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Zorluk: OrtaWheel and Axle

A driver operates a heavy-duty steering wheel connected directly to a steering column (axle). The steering wheel has a radius of 16 inches16 \text{ inches}, and the steering column has a diameter of 4 inches4 \text{ inches}. If the driver applies an effort force of 20 pounds20 \text{ pounds} to the outer rim of the steering wheel, what is the resulting output force exerted by the steering column? (Assume a perfectly efficient system.)

  1. A
    2.5 pounds2.5 \text{ pounds}
  2. B
    5 pounds5 \text{ pounds}
  3. C
    80 pounds80 \text{ pounds}
  4. 160 pounds160 \text{ pounds}Cevap

Cevap

160 pounds160 \text{ pounds}
The mechanical advantage of a wheel and axle when effort is applied to the wheel is the radius of the wheel divided by the radius of the axle. The wheel's radius is 16 inches16 \text{ inches}. The axle's diameter is 4 inches4 \text{ inches}, meaning its radius is 2 inches2 \text{ inches}. The mechanical advantage is 16/2=816 / 2 = 8. Multiplying the 20 pound20 \text{ pound} input force by the mechanical advantage of 88 gives a total output force of 160 pounds160 \text{ pounds}.

Adım Adım Çözüm

1
Determine the radius of the steering column (axle).
The diameter is 4 inches4 \text{ inches}, so the radius is 2 inches2 \text{ inches}.
Mechanical advantage must be calculated by comparing equivalent dimensions, such as the radii of both components.
2
Calculate the Ideal Mechanical Advantage (IMA) of the wheel and axle.
IMA=Radius of WheelRadius of Axle=162=8\text{IMA} = \frac{\text{Radius of Wheel}}{\text{Radius of Axle}} = \frac{16}{2} = 8.
When effort is applied to the larger wheel, the system acts as a force multiplier based on the ratio of the radii.
3
Calculate the output force exerted by the steering column.
Output Force=Effort Force×IMA=20×8=160 pounds\text{Output Force} = \text{Effort Force} \times \text{IMA} = 20 \times 8 = 160 \text{ pounds}.
The system multiplies the driver's input force by the mechanical advantage to turn the steering mechanism.

Anahtar Kavram

Ideal Mechanical Advantage of a Wheel and Axle
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Konular

Wheel and Axle

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