Two air-track gliders of equal mass are initially moving inthesame direction alo
ID: 1682408 • Letter: T
Question
Two air-track gliders of equal mass are initially moving inthesame direction along a straight line. The rearmost glider hasaninitial speed of 4.2 m/s and the forward glider has a speed of2.2m/s. If the collision is elastic, what is the speed of thefirstglider (rearmost) after the collision? What is the speed of the second glider (forward)? Two air-track gliders of equal mass are initially moving inthesame direction along a straight line. The rearmost glider hasaninitial speed of 4.2 m/s and the forward glider has a speed of2.2m/s. If the collision is elastic, what is the speed of thefirstglider (rearmost) after the collision? What is the speed of the second glider (forward)?Explanation / Answer
Kinetic energy and momentum, of the rearward (r) and forward (f) gliders , are conserved. KEr(before) + KEf(before)= KEr(after) + KEf(after) 1/2 m 4.3^2 + 1/2 m 2.5^2 = 1/2 m vr^2 + 1/2 m vf^2 PEr(before) + PEf(before) = PEr(after) + PEf(after m * 4.3 + m * 2.5 = m * vr + m * vf Simplifying both equations and putting together gives 24.74 = vr^2 + vf^2 6.8 = vr + vf We use substitution to solve first for vr (if we start with vf = 6.8 - vr), then for vf. Solutions are 4.3 and 2.5. Since the rearward glider cannot jump around the forward glider, and they are going in the same direction, the forward driver must be going faster (at 4.3) and the rearward glider must be going slower (at 2.5