ABE TUTORIALS

PROBLEM 14:

GEARS IN MESH HAVE THE FOLLOWING CHARACTERISTICS: DRIVEN GEAR = 25 TEETH; DRIVER GEAR = 40 TEETH RUNNING AT 100 RPM. THE DRIVEN GEAR IS ATTACHED TO A 1-METER-DIAMETER WHEEL. THERE IS A 10% SLIP ON THE WHEEL.

---

1. The rotational speed of the driven gear:

a. 100 rpm | b. 160 rpm | c. 50 rpm | d. 200 rpm | e. nota

View Solution

Formula: Driver Speed × Driver Teeth = Driven Speed × Driven Teeth

Calculation:
Driven Speed = (100 rpm × 40 teeth) / 25 teeth
Driven Speed = 4000 / 25 = 160 rpm

Result: b. 160 rpm

2. The linear speed of the driven gear (wheel):

a. 160 m/s | b. 17 m/s | c. 17 ft/min | d. 62.5 m/min | e. 8.5 m/s

View Solution

Formula: Velocity = π × Diameter × RPM

Calculation:
Velocity = 3.1416 × 1 m × 160 rpm = 502.66 m/min
Convert to m/s: 502.66 / 60 seconds ≈ 8.38 m/s

Result: e. 8.5 m/s (rounded)

3. The speed with slip:

a. 144 m/s | b. 15 m/s | c. 15.3 ft/min | d. 62.5 m/min | e. 7.65 m/s

View Solution

Formula: Actual Speed = Theoretical Speed × (1 - Slip)

Calculation:
Actual Speed = 8.5 m/s × (1 - 0.10)
Actual Speed = 8.5 × 0.9 = 7.65 m/s

Result: e. 7.65 m/s