Question

Determine the power transmitted by a gear of tractor gear box having size 12 cm, if it is rotating at 1350 RPM and transmitting 17.5 kg-m torque.

• A. 11 hp
• B. 33 hp
• C. 44 hp
• D. 66 hp

Hint:

To quickly estimate metric horsepower from torque in kg-m and RPM, use:
\[ HP \approx \frac{N \times T}{716.2} \] Here, $\frac{1350 \times 17.5}{716.2} = 32.98\text{ hp}$, saving valuable time during exams.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Rotational power transmitted by a shaft or gear is directly proportional to the applied torque and the angular velocity.
The physical dimension of the gear (size) does not affect the total power transmitted if torque and speed are already specified.
Key Formula or Approach:
The power ($HP$, in metric horsepower) transmitted is:
\[ HP = \frac{2 \pi N T}{4500} \] where:
$T$ = Torque in $\text{kg-m}$
$N$ = Rotational speed in $\text{RPM}$
$4500$ = Conversion constant to metric horsepower

Step 2: Detailed Explanation:
From the problem description:
Torque, $T = 17.5\text{ kg-m}$
Rotational speed, $N = 1350\text{ RPM}$
Substitute these values into the formula:
\[ HP = \frac{2 \times \pi \times 1350 \times 17.5}{4500} \] Simplify the constants:
\[ HP = \frac{2700 \times \pi \times 17.5}{4500} \] \[ HP = \frac{3 \times \pi \times 17.5}{5} = 0.6 \times \pi \times 17.5 \] \[ HP = 10.5 \times \pi \approx 10.5 \times 3.14159 \approx 32.99 \text{ hp} \] This value rounds to $33\text{ hp}$.
The gear size of $12\text{ cm}$ is redundant information, as torque and rotational speed are sufficient to calculate the transmitted power.

Step 3: Final Answer:
The power transmitted by the tractor gearbox gear is $33\text{ hp}$.