Question

An air-track glider with a mass of 239 g is moving at 0.81 m/s on a 2.4 m long air track. It collides elastically with a 513 g glider at rest in the middle of the track. The end of the track over which the struck glider moves is not level, but slants upward at an angle of 0.70o with respect to the horizontal. Will the glider reach the end of the track? Neglect the length of the gliders.

Answer 1

The collision is elastic so, we can conserve momentum

we can use standard equations for elastic collision to find final velocities of gliders

v1f = ( m1 - m2 / m1 + m2 ) v1i

v2f = ( 2m1 / m1 + m2) v1i

put in the values

v1f = ( 239 - 513 / 239 + 513 ) * 0.81 = - 0.295 m/s

v2f = ( 2 * 239 / 239 + 513) * 0.81 = 0.515 m/s

Now,

just equate the initial energy of glider 2 to the final energy of glider 2

note that initially , glider 2 only had kinetic energy and finally, it only had potential energy

so,

1/2 * m2 * v2f² = m2 *g * h

1/2 * v2f² = g * h

h = v2f² / 2g

h = 0.515² / 2 * 9.8

h = 0.014 m ( this is the height where glider 2 stops)

the distance covered along the track

x = 1.2 * tan 0.7

x = 0.0146

so, yes , it almost reaches the end