# Homework Help: Pushing blocks - static friction, force, and accel

1. Feb 21, 2010

### mybrohshi5

1. The problem statement, all variables and given/known data

A block of mass 1.2 kg rests on top of another block of mass 1.8 kg, which rests on a frictionless surface. The coefficient of static friction between the blocks is mu_s = 0.3.

(a) What is the maximum horizontal force that can be applied to the upper block so that the blocks accelerate together, without the upper block sliding on the lower one?

(b) Suppose that the force is applied to the lower block instead; what is the maximum horizontal force that can be applied in this case so that the blocks will accelerate together, without any slipping between the two?

2. Relevant equations

f=ma

μs=fs/n

3. The attempt at a solution

I tried this but it didnt work out to be right and i think i am leaving something out.

i found the normal force on the top block

n=1.2(9.8) = 11.76

then i found the fs

0.3 = fs/11.76

fs=3.528

i knew that wasnt right cause i didnt include anything about the bottom block moving with the top block so i found the fs of this bottom block as well

0.3 = fs/17.64

fs = 5.292

Not sure what to do now? i think if i add the two fs's together that will give me part (b) which would be 8.82 N for the force and i believe that is correct but im not sure how to get part (a)

Any help would be appreciated.

Thank you :)

2. Feb 21, 2010

### dr_k

(Part a) Draw a FBD for the bottom block, and then determine the maximum acceleration for the bottom block w/o the top block slipping. This maximum acceleration will be the acceleration for the top block as well, since they are moving together (no slipping). Be careful when you draw the FBDs for the top and bottom block, there are action-reaction pairs, fs and N, that must be treated carefully.

Last edited: Feb 21, 2010
3. Feb 21, 2010

### mybrohshi5

ok i drew my FBD for the bottom block but since i do not know the force that is pushing the blocks how can i find the acceleration?

thank you for the help :)

4. Feb 21, 2010

### mybrohshi5

Hang on i may have found it.

i found the fs for the bottom block

0.3=fs/(1.2+1.8)(9.8)

fs=8.82 (which is the answer for part (b)

8.82 = (1.2+1.8)(a)

a = 2.94 m/s^2

if this is right im not sure how to use this to find the force that can be applied to the top block with no slipping :(
is that correct?

5. Feb 21, 2010

### dr_k

Stick with (Part a) for now...

When you draw the FBD for the bottom block, where does the fs force come from? What object is providing this force, and in which direction does it point?

6. Feb 21, 2010

### mybrohshi5

ok. so on my FBD the fs force comes from the normal force times by the coefficient of static friction -----> 0.3[(1.2+1.8)(9.8)] = 8.82

this points in the opposite direction of the force being applied. so on my diagram i have the force we are trying to find pushing the blocks to the right so the fs force will be to the left.

7. Feb 21, 2010

### dr_k

The fmaxs does not include the mass of the bottom block. Take a look at this picture, label the forces, and then see if it agrees with your FBDs:

http://img16.imageshack.us/img16/4536/blocks3.jpg [Broken]

Last edited by a moderator: May 4, 2017
8. Feb 21, 2010

### mybrohshi5

yes you are right the fs is only determined by the top block cause its on a frictionless surface so there will be no friction on the bottom of the bottom block i forgot about that. yes that is what my FBD looks like.

ok so the fs is then

0.3=fs/(1.2*9.8)

fs = 3.528

is this correct?

would i then use this to solve for acceleration?

3.528=(3)a

a= 1.176????

9. Feb 21, 2010

### dr_k

Yes, this is fmaxs = mu_s m g

here you're using (m+M). Why? Look at the FBD for the bottom block.

10. Feb 21, 2010

### mybrohshi5

i thought i had to use the total mass because both blocks are moving with a certain acceleration.

but from the bottom FBD i would only use the mass of the bottom block......OH BECAUSE THE BLOCKS HAVE THE SAME ACCELERATION SO YOU JUST HAVE TO FIND THE ACCELERATION OF THE LARGER MASS CORRECT?

3.528 = 1.8(a)

a = 1.96 m/s^2

then to solve for part (a)

F = (3)(1.96)

= 5.88 N and that is correct :)

does that all look right?

11. Feb 21, 2010

### dr_k

Yes, that's the answer, but note how you quickly wrote

Fmax = (m+M)amax

This equation comes from a FBD for the system (m+M), which is a FBD that we haven't drawn yet. See if you can get the same result using the FBD for the small block, which we have a picture for.

12. Feb 21, 2010

### mybrohshi5

so using the small FBD i would....

F = (1.2)(1.96) = 2.352

then i would add this force to the fs force correct to get the total force in the x direction that is allowed to be applied to the top block with no slipping.

F_total = 2.352 + 3.528 = 5.88 N :)

is that the right way to do it?

hmmmmm now the right way to do part (b).....

13. Feb 21, 2010

### dr_k

Sort of. You're confusing some ma's with F's, etc.

Just use the FBD...

The FBD for the top block says

F-fs = max

and therefore

Fmax = fmaxs + mamaxx

Just remember, for a problem like this, you can make a FBD for each mass separately, and then you can also make one for the system. The one for the system would not have fs and N, these are reaction-action pairs that cancel since they are "internal" to the system.

Onward to (Part b)...

14. Feb 21, 2010

### mybrohshi5

Thank you so much for explaining that last part. that really makes sense and i think that is how my professor will want to see the work done.

ok so part b

the fs would be different so i found that

fs = 1.8(9.8)(0.3) = 5.292

now to find the Fmax i would do the same as in part a

Fmax - fs = ma

Fmax = (1.8)(1.96) + 5.292

Fmax = 8.82 N

Look ok?

15. Feb 21, 2010

### dr_k

The answer is correct, 8.83N, but how you got it doesn't make sense to me.

Draw new FBDs, for the top and bottom block. fs changes direction for part (b), and then write down the equations for Newton's 2nd postulate.

16. Feb 21, 2010

### mybrohshi5

i didnt even think about that. yes fs does change direction when pushing the bottom block

im not sure how to come up with a newtons 2nd equation for this?

would it be

Fmax - fs(of the bottom block) = ma

17. Feb 21, 2010

### dr_k

No, you have to be careful with m and M, they're not the same thing. Here's a picture to get you started again:

http://img705.imageshack.us/img705/6676/blocks4.jpg [Broken]

Just do what Newton said to do! :)

Last edited by a moderator: May 4, 2017
18. Feb 21, 2010

### mybrohshi5

ok thats what i got for my FBD's

newtons law is f=ma

so you have the force we are trying to find pushing to the right and the fs of M is in the opposite direction.

is the acceleration the same or is it different? is it maybe different because you are pushing on the bottom block now so the fs will be greater which allows the acceleration to be greater?

19. Feb 21, 2010

### mybrohshi5

i think i maybe got it but it may not be the right way to find it.....

i found the new fs

fs = 0.3(1.8*9.8)

fs = 5.292

F=ma

5.292 = 1.8(a)

a = 2.94

Fmax = (m+M)(a)

Fmax = 3(2.94)

Fmax = 8.82 N

correct or am i still thinking about it wrong?

20. Feb 21, 2010

### dr_k

Newton says...

for m:

N - mg = 0
fs = mam

thus

amaxm = fmaxs/m = us g

for M:

F - fs = MaM

if aM = amaxm

then, for (Part b)

Fmax = us g (m+M)

--------------------------

The result for (Part a) was, Fmax = us g (m+M) m/M

----------------------------------------------------------

I recommend that you do this problem over, from scratch, writing down three FBDs, and their attendant Fnet equations, for (1) m alone, (2) M alone, and (3) m+M together, just to make sure you understand action-reaction pairs.

21. Feb 21, 2010

### mybrohshi5

Ok i will look at this problem again from the beginning and make sure i am understanding everything correctly. If i am confused i will let you know but i think after i read over all of the posts and look at everything again i will get it..... hopefully ;)

One quick question. What does the u_s stand for in the equations you posted above. Sorry i just have never used or seen a "u" in these types of equations.

Thanks again for all of your time and drawing up those FBD for me. You really are a great deal of help and you really know your stuff and how to explain things very clearly. I really appreciate it all so much. Thanks again :)

22. Feb 21, 2010

### dr_k

The lazy way to write (mu)_s:

us = $\mu_s$

This is actually a good instructional problem -- a decent problem to practice your FBDs.

Good Luck.