# 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?

The force is

The load is

The radius of the axle is

The radius of the wheel is

The effort is

The acceleration due to gravity is

Taking moments about the center of the axle

The force is

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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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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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