An accident has taken place, and the insurance company has sent their top physic
ID: 2078625 • Letter: A
Question
An accident has taken place, and the insurance company has sent their top physicist (you) to investigate. A 2000 kg truck (m2) has gotten into an accident with a 1500 kg car (m1). The two cars collided and stuck together leaving a straight, 50 m long skid mark (L). The mass of the two cars together (mT) is 3450 kg after the collision due to some parts falling off (ignore any physics involving the fallen parts). Assume that 100 kJ of energy was lost during the collision. The coefficient of kinetic friction between the tires and the ground is 0.83 for both cars.
If the speed limit is 30 m/s, determine which car was speeding, if at all, by obtaining the equation for each car’s velocity (in terms of given variables) and then calculating its speed.
Explanation / Answer
GIVEN, m2 = 2000 kg
m1 = 1500 kg
L = 50 m
mT = 3450 kg
Energy lost, U = 100 kJ
mu ( coefficient of fricition) = 0.83
speed limit V = 30 m/s
as the two vehicles stuc together after colliding, the total friction force = f = mu*mT*g = 0.83*3450*9.81 = 28090.935 N
Decelleration after collision, a = 28090.935 / mT = 8.14 m/s/s
energy lost due to friction = f*L = 28090.935 * 50 = 1404546.75 J = 1404.54675 KJ
U = 100 kJ
so, net energy lost = 1504.54675 kJ
Initial Energy of the vehicles = 1504.54675 kJ ( before collision)
combined velocity of the vehicles after collsion = v
2*a*L = v2
v^2 = 2*8.14*50 = 814
v = 28.53 m/s
let initial velocity of the truck be u, and that of car be w
then from conservation of momentum
m2*u + m1*w = mT*v
u = (3450*28.53 - 1500*w)/2000 = 49.21 - 0.75w
and from conservation of energy
1504.54675 kJ = 0.5*m2*u^2 + 0.5*m1*w^2
1504546.75 = 1000(49.21 - 0.75w)^2 + 750*w^2
1312.5W^2 - 73815W + 917077.35 = 0
W = 37.71212176736722, u = 20.925
or
w = 18.527878232632784, U = 35.314
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