Two masses are hung vertically around a pulley that can be...

Two masses are hung vertically around a pulley that can be neglected. When released from rest, mass 1 falls inside a liquid that always produces a force on this mass that is 5 N in the upward direction. Mass 2, on the other hand, is pulled up without air resistance. When mass 2 is 5 kg, the masses accelerated at a rate of 3 m/s/s. What is the mass of m1? What is the speed of the masses when mass 1 has fallen 4 meters. Sign not required.

Transcript

00:01 Here we're given two masses strung over a pulley.

00:04 Except here we have as mass one falls through this fluid, there is a constant force of five newtons directed upward, presumably a buoyant force.

00:16 And then m2 will just rise with no air resistance.

00:19 In the instance where m2 has a mass of five kilograms, it is measured to have an acceleration of three meters per second squared upwards.

00:29 Part a would be defined.

00:31 The mass of mass one and part two is to find the speed that the masses are moving once mass one has fallen four meters so let's start with part one trying to figure out the mass one i'm going to treat mass one and mass two as a system as one system in this curvy coordinate system so the forces in the counterclockwise direction will be m1 times g and the forces in the other direction are going to be m2g also that magical 5 newtons from the fluid and i knew that together with the net force on the system in that direction and that's going to equal the mass of the system which is m1 plus m2 times the acceleration of the system which was given.

01:34 So here we can do some algebra and isolate m1.

01:37 Just we're going to go m1g minus m1a equals m2a plus m2g plus 5 newtons.

01:55 Solve for m1 g minus a we can yeah we could pull out m2a plus g plus g plus g forget the five.

02:10 Now we can solve for m1, which would equal m2, a plus g, divided by g minus a plus 5.

02:25 We can plug in our values we're given five kilograms times our acceleration is three, g is 9 .8.

02:34 So that would be 12 .8 plus 5 over 9 .5.

02:44 0 .8 minus 3, 6 .8...