At a stop light, a truck of mass, mT = 1.10 x 10^4 kg, fails to hit its brakes until it has hit a car of mass,
mC = 1.60 x 10^3 kg. The car is initially at rest, and the truck is moving with velocity, vi. At the instant of contact, both vehicles lock their brakes. This occurs on dry concrete, and the skid marks left on the pavement are 5.6 meters in length. The coefficient of kinetic friction between rubber and dry concrete is µk = 0.80. The combined mass of the car and truck goes straight ahead in one direction.
a) Determine the velocity of the combined truck and car immediately after the collision.
b) Determine the velocity of the truck the moment before the collision, vi.
c) Assume the collision happens over ?t = 0.10 s. What force does the truck apply to the car?
d) The force of impact does not exceed the tensile strength of the aluminum frame of the car. Instead, the frame compresses and later returns to its original shape. If we can model the frame as two pieces of aluminum that are 7.50 m in length, 3.0 cm wide, and 1.5 cm high, how much (in meters) does the frame compress under the applied force?
(Possibly useful information: the Young's modulus of aluminum = 7.0 x 1010 Pa)
e) How much energy (in joules) is lost in the collision?
f) Estimate the amount of energy stored in the frame of the car when it is compressed as a percentage of the total energy lost. (There is a hint on page 283 of College Physics for this.)