A car of mass 1400kg moving south at 11m/s collides into another car of mass 1800kg moving east at 30m/s.The cars are stock together after the collision.Determine the velocity of the cars immediately after the collision.
Do a vector sum of the two momentums, then set that equal to (m1+m2)vf
you'll have to do a tan-1 for the direction
To determine the velocity of the cars immediately after the collision, we can use the principles of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is defined as:
p = m * v
Where:
p = momentum
m = mass
v = velocity
In this case, we have two cars colliding, so the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision, the momentum of the first car (Car 1) is calculated as:
p1 = m1 * v1
= 1400 kg * (-11 m/s) [Negative sign indicates southward direction]
Before the collision, the momentum of the second car (Car 2) is calculated as:
p2 = m2 * v2
= 1800 kg * 30 m/s [Positive sign indicates eastward direction]
The total initial momentum (p_initial) before the collision is therefore:
p_initial = p1 + p2
After the collision, the cars stick together and move as a single object. Let's assume the final velocity of the cars as vf.
The total final momentum (p_final) after the collision is:
p_final = (m1 + m2) * vf
Since momentum is conserved, we can set up an equation by equating the initial momentum to the final momentum:
p_initial = p_final
Therefore:
p1 + p2 = (m1 + m2) * vf
Substituting the values, we get:
(1400 kg * (-11 m/s)) + (1800 kg * 30 m/s) = (1400 kg + 1800 kg) * vf
Simplifying further, we get:
-15400 kg·m/s + 54000 kg·m/s = 3200 kg * vf
Adding the values on the left side gives:
38600 kg·m/s = 3200 kg * vf
Finally, dividing both sides by 3200 kg:
vf = 38600 kg·m/s / 3200 kg
vf ≈ 12.06 m/s
Therefore, the velocity of the combined cars immediately after the collision is approximately 12.06 m/s.