Solved Problem: You've just been involved in an accident in which the damage is significant but none is hurt. While driving east through an intersection you are broadsided by a large sport utility vehicle travelling north. What speed and direction do the two vehicles move off with just after the collision. Assume that the collision is perfectly inelastic. Question: Determine the velocity of the two just after the collision. Known: m, = 1000 kg, m₂ = 2000 kg, v = 10 m/s and v₁ = 20 m/s. Principle: Conservation of Momentum in 2D Approach: Determine initial and final momenta and solve for velocity psystem initial = Paystem final I: Printal = m1v₁, = (m₁ + m₂) v₁, cost=Pzfinal y: Pyinitial = M2V2, = (m₁ + m₂) v2, sine = Pyfinal Let v₁, v2, = V, Taking the ratio of the two: initial: before collision +y VI; final: after collision +y 0 +

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Solved Problem: You've just been involved in an accident in which the damage is significant but none is hurt. While driving east through an
intersection you are broadsided by a large sport utility vehicle travelling north. What speed and direction do the two vehicles move off with just
after the collision. Assume that the collision is perfectly inelastic.
Question: Determine the velocity of the two just after the collision. Known: m, = 1000
kg, m, = 2000 kg. V = 10 m/s and V = 20 m/s. Principle: Conservation of Momentum in
2D Approach: Determine initial and final momenta and solve for velocity
?
I: Printtal =
1v₁, = (m₁ + m₂)v₁,cost = Pzfinal
y: Pyinitial = M2V2, = (m₁ + m₂) v2, sine = Pyfinal
Let v₁, V2, V, Taking the ratio of the two:
(m₁ + m₂)V sino
(m₁ + m₂)V cose
M202₁
psystem
initial
Then tane =
M₂021
mici,
Pystem
final
2000 kg x 20m
1000 kg x 10"
mivi, = (m₁ + m₂)V cost-V
sino
cose
=tand
40=tan(4) = 75.96°
1000 kg x 10 m/s
(1000+2000) kg x cos(75.96)
2000) kg x
Show that the two vehicles skid a distance of 11.7 m on the pavement before coming to a rest.
mi
(m₁ + m₂) cost
initial: before collision
+y
V1;
= 13.74 m/s
+X
?
final: after collision
+
Calculate the acceleration of your
car (vehicle 1) for a collision time
of 1 sec. Express it as a fraction
of g. Explain how airbags can
save your life in a collision.
Transcribed Image Text:Solved Problem: You've just been involved in an accident in which the damage is significant but none is hurt. While driving east through an intersection you are broadsided by a large sport utility vehicle travelling north. What speed and direction do the two vehicles move off with just after the collision. Assume that the collision is perfectly inelastic. Question: Determine the velocity of the two just after the collision. Known: m, = 1000 kg, m, = 2000 kg. V = 10 m/s and V = 20 m/s. Principle: Conservation of Momentum in 2D Approach: Determine initial and final momenta and solve for velocity ? I: Printtal = 1v₁, = (m₁ + m₂)v₁,cost = Pzfinal y: Pyinitial = M2V2, = (m₁ + m₂) v2, sine = Pyfinal Let v₁, V2, V, Taking the ratio of the two: (m₁ + m₂)V sino (m₁ + m₂)V cose M202₁ psystem initial Then tane = M₂021 mici, Pystem final 2000 kg x 20m 1000 kg x 10" mivi, = (m₁ + m₂)V cost-V sino cose =tand 40=tan(4) = 75.96° 1000 kg x 10 m/s (1000+2000) kg x cos(75.96) 2000) kg x Show that the two vehicles skid a distance of 11.7 m on the pavement before coming to a rest. mi (m₁ + m₂) cost initial: before collision +y V1; = 13.74 m/s +X ? final: after collision + Calculate the acceleration of your car (vehicle 1) for a collision time of 1 sec. Express it as a fraction of g. Explain how airbags can save your life in a collision.
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