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A spur gear transmits 10 kW at a pitch line velocity of 10 m/s; driving gear has a diameter of 1.0 m. Find the tangential force between the driver and the follower, and the transmitted torque respectively.
  • a)
    1 kN and 0.5 kN-m
  • b)
    10 kN and 5 kN-m
  • c)
    0.5 kN and 0.25 kN-m
  • d)
    1 kN and 1 kN-m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A spur gear transmits 10 kW at a pitch line velocity of 10 m/s; drivin...
Power transmitted = Force x Velocity 

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A spur gear transmits 10 kW at a pitch line velocity of 10 m/s; drivin...
To find the tangential force and transmitted torque in a spur gear system, we can use the following formulas:

Tangential force (Ft) = Power (P) / Pitch Line Velocity (V)
Transmitted torque (T) = Power (P) / Angular velocity (ω)

Given data:
Power (P) = 10 kW
Pitch Line Velocity (V) = 10 m/s
Diameter of the driving gear (D) = 1.0 m

Let's calculate the tangential force and transmitted torque step by step:

1. Calculate the radius of the driving gear:
Radius (r) = Diameter (D) / 2 = 1.0 m / 2 = 0.5 m

2. Calculate the angular velocity:
Angular velocity (ω) = Velocity (V) / Radius (r)
= 10 m/s / 0.5 m
= 20 rad/s

3. Calculate the tangential force:
Tangential force (Ft) = Power (P) / Pitch Line Velocity (V)
= 10 kW / 10 m/s
= 1000 N = 1 kN

4. Calculate the transmitted torque:
Transmitted torque (T) = Power (P) / Angular velocity (ω)
= 10 kW / 20 rad/s
= 500 N-m = 0.5 kN-m

Therefore, the tangential force between the driver and the follower is 1 kN and the transmitted torque is 0.5 kN-m. Hence, the correct answer is option 'A' (1 kN and 0.5 kN-m).
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A spur gear transmits 10 kW at a pitch line velocity of 10 m/s; driving gear has a diameter of 1.0 m. Find the tangential force between the driver and the follower, and the transmitted torque respectively.a)1 kN and 0.5 kN-mb)10 kN and 5 kN-mc)0.5 kN and 0.25 kN-md)1 kN and 1 kN-mCorrect answer is option 'A'. Can you explain this answer?
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