(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 0.20-kilogram mass is sliding on a horizontal, frictionless air track with a speed of 3.0 meters per second when it instantaneously hits and sticks to a 1.3-kilogram mass initially at rest on the track. The 1.3-kilogram mass is connected to one end of a massless spring, which has a spring constant of 100 newtons per meter. The other end of the spring is fixed.

2. Relevant equations

F = -kx

KE = 1/2m(v)squared

momentum = mass x velocity

3. The attempt at a solution

The first couple parts of the problem ask you to solve for the linear momentum and kinetic energy of the masses before and immediately after collision. I interpreted "immediately after the impact" to indicate that I'm supposed to calculate the linear momentum/KE of the masses without taking the spring into account.

a. momentum before impact = 0.6 kg m/s

KE before impact = 0.9 Joules

b. momentum after impact = 0.6 kg m/s

KE after impact = 0.3 J

c. Determine the amplitude of the harmonic motion.

d. Determine the period of the harmonic motion.

I don't really know where to start onparts C and D- I thought to use F=mA to determine the spring force (F=-kX) needed to stop the motion of the mass since the k value is provided (100 n/m), but there's no A value to plug into F=mA. I suspect that KE initial + PE initial = KE final + PE final might factor in because at maximum amplitude PE = 0.3 J, but I don't know where. How might I solve this?

EDIT:

Took another crack at it; am I on the right track?

PE final = 0.3 Joules

PE = (1/2)k(x)squared

0.3 J= (1/2)*(100 N/m)*x squared

x = .0015 m

Would that be the amplitude? If so, how might I find the period?

EDIT 2:

Went Wikipedia hunting and came up with the formula T = 2pi ROOT(m/k). Plugged in all the numbers and came out with .76 seconds. I haven't a clue if that formula applies for a mass on an air track as it applies for a hanging mass, though, so please tell me whether I've got it right or all wrong.

In case you're curious, this problem is from the 1995 Physics AP free response section.

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# Simple Harmonic Motion on an air track

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