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An object with a mass of #3 kg# is hanging from an axle with a radius of #2 cm#. If the wheel attached to the axle has a radius of #5 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

Answer 1

Amelia Adams

The work is #=3.69J#

The load is #L=3gN#

The radius of the axle is #r=0.02m#

The radius of the wheel is #R=0.05m#

The effort is #=FN#

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

Taking moments about the center of the axle

#F*0.05=3g*0.02#

#F=3g*0.02/0.05=11.76N#

The force is #F=11.76N#

The distance is #d=2piR=2*pi*0.05=(0.1pi)m#

The work is #W=Fxxd=11.76xx0.1pi=3.69J#

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Answer 2

Sebastian Acosta

To calculate the work done, you can use the formula: ( \text{Work} = \text{Force} \times \text{Distance} ). The force exerted is the weight of the object, which is ( \text{Force} = \text{Mass} \times \text{Gravity} ). The distance is the circumference of the axle, ( \text{Distance} = 2 \pi \times \text{Axle radius} ). Plugging in the values, calculate the work.

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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.