How to determine the mass of the second block in a spring and block problem?

[heather32283]

Please help, I can not figure out if I would set up the equation as 3F=-kx

The problem is A 0.70-kg block is hung from and stretches a spring that is attached from the ceiling. A 2nd block is attached to the first one and the amount that the srping stretches from its unstrained length triples. What is the mas of the second block?

 

[OlderDan]

If F1 is -kx, then F2 is -3kx. F1 is the weight of the first block. F2 is the weight of the two blocks together.

 

[heather32283]

ok am I using the right equation for this problem, I know I have to find the mass

 

[OlderDan]

Yes, you have the right equation. You just need to relate the forces to one another, as outlined previously, and relate those forces (weights) to the masses of the objects involved.

 

[heather32283]

F1=F2 and use -kx=-3kx ??

 

[OlderDan]

F1 does not equal F2. From F1 = -kx and F2 = -3kx we find that F2 = 3F1 by substitution

 

[heather32283]

Im confused sorry

 

[OlderDan]

OK Let's step through it
The first block causes the spring to stretch a distance x. The force the spring provides is proportional to the stretch. It is -kx. The minus sign indicates that the force is in the direction opposite the stretch. Adding the second block triples the distance of stretch, but k stays the same. k is a property of the spring (as long as you don't stretch it too far and ruin it).

There are two cases

F1 = -kx
F2 = -3kx

If you replace the -kx in the second equation with F1 (because they are equal) you get

F2 = 3F1

Now F1 is equal in magnitude to the weight of the first block

F1 = M1g

and F2 is equal to the weight of the two blocks combined

F2 = M1g + M2g

Replce F2 and M1g with their equals

3F1 = F1 + M2g

Subtract F1 from both sides

2F1 = M2g

Replace F1 with its equal M1g

2M1g = M2g

divide both sides by g

2M1 = M2

The mass of the second block is twice the mass of the first block. Use the known mass of the first block to compute the mass of the second block

 

[heather32283]

i will work through it tonight

 

[heather32283]

I still can't figure it out

 

[OlderDan]

What do you not understand, the derivation I did to get the result 2M1 = M2, or where to go from there?