a stationary car is hit from behind by another car travelling at 40km per hr. After collision both cars remain locked together. The masses of the stationary car and the moving car are 1500kg and 1300kg respectively (use g=9.8ms-2)
a) is this an elastic or inelastic collision
b) calculate the velocity of the two cars immediatly after the collision
c) If the brakes of the stationary cars are applied before impact and the coefficient of friction between the wheels and the road surface is 0.4 calculate the decelaration of the cars.the time taken for the cars to come to rest and the distance travelled by the cars
a) To determine if the collision is elastic or inelastic, we need to assess whether kinetic energy is conserved before and after the collision.
In an elastic collision, kinetic energy is conserved, meaning that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
In an inelastic collision, kinetic energy is not conserved, and some energy is lost to other forms, such as heat or deformation.
b) To calculate the velocity of the two cars immediately after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Let's denote the velocity of the stationary car after the collision as V1 and the velocity of the moving car after the collision as V2.
Before the collision, the total momentum is given by:
Total momentum before = (mass of stationary car) x 0 + (mass of moving car) x velocity of moving car
After the collision, the total momentum is given by:
Total momentum after = (mass of stationary car + mass of moving car) x V1
Since the two cars remain locked together, their total mass after the collision is the sum of their individual masses.
Setting the two momentum equations equal to each other:
(mass of stationary car) x 0 + (mass of moving car) x velocity of moving car = (mass of stationary car + mass of moving car) x V1
Now we can calculate V1.
c) To calculate the deceleration of the cars, we can use the relationship between acceleration, force, and mass. The force causing the deceleration is the frictional force between the wheels and the road surface.
Frictional force = (coefficient of friction) x (normal force)
The normal force can be calculated using the weight of the cars, which is given by:
Weight = mass x gravity
The deceleration is given by:
Deceleration = (frictional force) / (mass of cars)
The time taken for the cars to come to rest can be calculated using the deceleration and the initial velocity. The equation for calculating time is:
Time = (final velocity - initial velocity) / deceleration
The distance traveled by the cars can be calculated using the equation:
Distance = (initial velocity) x (time) + (1/2) x (deceleration) x (time)^2
Now, we can plug in the given values and calculate the answers.