A 1500 kg car traveling at 17.6 m/s to the
south collides with a 5000 kg truck that is
initially at rest at a stoplight. The car and
truck stick together and move together after
the collision.
What is the final velocity of the two-vehicle
mass?
Answer in units of m/s
momentum before = (1500) 17.6
momentum after = (1500+5000) v
momentum after = momentum before
So basically 1500 * 17.6?
huh?
(1500)17.6/(1500+5000)
when the little car hits the stationary big truck, it slows down.
Yes, I got it. Thank you
To find the final velocity of the two-vehicle mass after the collision, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. So, we can express the initial momentum before the collision as:
Initial momentum of car = mass of car × velocity of car = 1500 kg × 17.6 m/s = 26,400 kg⋅m/s (to the south)
Since the truck is initially at rest, its initial momentum is zero:
Initial momentum of truck = mass of truck × velocity of truck = 0 kg⋅m/s
Now, if the two vehicles stick together and move together after the collision, we can calculate the total momentum of the combined mass after the collision.
Final momentum of combined mass = (mass of car + mass of truck) × final velocity of combined mass
The mass of the combined mass after the collision is the sum of the car's mass and the truck's mass:
Mass of combined mass = mass of car + mass of truck = 1500 kg + 5000 kg = 6500 kg
Substituting the values into the equation, we can solve for the final velocity of the combined mass:
Final momentum of combined mass = (1500 kg + 5000 kg) × final velocity of combined mass = 6500 kg × final velocity of combined mass
Since the total momentum before the collision is equal to the total momentum after the collision, we can set the two expressions equal to each other:
26,400 kg⋅m/s = 6500 kg × final velocity of combined mass
Now, we can solve for the final velocity of the combined mass:
Final velocity of combined mass = 26,400 kg⋅m/s / 6500 kg = 4.06 m/s (to the south)
Therefore, the final velocity of the two-vehicle mass is 4.06 m/s to the south.