Question

A spur is designed to transmit the power 10 kW at a pitch line velocity of 10 m/s. Diameter of driving gear is 1 m. The tangential force between the driver and the follower and the transmitted torque, respectively, are:
1. 1 kN and 0.5 kNm
2. 0.5 kN and 1 kNm
3. 0.5 kN and 0.5 kNm
4. 1 kN and 1 kNm

Answer 1

Correct Answer - Option 1 : 1 kN and 0.5 kNm

Concept:

Tangential force, T = r × F

Power, P = T × ω 

Velocity, V = r × ω 

Where P is power (W), r is the radius of the gear (m), ω is angular speed (rad/s), T is torque (Nm), F is tangential force (N), V is Velocity in (m)

Calculation:

Given:

P = 10 kW = 10000 W,  V = 10 m/s, Diameter D = 1 m, ∴ r = 0.5 m

V =  r × ω 

10 = 0.5 × ω 

ω = 20 rad/s

P = T × ω 

10000 = T × 20

T = 500 Nm = 0.5 kNm

T = r × F

500 = 0.5 × F

F = 1000 N = 1 kN