A 15500 N automobile travels at a speed of 41 km/h northward along a street, and a 7000 N sports car travels at a speed of 65 km/h eastward along an intersecting street.
a)If neither driver brakes and the cars collide at the intersection and lock bumpers, what will the velocity of the cars be immediately after the collision?
b)what direction in degrees?
c)What percentage of the initial kinetic energy will be lost in the collision?
To answer these questions, we will apply the principles of conservation of momentum and conservation of kinetic energy.
a) First, let's consider the initial momentum of the two cars before the collision. Momentum is calculated by multiplying the mass of an object by its velocity. However, in this case, we are given the weight (N) of the cars, not their mass. To find the mass, we need to divide the weight by the acceleration due to gravity (9.8 m/s^2).
For the 15500 N automobile:
Weight = mass * acceleration due to gravity
15500 N = mass * 9.8 m/s^2
mass = 15500 N / 9.8 m/s^2
Similarly, for the 7000 N sports car:
mass = 7000 N / 9.8 m/s^2
Next, we need to convert the speeds of the cars from km/h to m/s since momentum is calculated in SI units (meters per second).
For the automobile:
speed = 41 km/h * (1000 m / 1 km) * (1 h / 3600 s)
For the sports car:
speed = 65 km/h * (1000 m / 1 km) * (1 h / 3600 s)
Now we can calculate the initial momentum of each car using the formula:
momentum = mass * velocity
For the automobile, momentum = mass of automobile * velocity of automobile
For the sports car, momentum = mass of sports car * velocity of sports car
Add the individual momenta of the cars to find the total initial momentum before the collision.
During the collision, the two cars lock bumpers, meaning they combine and move as a single unit after the collision. According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can calculate the velocity of the cars after the collision by dividing the total momentum by the combined mass of the cars.
Velocity after the collision = Total momentum / Total mass
b) To determine the direction in degrees, we can use the inverse tangent function, which can be written as:
Direction = atan(Vy / Vx)
Where Vy is the velocity in the north-south direction and Vx is the velocity in the east-west direction.
c) Finally, to calculate the percentage of the initial kinetic energy lost in the collision, we need to compare the initial kinetic energy to the final kinetic energy. Kinetic energy is given by the formula:
Kinetic energy = 0.5 * mass * velocity^2
The percentage of energy lost is given by:
Energy lost = (Initial kinetic energy - Final kinetic energy) / Initial kinetic energy * 100%