# Newton's laws and pulley mass system

1. Apr 20, 2010

### dink87522

1. The problem statement, all variables and given/known data

The coefficient of friction between the block of mass m1 = 3.00 kg and the surface in the figure below is μk = 0.335. The system starts from rest. What is the speed of the ball of mass m2 = 5.00 kg when it has fallen a distance h = 1.45 m?

2. Relevant equations

Ff = UsN
T - mg = ma

Y = Yo + Vot + 1/2at^2 (maybe, I'm not sure)

3. The attempt at a solution

I found that a = 4.89m and that the tension in the string is 24.45N. I don't know how to then take teh distance 0f 1.45m travelled into consideration and work with this.

2. Apr 20, 2010

### thebigstar25

are you sure from the value you got for a? I feel that there is a mistake there? (please show that steps you followed to get the acceleration)

in case you are sure from your answer, then to get the speed I suggest you use the following equation:

vf^2 = vo^2 + 2ax, where vf: the final velocity, vo: the initial velocity, a:acceleration, x: the distance

you have vo =0 (from the question "the system starts from rest"), a (you got it), and x (given in the question)..

3. Oct 24, 2011

### janggeng

I'm using a simulation to solve acceleration and Tension ( g = 9.8 m/s^2)

a = 4.89 m/s^2

vo = 0
h = 0.5*a*t^2
t = root(2*h/a) = root(2*1.45/4.89) = 0.77 s

spreed of the system after 0.77 s is

vt = vo + at = 0 + (0.77 s)*(4.89 m/s^2) = 3.7653 m/s

_____________________
http://janggeng.com/newtons-laws-aplication-pulley-system-part-1/"

Last edited by a moderator: Apr 26, 2017
4. Oct 24, 2011

### dink87522

That looks like some pretty blatant self promotion :p although it does look like it would have been a handy application to help with learning mechanics.

5. Oct 24, 2011

### pgardn

I have a hunch your teacher probably wants you to be able to draw FBD for both masses allowing you to get two equations with T and a being your unknowns. Two equations, two variables, solve for a.

The rest is just simple kinematics. If the teacher had angled the plane the application that one poster wrote would be unusable. Its for one of many types of problems that could be given with simple statics or dynamics. I would think you would want to put pencil to paper and do it yourself. Then play with simulations. Or write your own.

So what are all the forces on the mass on the plane in the vertical and horizontal and all the forces in the vertical for the mass hanging... start there. a and T must be the same magnitude for both