Question

T(N) 1800 T = 2007 A 1 (8) 3 Given: The motor lifts the 20-kg crate with a variable force, T, as defined by the figure below. Find: a) The speed of the crate when t = 2 seconds, starting from rest. Show your work. Include appropriate diagrams. m/s b) The power output of the motor at t - 2 seconds. Show your work. w c) If the efficiency of the motor is € = 0.6, which of t) a following would be the best choice for the job? Conversion: 746 W = 1 hp. Show your reasoning.

Answer 1

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[ Given: m= 20kg force Tis variable as Iz & T= 200t2 Solution: given in graph and follows * FBD of Crate at any time t between t=o to t= 3 sec T ya as upward acceleration "mg Newtons second claw:- :: using ma = T- To mg But T= 200 t². mc = 200t² mg a = 200 t2 9 a = 200 42-9 m 20 0:10+- 9 velocity = fadt Or du dt :. ta Multiplying both sides with at and integratin. Sadr (10+2 - g) dt 10t3 - gt cs integration congle Since it starts ; at t=0, v=0 o to 3 constant from rest ; [c=0 0

- velocity expression becomes vs 1979-ge non v=10t² :. at t=2s ve 10(2):- 9(2) 10*8 10x8-9.81*2 -9.8142 IV - 7.046 misli velocity at t=2 Power at t= 2s a force a velocity (200x+2)(7.046) (200*(2)2](7.046] Power 5637.33w output of motor Motor efficiency ز 0.6= Power out put Power Input 5637.33 = 9395.55 w: Power input= 5637.33 0:6 In hp:- 9395:55 - 18th 12.6 hp 746 Select a motor with power rating higher than ..oup 12