An electric motor directly turns the rear solid axle of an industrial transport cart. The … — Armed Services Vocational Aptitude Battery (ASVAB)

An electric motor directly turns the rear solid axle of an industrial transport cart. The axle has a diameter of $4 \text{ inches}$ , and the attached drive wheels have a diameter of $24 \text{ inches}$ . If the motor applies a rotational force of $1200 \text{ lbs}$ at the outer surface of the axle, what is the resulting forward force exerted by the wheels against the ground? (Assume zero friction losses).

$200 \text{ lbs}$ Answer
B
$7200 \text{ lbs}$
C
$1200 \text{ lbs}$
D
$100 \text{ lbs}$

Answer

200 \text{ lbs}

In a vehicle drive system, the effort is applied to the smaller axle and the output is at the outer edge of the larger wheel. The mechanical advantage is the ratio of the input radius (

2 \text{ inches}

) to the output radius (

12 \text{ inches}

), which is

1/6

. Therefore, the

1200 \text{ lbs}

of input force is reduced to

1/6

of its value, resulting in

200 \text{ lbs}

of forward force.

Step-by-Step Solution

Identify the input and output components of the machine.

Input is applied to the axle. Output is delivered at the edge of the wheel.

Determining where force is applied dictates whether the system acts as a force multiplier or a speed/distance multiplier.

Determine the radius of both the input and output components.

Axle radius =

2 \text{ inches}

(

4 \div 2

). Wheel radius =

12 \text{ inches}

(

24 \div 2

Mechanical advantage must be calculated using consistent dimensions, typically the radius of rotation.

Calculate the Ideal Mechanical Advantage (IMA) of the system.

\text{IMA} = \frac{\text{Input Radius}}{\text{Output Radius}} = \frac{2}{12} = \frac{1}{6}

When an axle drives a wheel, the output force is distributed over a larger distance, resulting in a mechanical advantage of less than 1.

Calculate the output force.

\text{Output Force} = \text{Input Force} \times \text{IMA} = 1200 \text{ lbs} \times \frac{1}{6} = 200 \text{ lbs}

The output force is the product of the applied effort and the mechanical advantage.

Key Concept

Mechanical Advantage of Axle-Driven Systems

Alternative Method

You can also use diameters directly without converting to radii: IMA = (Input Diameter) / (Output Diameter) = 4 / 24 = 1/6. Then multiply by the 1200 lbs force to get 200 lbs.

Estimated Time:1m 30s

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Answer

Step-by-Step Solution

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