Question

If the difference in tension (T0−T′) between the two ends of the rope is 520N and the capstan has a diameter of 10.0cm and turns once in 0.90s, find the rate Pthermal at which thermal energy is being generated.

Give a numerical answer, in watts, rounded to the nearest 10 W.

Answer 1

\(\mathrm{P}(\) pressure \()=\mathrm{Fv}\)

\(\mathrm{F}=520 \mathrm{~N}\)

\(\mathrm{v}=\frac{\pi \times D}{t}=\frac{\pi \times 10 \times 10^{-2}}{0.90}=0.349\)

\(P=0.349 \times 520=181.5\)

\(\mathrm{Q}=\mathrm{mC}\left(T_{0}-T^{\prime}\right)\)

\(\mathrm{P}=\frac{d Q}{d t}\)

\(P=m C \frac{d T}{d t}\)

\(F=520 \mathrm{~N}\)

\(\mathrm{C}(\) specific heat \()=470 \mathrm{j} / \mathrm{kg} \mathrm{C}\)

let \(\mathrm{m}=6 \mathrm{~kg}\) ( mass is not given in the question)

\(\frac{d T}{d t}=\frac{P}{m C}\)

\(\frac{d T}{d t}=\frac{181.5}{6 \times 460}=0.065 \mathrm{deg} \mathrm{C} / \mathrm{sec}\)