An object with a mass of #8 kg# is hanging from an axle with a radius of #27 cm#. If the wheel attached to the axle has a radius of #45 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

Answer 1

The work done is #=79.8J#

The load #=(8g)N#

Radius of axle #r=0.27m#

Radius of wheel #R=0.45m#

Taking moments about the center of the axle

#F*0.45=8*g*0.27#

#F=(8*g*0.27)/0.45=47.04N#

Circumference of the axle, #d=2pi*0.27m#

Work done #=F*d#

#=47.04*2pi*0.27#

#=79.8J#

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Answer 2

To calculate the work required to turn the wheel a length equal to the circumference of the axle, you can use the formula:

[ \text{Work} = \text{Force} \times \text{Distance} ]

The force exerted to turn the wheel is the torque applied, which is calculated as the product of the force applied and the distance from the center of rotation. In this case, the force exerted is the gravitational force acting on the object hanging from the axle.

  1. Calculate the gravitational force acting on the object: [ \text{Force} = \text{mass} \times \text{gravity} ] [ \text{Force} = 8 , \text{kg} \times 9.8 , \text{m/s}^2 = 78.4 , \text{N} ]

  2. Calculate the torque applied to the wheel: [ \text{Torque} = \text{Force} \times \text{Radius of the wheel} ] [ \text{Torque} = 78.4 , \text{N} \times 0.45 , \text{m} = 35.28 , \text{Nm} ]

  3. The distance the wheel is turned is equal to the circumference of the axle, which is (2 \times \pi \times \text{radius of the axle}): [ \text{Distance} = 2 \times \pi \times 0.27 , \text{m} ] [ \text{Distance} = 1.7 , \text{m} ]

  4. Calculate the work: [ \text{Work} = \text{Torque} \times \text{Distance} ] [ \text{Work} = 35.28 , \text{Nm} \times 1.7 , \text{m} = 59.976 , \text{J} ]

So, it would take approximately 59.976 joules of work to turn the wheel a length equal to the circumference of the axle.

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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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