Question

A leather belt 100 mm wide and 10 mm thick with a safe permissible stress of 1.5 MPa is used for transmitting a maximum power of 15 KW. If the density of belt material is 1 g/cm^3, the velocity of belt for maximum power transmission will be ________

(a) 22.36 m/s

(b) 34.13 m/s

(c) 24.98 m/s

(d) 12.12 m/s

The question was asked during an online exam.

This intriguing question originated from Power Transmission System in chapter Ignition and Power Transmission of Farm Machinery

Answer 1

Right option is (a) 22.36 m/s

For explanation I would say: Area = 100*10*20^-6 = 10^-3m^2

Tmax = Pmax * Area

= 1.5 * 10 * 10^-3

Tmax = 1500 N

M = ρ*area

= 1000*10^-3 = 1 kg/m

For maximum transmission

Tmax = 3Tc

Tmax= 3mv^2

V = \(\sqrt{\frac{Tmax}{3m}} = \sqrt{\frac{1500}{3}} \)

V = 22.36 m/s