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

  • Thread starter Thread starter heather32283
  • Start date Start date
  • Tags Tags
    Block Spring
AI Thread Summary
To determine the mass of the second block in the spring and block problem, the relationship between the forces acting on the blocks must be established. The first block stretches the spring by a distance x, creating a force of F1 = -kx. When a second block is added, the stretch triples, leading to F2 = -3kx. By equating the forces and substituting, it is derived that 2M1 = M2, indicating that the mass of the second block is twice that of the first block. This relationship allows for the calculation of the second block's mass using the known mass of the first block.
heather32283
Messages
23
Reaction score
0
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?
 
Physics news on Phys.org
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.
 
ok am I using the right equation for this problem, I know I have to find the mass
 
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.
 
F1=F2 and use -kx=-3kx ??
 
F1 does not equal F2. From F1 = -kx and F2 = -3kx we find that F2 = 3F1 by substitution
 
Im confused sorry
 
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
 
i will work through it tonight
 
  • #10
I still can't figure it out
 
  • #11
What do you not understand, the derivation I did to get the result 2M1 = M2, or where to go from there?
 
Back
Top