Mechanics/Kinetics of Particles

[scluggy]

Two weights are hanging from a rope that goes through two pulleys as shown below:

_______
| O
| / \
| | |
\ / |
O |
| |
A B

A weighs 3 kg
B weighs 2 kg

B has an initial speed of 0.8 m/s

How far will B drop before A reaches a speed of 0,6 m/s?

The mass of the pulley and the cable can be neglected.

I have been trying to resolve this for some time now but will always get the wrong answer. The way I believe it should work is:

The potential energy + the kinetic energy for the system is the same at the start and end of this so we would have a conversion of energy from potential energy to kinetic energy. So I have set it up as having 0 potential energy to start off with (height = 0)

mgh = 2*9.81*0 = 0 and 3*9.81*0 = 0

The velocity for B would be twice that of the velocity for A due to the pulley system.

The initial kinetic energy would be:
0.5mv^2 = 0.5*2*0.8^2 and 0.5*3*-0.4^2

So the whole amount of energy for this would be
0.64-0.24 = 0.4

If we then set this equal to the same formula but for the A speed of 0.6 m/s we get
0.88 = (kinetic energy A) + (kineric energy B) + (potential energy A) + (potential energy B)

0.4 = 0.5*3*-0.6^2 + 0.5*2*1.2^2 + 3*9.81*h/2 + 2*9.81*h

Which makes h = - 100 / 6867

This is incorrect as the answer should be 0.224

Can someone see where I am going wrong and perhaps help with how this should be resolved? I have been trying to resolve this issue for some time now with different methods but will always come up with the wrong answer.

Thankful for any suggestions!

 

[Doc Al]

The velocity for B would be twice that of the velocity for A due to the pulley system.

The initial kinetic energy would be:
0.5mv^2 = 0.5*2*0.8^2 and 0.5*3*-0.4^2

So the whole amount of energy for this would be
0.64-0.24 = 0.4

Your error is in having a negative kinetic energy! The KE of mass B is positive, not negative.

Regardless of your sign convention, the speed is squared so the KE is always positive. (To maintain sanity, I would choose a sign convention of up = +, down = -.)

 

[scluggy]

Thank you so much! I was really struggling with this problem but now it's solved thanks to your help