- #1
chahud42
Homework Statement
A light spring of force constant 3.90 N/m is compressed by 8.00 cm and held between a 0.250 kg block on the left and a 0.530 kg block on the right. Both blocks are at rest on a horizontal surface. The blocks are released simultaneously so that the spring tends to push them apart. Find the maximum velocity each block attains if the coefficient of kinetic friction between each block and the surface is the following. In each case, assume that the coefficient of static friction is greater than the coefficient of kinetic friction. Let the positive direction point to the right.
We have to find the final velocities of both masses for μk values of .000, .100, and .483.
Homework Equations
Conservation of momentum, Newtons second law, conservation of energy
The Attempt at a Solution
Initially, the blocks are at rest and the spring is compressed. So the initial momentum of the system is 0, but there is a force in the spring which is equal to F=kx=(3.9Nm)(.08m)=.312N
So, once the spring is released, it pushes on each block with this force. The momentum of each block is increased to P1=m1v1 and P2=m2v2. We can't go much further with this because the only 2 unknowns with using conservation of momentum are the velocities, which is what we need.
So I started to look at F=kx=ma. I can use kx/m=a to solve for the accelerations of the blocks caused by the spring. I got that a1=1.25m/s2 and a2=.59m/s2. Then I wanted to use this in the formula v2=vo2+2aΔx to solve for the velocity. For the velocity of block one i got v=.45m/s. This was wrong so I didn't even bother to go further because something in my solution is wrong. None of my classmates or I can solve this. Where did we go wrong?
One thought I had was that the force exerted on each block won't be equal to kx, but kx/2 because the force is shared over two separate masses. But I tried this and this didn't work either. I'm fresh out of ideas.