Question

Two cars collide in an intersection: a 2200kg SUV that had been headed East and a 1500kg sports car that had been headed North. The cars deformed and remained together after colliding, sliding to rest 5.0m from the crash. The angle from the crash to the resting point is 35^o N of E. Coefficient of sliding (kinetic) friction is μ=0.80 for both vehicles. There are 8m long skid marks leading into the intersection indicating that the northbound car locked its brakes before hitting the truck.

1. Draw a sketch of the situations
2. What is the speed of the car-SUV system immediately after the collision?
3. What is the speed of the SUV immediately before the collision?
4. What is the speed of the car immediately before the collision?
5. What is the speed of the car before it locks its brakes?
6. The speed limit is 35 mph. Were either of the vehicles speeding? Which one(s) and by how much?

Answer 1

A.

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B.

Fnet = ma

umg = ma

a = ug

a = 0.80 * 9.8

a = 7.84 m/s2

v2 - u2 = 2ad

final velocity, v = 0 ,

so

u = sqrt ( 2 * 7.84 * 5)

u = 8.854 m/s

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C)

SUV was moving in the east

so,

2200 * v = ( 2200 + 1500)8.854 cos 35

v = 12.198 m/s

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D)

sports car was movng in north

1500 * v = ( 2200 + 1500)8.854 sin 35

v = 12.5 m/s

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C)

work done by friction = change in K.E

-umg * d = 1/2 * 1500 ( 12.52 - u2 )

-0.8 * 1500 * 9.8 * 8 = 1/2 * 1500 ( 12.52 - u2 )

u = 16.7 m/s