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 #22 cm#?
The work is
The load Radius of axle Radius of wheel Taking moments about the center of the axle The force is The distance is The work is
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To calculate the work done to turn the wheel, we first need to determine the force exerted at the axle. The torque exerted by the hanging object can be calculated using the formula:
Torque = Force × Distance
The force exerted by the hanging object can be calculated using the formula:
Force = Mass × Acceleration due to gravity
The torque exerted by the hanging object on the axle is then transferred to the wheel, which can be calculated using the formula:
Torque = Force × Radius of the axle
Once we have the torque exerted on the wheel, we can calculate the work done to turn the wheel using the formula:
Work = Torque × Angle turned by the wheel
Given:
- Mass of hanging object (m) = 4 kg
- Radius of axle (r_axle) = 8 cm = 0.08 m
- Radius of wheel (r_wheel) = 24 cm = 0.24 m
- Distance turned by the wheel (d) = 22 cm = 0.22 m
- Acceleration due to gravity (g) = 9.8 m/s^2
Force = 4 kg × 9.8 m/s^2 Force = 39.2 N
Torque exerted by hanging object = Force × Radius of axle Torque = 39.2 N × 0.08 m Torque = 3.136 Nm
Torque exerted on the wheel = Torque exerted by hanging object
Work = Torque × Angle turned by the wheel Work = Torque × (Distance turned by the wheel / Radius of wheel) Work = 3.136 Nm × (0.22 m / 0.24 m) Work ≈ 2.88 Nm
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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.
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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