# Three blocks and two pulleys

## Homework Statement

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.

## Homework Equations

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

## 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?

rl.bhat
Homework Helper
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.

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?

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

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

rl.bhat
Homework Helper
if i found a, how do i find the speed of m2?

Use v = vo + at. vo is zero.

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.....

rl.bhat
Homework Helper
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.....

What is your value of a?

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

rl.bhat
Homework Helper
4g - T2 = 4a...(1)
T2 - T1 = 8a...(2)
T1 - 2g = 2a...(3)

From these equations find a.

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??

rl.bhat
Homework Helper
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.

yeahhhhhhhhhhh it fianely worked, thank you so mach!!