A pulley system uses a flat belt of c. s.a. 4x100 mm2 and density 11x100 kg/m3. The angle of lap is 165o on the smaller wheel. The coefficient of friction is 0.39. The maximum force allowed in the belt is 637 N. Calculate the power (kW) transmitted when the belt runs at 13 m/s and centrifugal force is included.

Note that the angle of lap is 165 degrees at the question above

So the power (kW) transmitted when the belt runs at 13 m/s and centrifugal force is included = 3.79782kW

Explanation:

Centrifugal force, Fc = pAv^2

Where p = density, A = c.s.a.  v = veelocity

= 11x100 kg/m3 X 4x100 mm2 X (13 m/s)^2

= 1100 kg/m3 X 400 mm2 x 10^-6 X 169m/s

= 74.36N

P v (f - Fc) (1-e^-μθ)

The θ = (165 degrees ÷ 180 degrees) X π = 2.878 rads  (π = 3.14)

So power p, = 10 (637 N - 74.36N) (1 - e^-0.39 x 2.878)

= 10 X 562.64 X 0.675

P = 3797.82 watts = 3.79782kW

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min