An object with a mass of #4 kg# is hanging from an axle with a radius of #5 m#. If the wheel attached to the axle has a radius of #35 m#, 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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The force required to keep the object from falling is 392 N.
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To find the force needed to keep the object from falling, we need to consider the gravitational force acting on the object and the torque required to balance it.
The gravitational force acting on the object is given by the formula:
[ F_g = mg ]
Where:
- ( m ) is the mass of the object (4 kg)
- ( g ) is the acceleration due to gravity (approximately ( 9.8 , m/s^2 ))
So, ( F_g = 4 \times 9.8 = 39.2 , N )
The torque ( \tau ) required to balance the gravitational force is given by:
[ \tau = F \times r ]
Where:
- ( F ) is the force applied to the wheel (which we want to find)
- ( r ) is the radius of the wheel (35 m)
Since the gravitational force acts at the center of the object, the torque due to the gravitational force is zero.
Therefore, the force needed to balance the object is the same as the gravitational force acting on it, which is ( 39.2 , N ).
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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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