# Maximum speed of object between 2 springs

by rolodexx
Tags: maximum, object, solved, speed, springs
 P: 14 1. The problem statement, all variables and given/known data A 1.50 kg box moves back and forth on a horizontal frictionless surface between two different springs, as shown in the accompanying figure. The box is initially pressed against the stronger spring, compressing it 4.00 cm, and then is released from rest. (I solved part A, B is: What is the maximum speed the box will reach?) 2. Relevant equations K$$_{i}$$ + EPE$$_{i}$$ = K$$_{f}$$ + EPE$$_{f}$$ .5mv$$^{2}$$ $$_{i}$$ + .5k$$_{i}$$x$$_{i}$$ $$^{2}$$ = .5mv$$^{2}$$$$_{f}$$ + .5k$$_{f}$$x$$^{2}$$$$_{f}$$ (sorry about the messed-up subscripts; I can't make it work right) 3. The attempt at a solution I solved for x$$_{}f$$ first, obtaining the correct answer of 5.66 cm. I then plugged in values for the other variables: m of 1.5 kg, initial velocity of 0 (because it started from rest?), initial k of 32 N/m, initial x of 4 cm, final k of 16 N/m, final x of 5.66 cm. I converted cm to m and tried to solve for final velocity, but I got .062 m/s and it's supposed to be 1.85 (I got it wrong enough times that it gave me the answer, I just don't know how to solve for it).
 P: 14 v$$_{f2}$$ = mv$$_{i}$$$$^{2}$$ + k$$_{i}$$x$$_{i}$$$$^{2}$$ - k$$_{f}$$x$$_{f}$$$$^{2}$$ I used the conservation of energy rule to set the initial and final kinetic energy and elastic potential energy equal to each other, then tried to solve for final kinetic energy by subtracting both sides by final elastic potential energy. Then I divided the final kinetic energy by the mass to get final velocity squared. On the other side, that left initial velocity squared (its mass canceled out when I divided by the mass from the other side) plus initial spring constant * inital compression, minus final spring constant * final compression After I plugged in the numerical values stated above, I took the square root to change final velocity squared to just final velocity.
 HW Helper P: 2,685 Maximum speed of object between 2 springs Your problem is that you have both the potential energy terms involved. When the block has potential energy in one spring, the other spring is not compressed at all. So, the total energy is either: $$TE=1/2k_ix_i^2$$ or $$TE=1/2k_fx_f^2$$ Thus, only one of the above should be involved in the equation you posted above.