After skidding down a snow-covered hill on an inner tube, Ashley is coasting acr

Question

After skidding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of +2.2 m/s. Britney runs after her at a velocity of +4.6 m/s and hops on the inner tube. Ashley's mass is 65 kg, and Britney's is 55 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow. a) How fast do the two of them slide across the snow together on the inner tube? b) Calculate the change in i. Ashley’s momentum, ii. Britney’s momentum, iii. Ashley’s kinetic energy, and iv. Britney’s kinetic energy. c) What kind of collision is this? Why? d) They go on sliding with the same speed (from part (a)) until they are stopped by a safety fence. What is the average force applied to them by the fence to stop them in 1.2 seconds?

After skidding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of +2.2 m/s. Britney runs after her at a velocity of +4.6 m/s and hops on the inner tube. Ashley's mass is 65 kg, and Britney's is 55 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow. V02 vol a) How fast do the two of them slide across the snow together on the inner tube? b) Calclate the change in i. Ashley's momentum, ii. Britney's momentum, ii. Ashley's kinetic energy, and iv. Britney's kinetic energy c) What kind of collision is this? Why? d) They go on sliding with the same speed (from part (a)) until they are stopped by a safety fence. What is the average force applied to them by the fence to stop them in 1.2 seconds?

Explanation / Answer

Applying conservation of momentum

m1 u1  + m2u2 = (m1 + m2 )v

65(2.2) + 55(4.6) = (65 + 55)v

396 = 120v

v = 3.3 m/s

two of them slide together at a speed of 3.3 m/s.

b) Change in Ashley's momentum = m1v - m1u1 = m1(v-u1) = 65 (3.3 -2.2) = 71.5 Kgm/s

Change in Britney's momentum = m2v - m2u2 = m1(v-u2) = 55 (3.3 - 4.6) = - 71.5 Kgm/s

Change in ashley's kinetic energy = (1/2)m1v2 - (1/2) m1u12 = (1/2)m1(v2-u12 ) = (1/2)65 (3.32 -2.22) = 196.63 J

Change in Britney's kinetic energy = (1/2)m2v2 - (1/2) m2u22 = (1/2)m2(v2-u22 ) = (1/2)55 (3.32 - 4.62) = -282.43 J

c) this is an perfectly inelastic collision because after the collision the two bodies sticj together and travel together with same velocity.

d) force will be equal to rate of change of momentum

momentum of both = (m1 + m2 )v = (65 + 55)v = 120(3.3) =396 Kgm/s

final momentum after applying force = 0

F = 396 -0 /t

F = 396 /1.2

F = 330 N

the force must be 330 N

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