How Do You Calculate Torque in Mechanical Situations?

[hshphyss]

1.) A mechanic jacks up a car to an angle of 8.0° to change the front tires. The car is 3.20 m long and has a mass of 1160 kg. Its center of mass is located 1.12 m from the front end. The rear wheels are 0.40 m from the back end. Calculate the torque exerted by the car around the back wheels.
--I'm not sure how to set this up. I know the equation for torque is t=fr sin(theta)
2.) A bucket filled with water has a mass of 71 kg and is attached to a rope that is wound around a 0.035 m radius cylinder. A crank with a turning radius of 0.15 m is attached to the end of the cylinder. What minimum force directed perpendicularly to the crank handle is required to raise the bucket?
--I think this is a moment of inertia problem... so for that shape it would be MR^2 but after you find that what would you plug that into?
Thank-you

 

[lightgrav]

1) "r" points from the axis of rotation (the back wheels) to the point where the Force is applied. The first Force that you need to consider is the Force applied TO the car BY THE EARTH (gravity), which is downward. The angle that you take the sin of (in "sin theta") is the angle from the "r" direction to the "F" direction (swept thru by your fingers as they more from "along r" to "along F". In your case, it is MORE than 90 degrees.

[the wording "torque applied BY the car around the back wheels" implies that
there is some OTHER object, besides the car, that this torque is applied TO. I can't think of any ... the car cannot apply a torque to itself!]

2) the MINIMUM Force needed to raise the bucket will have zero acceleration of the bucket, and zero angular acceleration of the drum.
So you do NOT need to compute the moment of rotational Inertia.