In a car crash, Car A rear ends Car B that stopped at a red light. After the crash, Car A and Car B meld together moving at a speed of 14 m/s. Car A has a mass of 1750 kg. Car B has a mass of 2000 kg.
Calculate the initial momentum of Car A.
So far I have Va=?
Ma= 1750 kg
Vb=0 m/s
Mb=2000 kg
Vf=14 m/s
Pf=52500 kg m/s
Pb= 0 kg m/s
Okay because the cars travel together afterwards this is an inelastic collision. SO you would need the formula
Ma*Va+Mb*Vb=(Ma+Mb)Vf
because car B is at rest it can be simplified to
Ma*Va=(Ma+Mb)Vf
Now you have all the values except Va, so first solve for Va
The when you find Va you can find the momentum
Since momentum is simply p=mv; just multiply Va and Ma
To calculate the initial momentum of Car A, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
In this case, we can write the equation as follows:
Initial momentum of Car A + Initial momentum of Car B = Final momentum of combined cars
P_initial(A) + P_initial(B) = P_final
Now, we need to calculate the initial momentum of Car A. The formula for momentum is given by:
Momentum (P) = mass (m) × velocity (v)
So, for Car A, the initial momentum is:
P_initial(A) = M(A) × V(A)
Given:
M(A) = 1750 kg
V(A) = velocity of Car A (which is what we need to find)
We can substitute these values into the equation to calculate the initial momentum of Car A:
P_initial(A) = 1750 kg × V(A)
Since Car A rearends Car B, we know that the initial velocity of Car B is 0 m/s. Therefore, we can infer that the initial velocity of Car A is also 0 m/s.
Substituting V(A) = 0 m/s:
P_initial(A) = 1750 kg × 0 m/s
P_initial(A) = 0 kg m/s
So, the initial momentum of Car A is 0 kg m/s.