# An object with a mass of #4 kg# is hanging from an axle with a radius of #8 cm#. If the wheel attached to the axle has a radius of #24 cm#, how much work would it take to turn the wheel #4 cm#?

The work 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

Plugging in the value of

The force is

The distance is

The work is

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To calculate the work required to turn the wheel by 4 cm, we first need to find the distance the object moves when the wheel turns by 4 cm. Since the axle and the object are connected, they move together. The ratio of the radii of the axle and the wheel is 1:3 (8 cm : 24 cm), so the distance the object moves is 4 cm * 3 = 12 cm.

Next, we calculate the work done using the formula:

[Work = Force \times Distance]

The force required to move the object is equal to the force of gravity acting on it, which is (mass \times gravitational\ acceleration = 4 kg \times 9.81 m/s^2).

Plugging in the values, we get:

[Work = 4 kg \times 9.81 m/s^2 \times 0.12 m]

[Work = 4.7052 N \times 0.12 m]

[Work = 0.5646 Nm]

Therefore, it would take approximately 0.5646 Nm of work to turn the wheel by 4 cm.

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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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