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 #1 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

Answer 1

The work is #=7.39J#

The load #L=(3g)N#

Radius of axle #r=0.02m#

Radius of wheel #R=0.01m#

Taking moments about the center of the axle

#F*R=L*r#

#F*0.01=3*g*0.02#

#F=(3*g*0.02)/0.01=58.8N#

The force is #F=58.8N#

The distance is #d=2*pi*0.02=0.04pi#

The work is #W=F*d=58.8*0.04pi=7.39J#

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Answer 2

The work required to turn the wheel a length equal to the circumference of the axle is equal to the force applied multiplied by the distance over which the force is applied, which is also known as torque. In this case, the torque can be calculated as the product of the force exerted by the object and the radius of the axle. The force exerted by the object can be calculated using Newton's second law (F = ma), where m is the mass of the object and a is the acceleration due to gravity (approximately 9.8 m/s^2). Then, the work can be calculated as the torque multiplied by the angle through which the wheel is turned (in radians). Since the angle required to turn the wheel a length equal to the circumference of the axle is 2π radians, the work can be calculated using this formula.

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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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