A primary driving gear with 20 teeth operates at a speed of 120\text{ rpm}. Match each pot… — Armed Services Vocational Aptitude Battery (ASVAB)

A primary driving gear with 20 teeth operates at a speed of $120\text{ rpm}$ . Match each potential driven gear, identified by its tooth count, to the resulting output speed it would produce when directly meshed with this driving gear.

Driven gear with 10 teeth $240\text{ rpm}$
Driven gear with 20 teeth $120\text{ rpm}$
Driven gear with 40 teeth $60\text{ rpm}$
Driven gear with 60 teeth $40\text{ rpm}$

Cevap

The 10-tooth gear matches to

240\text{ rpm}

, the 20-tooth gear matches to

120\text{ rpm}

, the 40-tooth gear matches to

60\text{ rpm}

, and the 60-tooth gear matches to

40\text{ rpm}

The correct matches are derived using the fundamental gear ratio principle: the speed of a driven gear is inversely proportional to its number of teeth compared to the driving gear.

Adım Adım Çözüm

Calculate the constant proportional value of the driving gear by multiplying its teeth by its speed.

20 \text{ teeth} \times 120\text{ rpm} = 2400

In a meshed gear system, the product of a gear's tooth count and its rotational speed remains constant for all meshing gears (

T_1 \times S_1 = T_2 \times S_2

Determine the output speed for each driven gear by dividing the constant value by its respective tooth count.

2400 \div 10 = 240

;

2400 \div 20 = 120

;

2400 \div 40 = 60

;

2400 \div 60 = 40

This isolates the unknown speed variable (

S_2

) for each specific gear configuration.

Anahtar Kavram

Gear Ratios and Speed Inverse Proportionality

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