An object with a mass of #5 kg# is hanging from an axle with a radius of #30 m#. If the wheel attached to the axle has a radius of #9 m#, how much force must be applied to the wheel to keep the object from falling?

Answer 1

The force is #=1.63N#

The load #L=(5g)N#

Radius of axle #r=0.3m#

Radius of wheel #R=9m#

Taking moments about the center of the axle

#F*R=L*r#

#F*9=5*g*0.3#

#F=(5*g*0.3)/9=1.63N#

The force is #F=1.63N#

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Answer 2

The force required to keep the object from falling is 14.44 N.

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Answer 3

To calculate the force required to keep the object from falling, we can use the principle of torque equilibrium. The force required can be calculated using the formula:

[ F = \frac{m \cdot g \cdot R}{r} ]

Where:

  • ( F ) is the force required to keep the object from falling,
  • ( m ) is the mass of the object (5 kg),
  • ( g ) is the acceleration due to gravity (approximately 9.8 m/s²),
  • ( R ) is the radius of the axle (30 m), and
  • ( r ) is the radius of the wheel (9 m).

Plugging in the values:

[ F = \frac{5 , \text{kg} \times 9.8 , \text{m/s}^2 \times 30 , \text{m}}{9 , \text{m}} ]

[ F = \frac{1470 , \text{N}}{9} ]

[ F \approx 163.33 , \text{N} ]

So, approximately 163.33 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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