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An object with a mass of #2 kg# is hanging from an axle with a radius of #3 m#. If the wheel attached to the axle has a radius of #8 m#, how much force must be applied to the wheel to keep the object from falling?

Answer 1

Charles Aeschliman

The force is #=7.35N#

Taking moments about the center of the axle

#2g*3=F*8#

#F=6/8g=7.35N#

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Answer 2

Nathan Ashcroft

The force required to keep the object from falling is equal to the gravitational force acting on the object, which is given by ( F = mg ), where ( m ) is the mass of the object and ( g ) is the acceleration due to gravity (approximately ( 9.8 , \text{m/s}^2 )). The force is applied at the outer radius of the wheel. So, the force required can be calculated using the equation ( F = \frac{mg \times \text{wheel radius}}{\text{axle radius}} ). Substituting the given values, ( m = 2 , \text{kg} ), ( g = 9.8 , \text{m/s}^2 ), wheel radius = 8 m, and axle radius = 3 m, we get:

[ F = \frac{2 \times 9.8 \times 8}{3} ]

[ F = \frac{156.8}{3} ]

[ F \approx 52.27 , \text{N} ]

So, approximately 52.27 N 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.