Could someone PLEASE quickly check if my work is right?

[Lawcheehung]

Homework Statement

Basically there's a 1.00 kg object hanging in the air attached to a string which is attached to a 0.1487 kg object that is on a table, and they're connected with a pulley.

the 1.00 kg object pulls the 0.1487 kg a distance of 0.89 m in 1.22 s and then stops when it hits the ground, i need to find the coefficient of friction


ok so..


first i found the final velocity of the object
which is 0.89 m / 1.22 s which gave me a final velocity of 0.7295 m/s

then i found the acceleration of the entire body by doing

a = (vf - vi)/t which gave me an acceleration of 0.597957 m/s^2


The Fnet of the entire body is

Fnet = [(0.100kg ) + (0.1487kg )] * (0.597957 m/s^2)
= 0.14871 N
This is the actual net force with the friction



so the acceleration of the 0.100 kg falling down without the tension should be just

mg = (0.100)(9.8)
= 0.98 N


so the friction force should be
0.98 N - 0.14871 N
= 0.83129 N

This is the friction force.

The coefficient of friction is

Ff = uFn
so 0.83129 N = u(mg)
0.83129 N = u(0.1487 kg * 9.8 m/s^2)

u = 0.5704


Please i need help URGENT

 

[Rake-MC]

Well I can tell you that you got the final velocity wrong in your first equation. You completely ignored the fact that the object is accelerating under the force of gravity. What you did was the average velocity perhaps.
Try this: V_final = V_initial + at