Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1050Kg and was approaching at 8.00m/s due south. The second car has a mass of 700Kg and was approaching at 20.0m/s due west.
A) Calculate the final velocity of the cars.(Note that since both cars have an initial velocity, you cannot use 7.6a and b. You msut look for other simplifying aspects.)
_______m/s
B) How much kinetic enregy is lost in the collision? (This energy goes into deformation of the cars.)
________J
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Answer
a scooter and a rider together have a mass of 275kg. if the scooter slows with the acceleration of 4.50m/s^2, what is the net force of the acooter and the rider together?
To calculate the final velocity of the cars after the collision, we can use the principle of conservation of momentum.
A) Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Momentum is given by the equation:
Momentum = mass x velocity
Let's consider the momentum in the x-direction (east-west) and the y-direction (north-south) separately.
In the x-direction:
The first car has an initial velocity of 0 m/s in the x-direction (since it was approaching from the south).
The second car has an initial velocity of -20.0 m/s in the x-direction (as it was approaching from the west).
After the collision, the two cars stick together, so their final velocity in the x-direction will be the same.
Using the conservation of momentum equation for the x-direction:
(mass of car 1 x velocity of car 1) + (mass of car 2 x velocity of car 2) = (total mass of cars x final velocity in x-direction)
(1050 kg x 0 m/s) + (700 kg x (-20.0 m/s)) = (1050 kg + 700 kg) x final velocity in x-direction
Simplifying this equation, we get:
-14000 kg m/s = 1750 kg x final velocity in x-direction
Dividing both sides by 1750 kg, we find:
Final velocity in x-direction = -8 m/s (west)
In the y-direction:
The first car has an initial velocity of 8.00 m/s in the y-direction(since it was approaching from the south).
The second car has an initial velocity of 0 m/s in the y-direction (as it was approaching from the west).
After the collision, the two cars stick together, so their final velocity in the y-direction will be the same.
Using the conservation of momentum equation for the y-direction:
(mass of car 1 x velocity of car 1) + (mass of car 2 x velocity of car 2) = (total mass of cars x final velocity in y-direction)
(1050 kg x 8.00 m/s) + (700 kg x 0 m/s) = (1050 kg + 700 kg) x final velocity in y-direction
Simplifying this equation, we get:
8400 kg m/s = 1750 kg x final velocity in y-direction
Dividing both sides by 1750 kg, we find:
Final velocity in y-direction = 4.8 m/s (north)
Therefore, the final velocity of the cars after the collision is approximately 4.8 m/s north and -8 m/s west.
B) To calculate the kinetic energy lost in the collision, we need to find the difference between the initial kinetic energy and the final kinetic energy.
Initial kinetic energy = 1/2 x mass x (speed)^2
For the first car:
Initial kinetic energy of the first car = 1/2 x 1050 kg x (8.00 m/s)^2
For the second car:
Initial kinetic energy of the second car = 1/2 x 700 kg x (20.0 m/s)^2
Total initial kinetic energy = Initial kinetic energy of the first car + Initial kinetic energy of the second car
Final kinetic energy = 1/2 x (Total mass of cars) x (Final velocity)^2
So, the kinetic energy lost in the collision = Total initial kinetic energy - Final kinetic energy
Substituting the values into the formulas and calculating, we can find the kinetic energy lost in the collision.