so you use a 1.34 kW motor to lift the 84.7 kg sofa 16.3 m fom the street.(A) How much time does the lift take?t= ?
Let's see, let's start by calculating the change in gravitational potential the sofa will undergo being lifted from the ground to the sixth floor. i.e. Find the potential energy the sofa will have 6 floors up, thats the energy we need to move the sofa up. We can define potential as the work needed to move an object against a Force. Let gravity be that force, Thus Work = Force * Distance U = mgh = (84.7)(9.8)(16.3) kg m^2 /s^2 = 13529.978 joules 1.34 kW is a unit of power, 1 kW = 1000 W, 1 W = 1j/s, so we have 1340 j/s. Power = work/time time = Work / power. The work needed to be done is the potential energy of the sofa when it is lifted to the sixth floor (fun fact, drop a sofa from the 6th floor and the energy is converted from potential to kinetic, also you'll be arrested). So t = 13529.978 j / 1340 j/s = 10.1seconds
