An object with a mass of #18 kg# is hanging from an axle with a radius of #15 cm#. If the wheel attached to the axle has a radius of #60 cm#, how much force must be applied to the wheel to keep the object from falling?
The force is
The load Radius of axle Radius of wheel Taking moments about the center of the axle The force is
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To keep the object from falling, the force applied to the wheel must equal the force of gravity acting on the object. The force of gravity can be calculated as the product of the mass of the object and the acceleration due to gravity (9.81 m/s²).
( F_{gravity} = m \times g )
( F_{gravity} = 18 , \text{kg} \times 9.81 , \text{m/s}^2 )
( F_{gravity} = 176.58 , \text{N} )
The force applied to the wheel can be calculated using the formula for torque:
( \tau = F \times r )
Where ( \tau ) is the torque, ( F ) is the force applied, and ( r ) is the radius of the wheel.
Since the object is hanging, the torque due to the weight of the object must be balanced by the torque applied to the wheel:
( F \times r_{wheel} = F_{gravity} \times r_{axle} )
Substituting the given values:
( F \times 60 , \text{cm} = 176.58 , \text{N} \times 15 , \text{cm} )
( F \times 0.6 , \text{m} = 176.58 , \text{N} \times 0.15 , \text{m} )
( F = \frac{176.58 , \text{N} \times 0.15 , \text{m}}{0.6 , \text{m}} )
( F = \frac{26.49 , \text{N} \cdot \text{m}}{0.6 , \text{m}} )
( F = 44.15 , \text{N} )
Therefore, approximately 44.15 N of force must be applied to the wheel to keep the object from falling.
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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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