An object with a mass of #5 kg# is hanging from an axle with a radius of #18 m#. If the wheel attached to the axle has a radius of #6 m#, how much force must be applied to the wheel to keep the object from falling?

Answer 1

The force is #F=147N#

The load is #L=5gN#

The radius of the axle is #r=18m#

The radius of the wheel is #R=6m#

The effort is #=FN#

The acceleration due to gravity is #g=9.8ms^-2#

Taking moments about the center of the axle

#F*6=5g*18#

#F=(5g*18)/6=147N#

The force is #F=147N#

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Answer 2

To keep the object from falling, a force equal to the weight of the object must be applied to the wheel. The force required is given by the formula:

[ F = \frac{m \cdot g \cdot r_1}{r_2} ]

Where:

  • ( F ) is the force applied to the wheel,
  • ( m ) is the mass of the object (5 kg),
  • ( g ) is the acceleration due to gravity (approximately (9.81 , \text{m/s}^2)),
  • ( r_1 ) is the radius of the axle (18 m),
  • ( r_2 ) is the radius of the wheel (6 m).

Plugging in the values:

[ F = \frac{5 , \text{kg} \times 9.81 , \text{m/s}^2 \times 18 , \text{m}}{6 , \text{m}} ]

[ F = \frac{882.45 , \text{N} \cdot \text{m}}{6 , \text{m}} ]

[ F = 147.075 , \text{N} ]

Therefore, approximately 147.075 Newtons of force must be applied to the wheel to keep the object from falling.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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