A big truck has a mass of 5,000kg. It is moving down the road at a velocity of 15m/s. As it approaches a stop sign, the driver tries to stop, but the truck slides on ice and hits a car (mass = 500kg) that is stopped. After the collision, they move separately, the truck continuing on at a velocity of 9m/s.
What is the velocity of the car after the collision?
Alright, so I know the formula and all that jazz, but the thing that I'm really having trouble with is UNDERSTANDING how to use the formula here.
Like, I don't know how, " m1 • v1(before) + m2 • v2(before) = m1 •v1(after) + m2 • v2(after) " <--- that, is going to help me figure out that the velocity of the car is.
If someone can PLEASE explain this to me and how me how it's suppose to work, that would be awesome.
Thanks
momentum before = 5000*15 + 500*0
momentum after = 5000*9 + 500*V
they are the same (Newton #1)
so
5000*15 = 5000*9 + 500 V
Of course! I'd be happy to explain how to use the formula in this situation.
First, let's take a closer look at the formula:
m1 • v1(before) + m2 • v2(before) = m1 •v1(after) + m2 • v2(after)
In this formula, "m1" represents the mass of the first object (the truck), "v1(before)" represents the velocity of the first object before the collision (15 m/s for the truck), "m2" represents the mass of the second object (the car), "v2(before)" represents the velocity of the second object before the collision (0 m/s because the car is stopped), "v1(after)" represents the velocity of the first object after the collision (9 m/s for the truck), and "v2(after)" represents the velocity of the second object after the collision (which we need to find - the velocity of the car).
To use this formula, we need to rearrange it to solve for "v2(after)". Here's how:
1. Start with the original equation:
m1 • v1(before) + m2 • v2(before) = m1 •v1(after) + m2 • v2(after)
2. Rearrange the equation to isolate "v2(after)" by bringing the terms involving "v2(after)" to one side of the equation:
m2 • v2(before) - m2 • v2(after) = m1 •v1(after) - m1 • v1(before)
3. Factor out "m2":
m2 • (v2(before) - v2(after)) = m1 • (v1(after) - v1(before))
4. Solve for "v2(after)" by dividing both sides of the equation by "m2":
v2(before) - v2(after) = (m1/m2) • (v1(after) - v1(before))
Now, let's plug in the values given in the problem and solve for "v2(after)":
m1 = 5000 kg (mass of the truck)
v1(before) = 15 m/s (velocity of the truck before the collision)
m2 = 500 kg (mass of the car)
v1(after) = 9 m/s (velocity of the truck after the collision)
Plugging these values into the equation, we get:
0 m/s - v2(after) = (5000 kg / 500 kg) • (9 m/s - 15 m/s)
Simplifying further:
- v2(after) = 10 • (-6 m/s) = -60 m/s
Therefore, the velocity of the car after the collision is -60 m/s. The negative sign indicates that the car is moving in the opposite direction of the truck.