# An object with a mass of #24 kg# is hanging from an axle with a radius of #14 m#. If the wheel attached to the axle has a radius of #16 m#, how much force must be applied to the wheel to keep the object from falling?

The force is

The load L=(24g)N#

Radius of axle

Radius of wheel

Taking moments about the center of the axle

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To find the force required to keep the object from falling, we need to calculate the torque exerted on the wheel by the hanging object. Torque is given by the formula:

Torque = Force × Distance

where Force is the force applied to the wheel and Distance is the distance from the point where the force is applied to the axis of rotation.

The distance from the axle to where the object is hanging is 14 m. The radius of the wheel is 16 m. Since the force is acting perpendicular to the radius of the wheel, the distance is the sum of the radii of the wheel and the axle.

So, Distance = 14 m + 16 m = 30 m

Now, we need to find the torque exerted by the hanging object. The force exerted by the object is equal to its weight, which is given by:

Force = Mass × Gravity

where Mass is the mass of the object and Gravity is the acceleration due to gravity.

Force = 24 kg × 9.8 m/s^2

Now, we can calculate the torque:

Torque = Force × Distance

Finally, we find the force required to keep the object from falling by rearranging the formula for torque:

Force = Torque / Distance

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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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