# Two blocks and a massless horizontal spring question?

1. May 16, 2013

### nitin4422

1. Two masses of m1 and m2 is connected by a massless undeformed spring rest on a horizontal plane.Find the minimum constant force Fmin that has to be applied on m2 so that other block get shifted if D is the coefficient of friction between blocks and surface

2. Relevant equations-spring force kx

3. i have tried to use conservation of energy for this question as block m1 will have potential energy D^2mi^2g^/k and when it will start moving its potential energy will change into the kinetic energy ....please help i am really stuck on this question

2. May 16, 2013

### CWatters

Wrong approach. Just look at the forces....

Ignore mass 2 for the moment. What force must the spring exert on mass 1 to move it?

Then draw a free body diagram for mass 2.

Edit: Sorry I had the numbers 1 and 2 the wrong way around when I first replied. Have fixed that now.

3. May 16, 2013

### nitin4422

ok spring force required to move the mass m1 will be kx greater than or equal to Dm1g .now after drawing the free body diagram of mass 2 i have got F-Dm2g-kx=m2a (here a is the acceleration of mass 2).now if i put the value of kx from equation 2 to equation 1 i am getting the answer with m2a in it but the given answer is (m1/2+m2)Dg

4. May 16, 2013

### Staff: Mentor

An energy approach is the right way to go, but you'll need to analyze forces as well. Hint: For m1 to start moving, what must be the compression of the spring?

5. May 16, 2013

### DEvens

I disagree with the given answer.

To move block 1 at constant speed you need to shove it with force m1 D g.
To move block 2 ditto you need force m2 D g.
To move both blocks you need (m1 + m2) D g. And the fact they are connected by a spring won't make any difference. With both blocks at constant speed the spring is constant length.
Dan

6. May 16, 2013

### Staff: Mentor

You want the minimum force that will make the second block (m1) just start to move.

7. May 16, 2013

### haruspex

CWatters and DEvens, you're both overlooking that since the force required must be more than m2Dg, m2 will acquire some momentum. That will later assist in moving m1.

8. May 16, 2013

### Tanya Sharma

Shouldn't the coefficient of friction between the blocks and the surfaces be different ? For the force applied on m2 ,we will be dealing with kinetic friction .While for block m1 to just move ,we have to deal with static friction .

9. May 17, 2013

### haruspex

It would seem that in this question the two are to be taken to have the same value.

10. May 17, 2013

### nitin4422

I took the blocks and spring as one system and calculated acceleration on each box a=F-D(m1+m2)g/(m1+m2) then i tried to solve it from a non inertial frame with a a psuedo force on mass m1 and used conservation of energy i tried this but no answer instead i found maximum elongation in the string 2m1{F-D(m1+m2)g}/m1+m2 sorry if its totally wrong

11. May 17, 2013

### Staff: Mentor

Realize that the blocks do not have the same acceleration. You cannot treat the system as a single rigid body.

12. May 17, 2013

### nitin4422

i think force F on the mass2 will stretch the spring to the right side of the block of mass1 therefore block of mass 1 will have a tension force kx due to the spring so in order to move the mass spring force will have to apply force equal to or greater to Dm1g therefore kx> or equal to Dm1g so x must be> or equal to Dm1g/k so.. i think compression should be equal to Dm1g/k am i thinking right?

13. May 17, 2013

### Staff: Mentor

Excellent. Now realize that that compression distance is the distance that block 2 must move through and thus the distance over which the applied constant force F must act. Now it's time to apply energy methods.

14. May 17, 2013

### DEvens

The "given" answer is (m1/2 + m2) Dg, when pulling on mass m2.

Suppose that mass m1 is very much larger than m2, such that you can ignore m2 in the result. The given answer is thus claiming that, somehow, you only need to pull half as hard as you'd need to in order to move m1 without the spring.

Or, to take a really extreme case, let m2 be zero. So this is claiming that by pulling on the other end of the spring it requires only half the force required to move m1 as by pulling it directly.

What?
Dan

15. May 17, 2013

### Staff: Mentor

Imagine the masses are arranged, from left to right, as m2, spring, m1. Your task is to find the minimum constant force to push m2 so that m1 just begins to move. To find the minimum force, you will take advantage of any speed you give to m2 when you push it.

Yep. Realize that since the force of the spring is not constant, that your constant applied force ends up giving m2 speed with which to further compress the spring.

Let's just make m2 be very small. (Not sure it makes sense to have it zero, but a small m2 makes your point just the same.) The same considerations as above apply.

The trick is that you are applying a constant force that is greater than the spring compression force (at least much of the time). So you are building up speed that can end up compressing the spring more and moving m1.

16. May 17, 2013

### haruspex

It says pushing, but it also works for pulling.
As Doc Al says, you can be misled by setting m2 to zero. As m2 becomes very small, its initial acceleration (when there's no resistance from the spring yet) becomes arbitrarily large. Since the force will always be at least m1/2, the energy invested in pulling/pushing distance x is at least m1x/2. When x is small, that must exceed the energy going into the spring, kx2/2. So no matter how small you make m2, there's a lower bound on the KE it gets.
Ever seen a bungee cord used?

17. May 19, 2013

### Tanya Sharma

Hello nitin4422

Were you able to solve the problem ? If not , what difficulty are you facing ?