a frictionless pulley of unknown mass M and radius r = 0.200 m which is used to draw water from a well. A bucket of mass m = 1.50 kg is attached to a massless cord wrapped around the pulley. The bucket starts from rest at the top of the well and falls for t = 3.00 s before hitting the water h = 6.89 m below the top of the well.

What is the Tension of the Cord

My partner and I keep usinng the Tension Formula F= mass * acceleration. We found a an linear acceleration of 1.531 m/s2.

any help with the formula would be appreciated

Nhatkiem

Lets first figure out acceleration in the y direction



the final position is (yf) is 0, the initial position (y0) is 6.89, and the initial velocity(v0y) in the y direction is 0, and time (t) is 3.




This is OVERALL acceleration. We have two forces in play here causing this direction. Weight, and Tension which are acting in opposite directions.




Fg is the force due to gravity (weight) and T is tension. If the overall acceleration is -2.3 m/s^2 downwards, it would mean that there is an acceleration upward of (9.8-2.3) to give an overall acceleration of -2.3. Mass here is the mass of the bucket + mass of the rope (But the rope's pass is said to be negligible.




I can't figure out why they would mention that the mass of the pulley was unknown and that the radius of the pulley was 0.2. Perhaps I am missing something but it would seem to be extraneous information. (If the pulley had somehow become dislodged and attached to the bucket, then we would use its mass but again I don't understand why they tell us it's radius.)