Three blocks connected by two strings: tensions?

[ddtozone]

Homework Statement

Three blocks on a frictionless surface are connected by strings like so (from left to right):
Block 1 (m=10kg) to string with Tension 1 to Block 2 (m=20kg) to string with Tension 2 to Block 3 (m=30kg) to string with Tension 3.
The blocks are pulled to the right with force T3=60N.
Find T1 and T2.

Homework Equations

I'm not even sure... maybe
Fn=mg

The Attempt at a Solution

I would guess T1 is 20N and T2 is 40N, because it's proportional to T3. But this doesn't seem correct. Could I please get some feedback?


Thank you!

 

[NascentOxygen]

T3 accelerates 3 blocks, T2 accelerates 2 blocks, etc.

 

[quietrain]

if i am not wrong,

consider the entire system of 3 blocks

force to the right 60N = mass of 3 blocks (60kg) x acceleration

'a' is the same for the entire system. so , 'a' is the same for each block

so your acceleration is = 60/60 = 1

so for tension 1, which pulls only block 1, to have a = 1, it must have a force acting on it by f=ma = (10kg)(1) = 10N, so tension is = 10N

for tension 2, which pulls block 1 and block 2, a = 1, f=ma = (10+20)(1) = 30N

for tension 3, which pulls block 1,2,3, a = 1, f= ma = (10+20+30)(1) = 60N

 

[ddtozone]

Thanks a ton! That makes much more sense.

 

[rwisz]

Your initial intuition is correct, but there are a few things to consider in order to get the correct solution. First, it's important to remember that the tension in a string is the same throughout the entire string. This means that T1, T2, and T3 are all equal to each other. So, in your initial guess, T1 should actually be 60N as well.

Next, we can use Newton's second law (F=ma) to solve for the accelerations of each block. We know that the net force on each block is equal to the mass of the block times its acceleration. Since the blocks are all connected, they will all have the same acceleration.

For Block 1:
Fnet = T1 - T2 = m1a
For Block 2:
Fnet = T2 - T3 = m2a
For Block 3:
Fnet = T3 = m3a

We can then set up a system of equations and solve for T1 and T2:
T1 - T2 = m1a
T2 - T3 = m2a
T3 = m3a

Since we know that T1, T2, and T3 are all equal, we can substitute T3 for T1 and T2 in the first two equations:
T3 - T3 = m1a
T3 - T3 = m2a

Simplifying, we get:
0 = m1a
0 = m2a

Since m1 and m2 are both non-zero, this means that a (the acceleration) must be 0. This makes sense because the blocks are on a frictionless surface and there are no external forces acting on them besides the tension in the strings.

So, now we can solve for T1 and T2:
T1 = T3 = 60N
T2 = T3 = 60N

So, the tensions in the strings are all equal to 60N. This makes sense because the blocks are all connected and will experience the same amount of force.

I hope this helps clarify the solution for you! It's always important to remember to consider all the forces acting on a system and use Newton's laws to solve for unknowns.