To calculate the power required, both the force pulling the elevator up and the elevator's velocity must be determined.

The elevator's velocity, v_e, is a constant 1 m/s and thus there is no acceleration (dv/dt = a = 0). The mass and dimensions of the elevator are given.

The counterweight, c, free-body diagram gives

     T_c = m_c g

Remember, acceleration is assumed to be zero.

Using the free-body diagram for the elevator, e, and summing the forces in the vertical direction gives

     T_c + T_e = m_bg + m_eg

where m_b is the mass of the bricks. Combining with the counterweight cable tension gives

     T_e = (m_b + m_ec)g

If the counterweight mass m_c is 800 kg, then the tension in the cable is

     T_e = (1000 + 1000 - 800) 9.81
         = 11.78 kN

The required power output is

     P_o = T_e v_e
          = 11.78 (1)
          = 11.78 kW

Motors and mechanical equipment will lose energy from other sources, such as friction. Thus the motor has to deliver more power than what is actually being lifted.The, mechanical efficiency, η, is

     
     0.8 = 11.78/P_i
     P_i = 14.73 kW

Counterweight = 0 kg

If the counterweight mass, m_c, is 0 kg, then tension in the cable will be

     T_e = (1000 + 1000 - 0) 9.81
         = 19.62 kN

The required power output is

     P_o = T_e v_e
          = 19.62 (1)
          = 19.62 kW

Considering the motor efficiency, η, gives

     
     0.8 = 19.62/P_i
     P_i = 24.53 kW

Comparison between the elevator with and without the counterweight can now be done.

     P_{c = 800} = 14.73 kW
     P_{c = 0} = 24.53 kW

The increase in power without the counterweight is

     (24.53 - 14.73)/14.73 = 67%