# An object with a mass of #3 kg# is hanging from an axle with a radius of #6 cm#. If the wheel attached to the axle has a radius of #9 cm#, how much force must be applied to the wheel to keep the object from falling?

The force is

The load is

The radius of the axle is

The radius of the wheel is

The effort is

Taking moments about the center of the axle

The force is

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To find the force required to keep the object from falling, we need to calculate the torque exerted by the weight of the object and counteract it with an equal and opposite torque.

First, calculate the torque exerted by the weight of the object: Torque = Force × Distance Torque = (mass × gravitational acceleration) × Distance from the center of rotation Torque = (3 kg × 9.8 m/s^2) × 0.06 m (converted from 6 cm to meters)

Next, calculate the torque needed to counteract the weight: Torque = Force × Distance Torque = Force × 0.09 m (radius of the wheel)

Since the torque exerted by the weight must be balanced by the torque applied to the wheel: Force × 0.09 m = (3 kg × 9.8 m/s^2) × 0.06 m

Solve for force: Force = (3 kg × 9.8 m/s^2 × 0.06 m) / 0.09 m

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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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