A drunken driver crashes his car into a parked car that has its brakes set. The two cars move off together (perfectly inelastic collision), with the locked wheels of the parked car leaving skid marks 6.0 m in length.
If the mass of the moving car is 2130kg and the mass of the parked car is 1290 kg how fast was the first car travelling when it hit the parked car?
Assume that the driver of the moving car made no attempt to brake and that the coefficient of friction between the tires and the road is 0.18.
The momenum moving car=momenutum after.
2130*V=(2130+1290)Vf
Now, after the crash,
Vf^2=2 a d
where a=forcfriction/totalmass
= totalmass*g*.18/totalmass * d=.18g*d
vf^2=.18gd
solve for vf in that. then put in in the first equation above, solve for V, the velocity of the moving car beffore the crash. Check my thinking.
3.58m/s
To solve this problem, we can use the principles of conservation of momentum and the work-energy principle.
First, let's calculate the initial momentum of the moving car before the collision. Momentum (p) is given by the equation p = mv, where m is the mass and v is the velocity.
The momentum before the collision can be written as:
p1 = m1 * v1
The momentum of the parked car (p2) is initially zero because it is not moving.
Since the two cars become stuck together after the collision, we can use the equation for conservation of momentum:
p1 + p2 = p' (final momentum)
Since we want to find the initial velocity of the moving car, which is denoted by v1, we rewrite the equation as:
m1 * v1 + m2 * 0 = (m1 + m2) * v'
Now let's calculate the final momentum, p':
The total mass of the two cars after the collision is the sum of their individual masses:
m' = m1 + m2
m' = 2130 kg + 1290 kg = 3420 kg
The final velocity of the two cars stuck together can be determined by using the skid marks and the coefficient of friction.
In an inelastic collision, the work done by friction is equal to the change in kinetic energy, and the change in kinetic energy is equal to the work done by friction. So we can write:
W = ΔKE
The work done by friction can be calculated using the equation:
W = μ * N * d
Where μ is the coefficient of friction, N is the normal force (equal to the weight of the cars), and d is the distance over which the work is done (the skid mark length).
The change in kinetic energy (ΔKE) is equal to the initial kinetic energy (KE1) minus the final kinetic energy (KE').
Since the parked car does not move, the final kinetic energy is zero, and thus ΔKE can be simplified to:
ΔKE = KE1
We can write the equation as:
μ * N * d = (1/2) * m' * v'^2
Rearranging the equation for the final velocity, v', we get:
v' = √((2 * μ * N * d) / m')
To find the normal force (N), we use the equation:
N = m1 * g
Where g is the acceleration due to gravity.
Substituting these values into the equation for v', we can find the final velocity after the collision.
Finally, we can substitute the initial and final velocities into the conservation of momentum equation to find the initial velocity.
v1 = (m' * v' - m2 * 0) / m1
Now, let's plug in the given values and calculate the final answer: