This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
16. A machine of efficiency of 70\% is used to raise a body of mass 80 kg through a vertical distance of 3 m in 40 seconds. Calculate the power input (Take g=10 m/s^2). Given: Efficiency = 70\% = 0.70 Mass m = 80 kg Vertical distance h = 3 m Time t = 40 s Acceleration due to gravity g = 10 m/s^2 Step 1: Calculate the work output (W_out). The work done by the machine is to raise the body, which is equal to the change in its potential energy. W_out = mgh Substitute the given values: W_out = (80 kg)(10 m/s^2)(3 m) W_out = 2400 J Step 2: Calculate the power output (P_out). Power output is the work output divided by the time taken. P_out = W_outt Substitute the calculated work and given time: P_out = 2400 J40 s P_out = 60 W Step 3: Calculate the power input (P_in). The efficiency of a machine is the ratio of power output to power input. = P_outP_in Rearrange the formula to solve for P_in: P_in = P_out Substitute the calculated power output and given efficiency: P_in = 60 W0.70 P_in ≈ 85.71 W The power input is 85.71 W.