An object with a mass of #8 kg# is hanging from an axle with a radius of #5 cm#. If the wheel attached to the axle has a radius of #25 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?
The work is
The load is The radius of the axle is The radius of the wheel is The effort is The acceleration due to gravity is 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 required to turn the wheel a length equal to the circumference of the axle, we use the formula:
[ \text{Work} = \text{Force} \times \text{Distance} ]
The force exerted by the hanging object can be calculated using the formula for torque:
[ \text{Torque} = \text{Force} \times \text{Lever Arm} ]
where the lever arm is the radius of the axle. We can rearrange this formula to solve for force:
[ \text{Force} = \frac{\text{Torque}}{\text{Lever Arm}} ]
The torque exerted by the hanging object can be calculated as the product of its mass (8 kg) and the force of gravity (9.8 m/s^2), multiplied by the radius of the axle (0.05 m):
[ \text{Torque} = \text{mass} \times \text{gravity} \times \text{radius} ]
Substituting the given values:
[ \text{Torque} = 8 , \text{kg} \times 9.8 , \text{m/s}^2 \times 0.05 , \text{m} ]
[ \text{Torque} = 3.92 , \text{Nm} ]
Now, we can calculate the force exerted by the hanging object:
[ \text{Force} = \frac{3.92 , \text{Nm}}{0.05 , \text{m}} ]
[ \text{Force} = 78.4 , \text{N} ]
The distance the force acts over is the circumference of the axle, which is ( 2 \times \pi \times \text{radius of axle} ):
[ \text{Distance} = 2 \times \pi \times 0.05 , \text{m} ]
[ \text{Distance} = 0.314 , \text{m} ]
Now, we can calculate the work:
[ \text{Work} = \text{Force} \times \text{Distance} ]
[ \text{Work} = 78.4 , \text{N} \times 0.314 , \text{m} ]
[ \text{Work} = 24.57 , \text{J} ]
Therefore, it would take 24.57 Joules of work to turn the wheel a length equal to the circumference of the axle.
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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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