A 1,906 kg car stopped at a traffic light is struck from the rear by a 953-kg car. The two cars become entangled, moving along the same path as that of the originally moving car. If the smaller car were moving at 26.7 m/s before the collision, what is the velocity of the entangled cars after the collision? (Assume the smaller car initially moves in the positive direction.) SOLUTION Conceptualize This kind of collision is easily visualized, and one can predict that after the collision both cars will be moving in the same direction as that of the initially moving car. Because the initially moving car has only half the mass of the stationary car, we expect the final velocity of the cars to be relatively --Select-- Categorize We identify the two cars as an isolated system in terms of momentum in the horizontal direction and apply the impulse approximation during the short time interval of the collision. The phrase "become entangled" tells us to categorize the collision as perfectly --Select-- Analyze The magnitude of the total momentum of the system before the collision is equal to that of the ---Select--- car because the larger car is initially at rest. (Use the following as necessary: m,, m2, and ve) Use the isolated system model for momentum: Ap = 0 → P, = Pp→m,v; = Solve for v, (in m/s) and substitute numerical values (Indicate the direction with the sign of your answer.): m/s V = m1 + m2 Finalize Because the final velocity is positive, the direction of the final velocity of the combination is ---Select--- v the velocity of
A 1,906 kg car stopped at a traffic light is struck from the rear by a 953-kg car. The two cars become entangled, moving along the same path as that of the originally moving car. If the smaller car were moving at 26.7 m/s before the collision, what is the velocity of the entangled cars after the collision? (Assume the smaller car initially moves in the positive direction.) SOLUTION Conceptualize This kind of collision is easily visualized, and one can predict that after the collision both cars will be moving in the same direction as that of the initially moving car. Because the initially moving car has only half the mass of the stationary car, we expect the final velocity of the cars to be relatively --Select-- Categorize We identify the two cars as an isolated system in terms of momentum in the horizontal direction and apply the impulse approximation during the short time interval of the collision. The phrase "become entangled" tells us to categorize the collision as perfectly --Select-- Analyze The magnitude of the total momentum of the system before the collision is equal to that of the ---Select--- car because the larger car is initially at rest. (Use the following as necessary: m,, m2, and ve) Use the isolated system model for momentum: Ap = 0 → P, = Pp→m,v; = Solve for v, (in m/s) and substitute numerical values (Indicate the direction with the sign of your answer.): m/s V = m1 + m2 Finalize Because the final velocity is positive, the direction of the final velocity of the combination is ---Select--- v the velocity of
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Transcribed Image Text:Carry Collision Insurance!
A 1,906 kg car stopped at a traffic light is struck from the rear by a 953-kg car. The two cars become entangled, moving along the
same path as that of the originally moving car. If the smaller car were moving at 26.7 m/s before the collision, what is the velocity
of the entangled cars after the collision? (Assume the smaller car initially moves in the positive direction.)
SOLUTION
Conceptualize This kind of collision is easily visualized, and one can predict that after the collision both cars will be moving in the
same direction as that of the initially moving car. Because the initially moving car has only half the mass of the stationary car, we
expect the final velocity of the cars to be relatively ---Select---
Categorize We identify the two cars as an isolated system in terms of momentum in the horizontal direction and apply the impulse
approximation during the short time interval of the collision. The phrase "become entangled" tells us to categorize the collision as
perfectly -Select---
Analyze The magnitude of the total momentum of the system before the collision is equal to that of the ---Select--- car because
the larger car is initially at rest. (Use the following as necessary: m,, m2, and ve)
Use the isolated system model for momentum:
Ap = 0 → P, = Pf→ m,v; =
Solve for v, (in m/s) and substitute numerical values (Indicate the direction with the sign of your answer.):
m/s
V =
m1 + m2
Finalize Because the final velocity is positive, the direction of the final velocity of the combination is ---Select---
v the velocity of
the initially moving car as predicted. The speed of the combination is also much lower than the initial speed of the moving car.
EXERCISE
Hint
(a) What is the loss of kinetic energy (K, - K, in kJ) in the situation described in the Example?
kJ
(b) What if the 953 kg car actually moves backwards with a speed of 1.6 m/s right after the collision instead of having a perfectly
inelastic collision? What is the velocity
positive direction as defined in the Example. (Indicate the direction with the sign of your answer.)
heavier car (in m/s) immediately
the collision
Use the same
ention for
m/s
(c) What is the loss of kinetic energy (in kJ) in this case?
kJ
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