An object with a mass of #2 kg# is hanging from an axle with a radius of #14 m#. If the wheel attached to the axle has a radius of #21 m#, how much force is needed to raise the object?

Answer 1

The force is #F=13.1N#

The load is #L=2gN#

The radius of the axle is #r=14m#

The radius of the wheel is #R=21m#

The effort is #=FN#

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

Taking moments about the center of the axle

#F*21=2g*14#

#F=(2g*14)/21=13.1N#

The force is #F=13.1N#

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Answer 2

To calculate the force needed to raise the object, we can use the principle of torque. The torque (τ) exerted by a force (F) acting at a distance (r) from the pivot point (in this case, the axle) is given by:

τ = F * r

For the object hanging from the axle, the torque exerted by its weight is balanced by the torque exerted by the force needed to raise it. The torque due to the weight of the object is given by:

τ_weight = mg * r1

where: m = mass of the object (2 kg) g = acceleration due to gravity (approximately 9.8 m/s^2) r1 = radius of the axle (14 m)

τ_weight = 2 kg * 9.8 m/s^2 * 14 m = 274.4 N*m

To counteract this torque, the force needed to raise the object must exert an equal and opposite torque. The torque due to this force is given by:

τ_force = F * r2

where: r2 = radius of the wheel (21 m)

To find the force (F), we set the torques equal:

F * r2 = mg * r1

Solving for F:

F = (mg * r1) / r2

F = (2 kg * 9.8 m/s^2 * 14 m) / 21 m

F = 274.4 N

Therefore, the force needed to raise the object is 274.4 Newtons.

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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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