Newton's Second Law Concerning Net Force

[PeachBanana]

Homework Statement

• If we add a third block, leaving the 10 N force the
same, what happens to f3,
the net force on the 3 kg
block?

A. Increase
B. Decrease
C. Stay the Same
D. Not Enough Info.

Homework Equations

F net = m * a

The Attempt at a Solution

Ignore the colors in the attachment. All that matters are the numbers.
The acceleration of the system with only the two blocks is 1.25 m/s^2.

10 N = (3 kg + 5 kg) * a
a = 1.25 m/s^2

The acceleration of the system with the three blocks is now 0.625 m/s^2.

I'm trying to set up an equation to solve for the net force on the 3 kg block.

10 N + Force of block 3 on block 5 - Force of block 5 on block 3 = ...?
IF that's a correct equation.

 

[Simon Bridge]

10/8=1.25m/s/s ... what does this tell you about how many forces are acting on the blocks?

Is the acceleration of each block the same?

What is the relation between the net force on the block and it's acceleration?

 

[PeachBanana]

Hmm. I know with the same force, more mass gives less acceleration so 10N / 8 kg = 1.25 m/s^2 tells me there is less mass, I think. The acceleration of each block is the same (does this also mean the net force on each block is the same?), they kind of act as a system. The relationship between the net force and acceleration is mass.

F / a = m
a = F / m
So when we add a third block, we've increased mass but left force alone. This means acceleration on each block decreases. I'm thinking this means the net force on each block decreases too?

 

[Simon Bridge]

the acceleration of each block is the same (does this also mean the net force on each block is the same?)

The acceleration for each block is the same, but the mass of each block is different - what does this mean about the net force on each block given you know F=ma?

So when we add a third block, we've increased mass but left force alone. This means acceleration on each block decreases.

Well done - so if you double the mass, you ________ the acceleration (fill in the blank).

Once you know the acceleration of each mass (they are the same remember) then you can use that, and the mass, to get the force on each mass.

 

[PeachBanana]

@Simon Bridge, thank you. That's much clearer now. Doubling mass = 1/2 acceleration.

F net on block 3 = (3 kg) (0.625 m/s^2) = 1.875 N

compared to only two blocks

F net on block 3 = (3 kg) (1.25 m/s^2) = 3.75 N

B.

 

[Simon Bridge]

Well done.

You can also do it by treating each block separately, so the 3kg block has 10N to the right and F1 to the left for 10-F1=3a; the 5kg block gets F1 to the right and F2 to the left, for F1-F2=5a; and the 8kg block has F2 to the right and nothing opposing, for F2=8a. That's three equations and three unknowns.

Note: the fact that the two block model works out so nice tells you they are on a frictionless surface.