A 10,000kg truck traveling 5m/s collides with a 1,500 kg Volkswagen traveling in the opposite direction at 14 m/s after the collision the truck and Volkswagen stick together. A) what is the final speed and direction of the mess immediately after the collision? (don't foget to define a positative direction) B) how much energery was lost?(heat, sound, vibrations and other etc) during the collision. (Hint calculate the KE of each vechile before and after the collision.
A. m1*V-m2*V2 = 10,000*5-1,500*14=29,000
m1*V+m2*V = 29,000
10,000*V + 1500*V = 29000
11,500V = 29000
V = 2.52 m/s. In the direction of the
truck.
B. KE1 = 0.5m1*V1^2 = 0.5*10,000*5^2 =
125,000 J. = 125 kJ. Before collision.
KE1 = 0.5*m1*V^2 = 0.5*10,000*2.52^2 = 31,752 J. = 31.75 kJ. After collision.
125-31.75 = 93.25 kJ. Lost during collision.
KE2 = 0.5*m2*V2^2 = 0.5*1500*14^2 = 147000 J. = 147 kJ. Before collision.
KE2 = 0.5m*V^2 = 0.5*1500*2.52^2 = 4763 J. = 4.763 kJ. After collision.
147 - 4.763 = 142 kJ. Lost during collision.
93.25kJ + 142kJ = 235 kJ = KE lost
during collision.
To answer the first part of the question, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, the momentum of the truck before the collision is (mass of the truck) * (velocity of the truck), and the momentum of the Volkswagen before the collision is (mass of the Volkswagen) * (velocity of the Volkswagen).
The total momentum before the collision is then the sum of the two momenta, considering the directions of the velocities. Since the truck is traveling to the right and the Volkswagen to the left, we can consider the positive direction to be to the right and the negative direction to be to the left.
The initial momentum of the system is given by:
momentum_initial = (mass of the truck) * (velocity of the truck) + (mass of the Volkswagen) * (velocity of the Volkswagen)
momentum_initial = (10,000 kg) * (5 m/s) + (1,500 kg) * (-14 m/s)
To calculate the final speed and direction, we need to determine the total mass and velocity of the system after the collision. Since the truck and the Volkswagen stick together, their combined mass is the sum of their individual masses.
total mass = mass of the truck + mass of the Volkswagen
total mass = 10,000 kg + 1,500 kg
To calculate the final velocity, we divide the initial momentum by the total mass:
momentum_final = momentum_initial / total mass
The final velocity can be determined by rearranging the equation:
velocity_system_final = momentum_final / total mass
Now, let's plug in the values and calculate:
momentum_final = (10,000 kg * 5 m/s + 1,500 kg * -14 m/s) / (10,000 kg + 1,500 kg)
velocity_system_final = (momentum_final) / (10,000 kg + 1,500 kg)
Simplifying these calculations will give you the answer to part A of the question.