Two identical cars hit each other and lock bumpers. If a car moving with a speed of 90km/h approaches a stationary car, what is the speed immediately after coupling cars.
You use and solve for V:
M1V1+M2V2=(M1+M2)V
I end up with the following because my question does not give the mass of the cars, it only states that they are identical, therefore M1=M2. I get:
90km/h=M1*V
What am i doing wrong?
You are not thinking. If M2=M1, then
V1+V2=2V
v= 45km/hr
Based on the given information, it seems there may be a misunderstanding. The formula you are using, M1V1 + M2V2 = (M1 + M2)V, is correct for the conservation of momentum but may not be necessary to solve this specific problem.
The speed immediately after coupling the cars can be determined by considering the law of conservation of kinetic energy. Since the cars are identical, their masses (M1 and M2) are the same. The formula for the conservation of kinetic energy is:
0.5 * M1 * V1^2 + 0.5 * M2 * V2^2 = 0.5 * (M1 + M2) * V^2
However, since M1 = M2, the formula simplifies to:
0.5 * M * V1^2 + 0.5 * M * V2^2 = M * V^2
Therefore, for this specific problem, you can solve for V directly using the equation:
(0.5 * M1 * V1^2 + 0.5 * M2 * V2^2) / M = V^2
So, in your case, you can directly calculate the speed immediately after coupling the cars using the formula above without multiplying by the masses in the initial equation.
In this problem, you are trying to find the speed immediately after the two cars couple together.
To solve this, you correctly set up the conservation of momentum equation:
M1V1 + M2V2 = (M1 + M2)V
However, you made a mistake when substituting the values. Instead of setting the speed of the moving car as 90 km/h, you need to convert it to the appropriate units.
The equation should be:
(M1)(90 km/h) + (M2)(0 km/h) = (M1 + M2)V
Since the stationary car has a speed of 0 km/h, we only consider the moving car's speed.
Now, you mentioned that both cars are identical, so let's assume that M1 = M2 = M (the mass of each car).
The equation becomes:
M(90 km/h) + M(0 km/h) = 2M(V)
Simplifying the equation further:
90M km/h = 2MV
Now, divide both sides of the equation by 2M:
90 km/h = V
Therefore, the speed immediately after the two cars couple together is 90 km/h.