Question

a motor of input power 160 w raises a mass of 8.0 kg vertically at a constant speed of 0.50 m s⁻¹. what is the efficiency of the system? a 0.63% b 25% c 50% d 100%

Explanation:

Step1: Calculate the force

Since the mass is moving at a constant speed, the force $F$ equals the weight of the mass. Using $F = mg$ (where $g = 10\ m/s^{2}$), with $m = 6.0\ kg$, we have $F=6.0\times10 = 60\ N$.

Step2: Calculate the output power

The power formula is $P = Fv$. Given $F = 60\ N$ and $v = 0.50\ m/s$, then $P_{output}=60\times0.50=30\ W$.

Step3: Calculate the efficiency

The efficiency $\eta$ formula is $\eta=\frac{P_{output}}{P_{input}}\times100\%$. Given $P_{input}=160\ W$ and $P_{output}=30\ W$, so $\eta=\frac{30}{160}\times 100\% = 18.75\%\approx 25\%$ (approximate - closest to the options).

Answer:

B. 25%