An object with a mass of #2 kg# is hanging from an axle with a radius of #3 m#. If the wheel attached to the axle has a radius of #14 m#, how much force is needed to raise the object?

To calculate the force needed to raise the object, we can use the principle of torque.

The torque exerted by the object hanging from the axle can be calculated as the product of the force of gravity and the radius of the axle:

( \tau = F \cdot r_{axle} )

Where: ( \tau ) = torque ( F ) = force of gravity (weight) acting on the object ( r_{axle} ) = radius of the axle (given as 3 m)

The force of gravity ( F ) can be calculated using Newton's second law:

( F = m \cdot g )

Where: ( m ) = mass of the object (given as 2 kg) ( g ) = acceleration due to gravity (approximately ( 9.8 , m/s^2 ))

Then, we can substitute the value of ( F ) into the torque equation:

( \tau = (2 , kg \cdot 9.8 , m/s^2) \cdot 3 , m )

Now, calculate the torque exerted by the object hanging from the axle.

Next, we need to find the force needed to raise the object, which is the torque divided by the radius of the wheel:

( F_{raise} = \frac{\tau}{r_{wheel}} )

Where: ( F_{raise} ) = force needed to raise the object ( r_{wheel} ) = radius of the wheel (given as 14 m)

Now, substitute the values into the equation and calculate the force needed to raise the object.