Question

A glider (?1) of mass 23.89 ?? is initially traveling to the right with a speed (?1?) of 4.52 ? ? . A second glider (?2 ) of mass 13.46 ?? is initially traveling to the left with a speed (?2?) of 9.62 ? ? .. The two gliders are on a frictionless track and have a perfectly elastic collision. After the collision, the second glider rebounds to the right with a speed (?2?) of 7.33 ? ? .

A) Determine the magnitude and direction of the velocity of glider #1 after the collision.

B) What is the impulse suffered by each glider during the collision? Note that you must show a calculation for each glider.

C) If during the collision the gliders remain in contact for 211.9 milliseconds, determine the average force exerted by each glider on the other (remember what Newton’s Third Law tells us about this interaction). Note that you must show a calculation for each glider

Answer 1

A) let the speed of glider 1 after collision be v1

By the conservation of momentum we have

initial momentum = final momentum

m1u1 + m2u2 = m1v1 + m2v2

23.89*4.52 + 13.46*-9.62 = 23.89v1 + 13.46 * 7.33

v1 = -5.03 m/s

so the glider 1 moves with 5.03 m/s to the left after collision

B) for glider 1 impulse = m(v1 - u1)

= 23.89 * ( -5.03 - 4.52) = -228.147 kg m/s

for glider 2 impulse = m(v2 - u2)

= 13.46*(7.33 - ( -9.62) ) = 228.147 kg m/s

C) force on glider 1 = impulse / time = -228..147 / 0.2119 = 1076.7 N ( to the left)

force on glider 2 = impulse / time = 228..147 / 0.2119 = 1076.7 N ( to the right)