# Three blocks and two pulleys

1. Oct 10, 2009

### marco101

1. The problem statement, all variables and given/known data
three blocks are relased at t=0 from the position shown in the figure. Assume that there is no friction between the table and M2, and that the two pulleys are massless and frictionless. The masses are: M1 = 3.0 kg, M2 = 9.0 kg, M3 = 5.0 kg.

M2 is the middle block connected to M1 (to the left) and M3 (to the right)

Calculate the speed of M2 at a time 1.75 s after the system is released from rest.

2. Relevant equations
Since they will all have the same acceleration, i was trying to look for a and then multiply that by the t.

3. The attempt at a solution

I set up this equation:
FM1 = Tension - M1*g = M1a
FM3 = Tension - M3*g = (M1 + M2 + M3)a

and i get a to be 1.4m/s^2 and Vf to be 2.45m/s but it is incorrect. Any help pls?

2. Oct 10, 2009

### rl.bhat

Tension in the two strings are not the same.
Note down which mass goes up and which mass goes sown.
Accordingly write down three equations for three masses.
You have three unknowns, T1, T2 and a. Solve for them.

3. Oct 10, 2009

### marco101

wait, how are the two tensions different though?
I know that FM1 = Tension - M1*g = M1a is correct, so is tension for Fm3 gonna be (m1+m2)a?

4. Oct 10, 2009

### rl.bhat

M3*g - T1 = M3*a ...(1)
T1 - T2 = M2*a....(2)
T1 - M1*g = M1*a ...(3)
Solve for a.

5. Nov 19, 2010

### leavex

if i found a, how do i find the speed of m2?

6. Nov 19, 2010

### rl.bhat

Use v = vo + at. vo is zero.

7. Nov 19, 2010

### leavex

i tried it doesnt work, i have the same question but but different m
m1=2 m2=8 m3=4
i get zero for answer and its wrong... i did exactly the same way you did above.....

8. Nov 19, 2010

### rl.bhat

What is your value of a?

9. Nov 19, 2010

### leavex

i solved id and got 0 for a
m3g-m1g-m1g=4-2-2=0

10. Nov 19, 2010

### rl.bhat

4g - T2 = 4a...(1)
T2 - T1 = 8a...(2)
T1 - 2g = 2a...(3)

From these equations find a.

11. Nov 20, 2010

### leavex

i did it doesnt wark i just dont know what do i do wrong......
i got a=1.962
t= 1.45
v=2.84 m/s
why is it wrong??

12. Nov 20, 2010

### rl.bhat

If you add (1) and (3), you get

T1 - T2 + 2g = 6a.

2g = 6a + T2 - T1 = 6a + 8a = 14a.

So a = 2g/14 = 2 * 9.8/14 = 1.4 m/s^2

Now find the velocity of m2.

13. Nov 20, 2010

### leavex

yeahhhhhhhhhhh it fianely worked, thank you so mach!!