a92adacb1e32_MD0008_00 Substituting the above equation into the power equation, 11ecba2d_12ff_79d3_a3bf_bbb009357d31_MD0008_00 The SI unit for power is the watt (W), and the value of g is 10 m/s². One horsepower (hp) is calculated using the values provided in the question for m, Δh, and t: 11ecba2d_12ff_79d4_a3bf_4772028579c5_MD0008_00 Because 1 hp is equal to 750 W, 2 hp is double this value, or 1,500 W. (Choices A and B) If the change in gravitational potential energy is calculated without gravitational acceleration g, the incorrectly calculated power of 1 hp is 75 W, and this valued doubled is 150 W. (Choice C) Calculated correctly, 1 hp is equal to 750 W, but the question asks for the value equal to 2 hp. Educational objective: Power P is the rate of work W done per unit time t: P = W/t. The work done to lift an object is equal to its change in gravitational potential energy ΔPE, which is the product of mass m, gravitational acceleration g, and the change in height Δh: ΔPE = mgΔh.

One Horsepower (Hp) Is the Amount of Power Required to Lift