Find The acceleration (Newton's Laws of Motion problem).

[All Pow3r]

Homework Statement

Fig. 4.3

A 5.0-kg block and a 4.0-kg block are connected by a 0.6-kg rod. The links between the blocks and the rod are denoted by A and B. A force F is applied to the upper block.In Fig. 4.3, the force in link B is 40 N. The acceleration of the blocks and rod assembly, including direction, is closest to:

1) zero
2) 2.4 m/s2, downward
3) 1.2 m/s2, downward
4) 2.4 m/s2, upward
5) 1.2 m/s2, upward

Homework Equations

we have to use Newton's Laws of Motion to find the answer.

The Attempt at a Solution

I tried to figure out the acceleration for each of 5.0-kg block, 4.0-kg block and 0.6-kg rod using these equations:

for the 5.0-kg block \ ƩF=ma ==> F - m1g - Fa = m1a ==> F-Fa = m1(a+g)

for 4.0-kg block \ ƩF=ma ==> Fb - m2g = m2a ==> Fb = m2(a+g)

for the 0.6-kg rod \ Fa + Fb ==> (F(m1+m2+m3) - m1F)/(m1+m2+m3) + (m2F)/(m1+m2+m3)and i could do that for the 4.0-kg block and 0.6-kg rod but i couldn't with the 5.0-kg block because F is unknown for me!- I find Fa and Fb this way :

First ƩF for the hole system is ƩF=ma ==> F-(m1+m2+m3)g = (m1+m2+m3)a
so, a = F/(m1+m2+m3) -g

for m1 ƩF=ma ==> F-Fa-m1g = m1a
so, F-Fa = m(a+g) = m1F/(m1+m2+m3) ==> Fa = F(m1+m2+m3)-m1F/(m1+m2+m3) ==> Fa = 0.48N

and Fb = 40N (Given in the question)
m1 = mass of 5.0-kg block
m2 = mass of 0.6-kg rod
m3 = mass of 4.0-kg block

Fa = Force of A
Fb = Force of B

 

[frogjg2003]

Read the rules: you must attempt a solution before we can help

 

[All Pow3r]

Read the rules: you must attempt a solution before we can help

sorry, i just put my attempt!

 

[frogjg2003]

Fa and Fb aren't the only forces acting on the rod.

 

[frogjg2003]

If you only want to answer the question, though, you only have to look at block B. The acceleration of the whole system is the same for each piece. You have an equation with only the acceleration as the unknown, so just solve for a there.

 

[All Pow3r]

Fa and Fb aren't the only forces acting on the rod.

I'm not sure what advantage i take from this information specifically!

 

[All Pow3r]

If you only want to answer the question, though, you only have to look at block B. The acceleration of the whole system is the same for each piece. You have an equation with only the acceleration as the unknown, so just solve for a there.

Here is my attempt:ƩF (for the block B) equals Fb - m2g = m2a ==> Fb = m2(a+g) ==> 40 = 4(a+9.8) ==> a=0.2 m/s2.
So, it closest to zero ( if i substitute g with value 10, a will be 0 ).
Is that correct ? or i should use the simple equation a = F/m ?

 

[frogjg2003]

Yes. I'm guessing this is for an exam? It's perfectly reasonable that they might have g=10m/s^2, especially if you're not allowed to use a calculator.
a=F/m is only true when F is the net force.

 

[All Pow3r]

Yes. I'm guessing this is for an exam? It's perfectly reasonable that they might have g=10m/s^2, especially if you're not allowed to use a calculator.
a=F/m is only true when F is the net force.

oh! That is way easier than i thought :)
it is kind of online Assignment.


Thanks.