The input power to a motor is 12W. The motor wastes 590 J of energy in 1.0 min. What is the efficiency of the motor?

Sure, let's solve this step by step:

Step 1: Convert the time from minutes to seconds because the power is given in Watts (which is Joules per second). So, 1.0 min = 60 seconds.

Step 2: Calculate the total energy input to the motor in the given time. The power is the rate of energy transfer, so Energy = Power x Time. Substituting the given values, we get Energy = 12W x 60s = 720 Joules.

Step 3: Calculate the useful energy output. The motor wastes 590 Joules, so the useful energy output is the total energy input minus the energy wasted. So, Useful Energy Output = 720J - 590J = 130 Joules.

Step 4: Calculate the efficiency. Efficiency is the ratio of the useful output energy to the total input energy, expressed as a percentage. So, Efficiency = (Useful Energy Output / Total Energy Input) x 100%. Substituting the values we calculated, we get Efficiency = (130J / 720J) x 100% = 18.06%.

So, the efficiency of the motor is approximately 18.06%.