Review 2 SECTION NAME- #2. Lets imagine two cars collide head-to-head. (a) One e

Question

Review 2 SECTION NAME- #2. Lets imagine two cars collide head-to-head. (a) One example is collision of a SUV and a smart car. Both cars get totaled. SUV with mass of 3500 kg was driving south at 200 km/h when the smart car with mass of 2000 kg was driving north at the wrong lane at 250 km/h. They collide head-to head. Assume they can only stay on this one lane and its frictionless. i) What is their total momentum before collision? ii) What is their final velocity? (b) The other example is collision of two amusement park bumper cars. Two bumper cars have the same mass of 800 g. The blue bumper car is heading toward east at 20 km/h when the green bumper car heads directly toward the blue car (west) at 20 km/h. This is a one lane bumper car race track i) What is their total momentum before collision? ii) What is their total kinetic energy before collision? ii) Find the final velocity of the blue bumper car and green bumper car.

Explanation / Answer

a) let m1 and m2 be the masses of the two cars

m1=3500kg

m2 = 2000kg

u1 = -200 km/h ( taking north as positive and south as negative)

u2 = 250 km/h

i) total momentum before collision is

P =m1u1+ m2u2

= 3500(-200) + 2000(250)

= -2x105 kg km/h

= 5.55 x 104 kgm/s towards south

ii) let v be the velocity after collision

miu1+m2u2 =(m1+m2)v

v = (2x105) / (5500) = 36.36 km/h

b) m1 =m2 =800 g

u1 = 20 km/h = 5.55 m/s

u2 = -20 km/h = -5.55 m/s

i) total momentum before collision

m1u1 +m2u2 = 0

ii) kinetic energy

= (1/2)(m1u12 +m2u22)

= 24.69 joules

iii) in perfectly elastic collisions of equal masses bodies exchange their velocities

hence velocity of blue car

v1 = 20km/h west

velocity of green car

v2 = 20 km/h east

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