A 328 kg car moving at 19.1 m/s hits from behind another car moving at 13.0m/s in the same direction. If the second car has a mass of 790kg and a new speed of 15.1m/s what is the velocity of the first car after the collision?
This is a conservation of momentum problem. I assume you know the first principles. Someone will be happy to critique your work.
P.S.: note the correct spelling of the subject
To solve this problem, we can apply the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
Let's denote the velocity of the first car after the collision as v1', and the velocity of the second car after the collision as v2'.
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
(m1 * v1) + (m2 * v2) = (m1 * v1') + (m2 * v2')
Here, m1 is the mass of the first car, m2 is the mass of the second car, v1 is the initial velocity of the first car, and v2 is the initial velocity of the second car.
Plugging in the given values:
(328 kg * 19.1 m/s) + (790 kg * 13.0 m/s) = (328 kg * v1') + (790 kg * 15.1 m/s)
Now we can solve for v1' by rearranging the equation:
(328 kg * 19.1 m/s) + (790 kg * 13.0 m/s) - (790 kg * 15.1 m/s) = (328 kg * v1')
(6268.8 kg·m/s) + (10270 kg·m/s) - (11909 kg·m/s) = 328 kg * v1'
(19529.8 kg·m/s) - (11909 kg·m/s) = 328 kg * v1'
7620.8 kg·m/s = 328 kg * v1'
Divide both sides by 328 kg:
v1' = 7620.8 kg·m/s / 328 kg
v1' ≈ 23.26 m/s
Therefore, the velocity of the first car after the collision will be approximately 23.26 m/s.
To find the velocity of the first car after the collision, 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.
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
Let's calculate the momentum of each car before the collision:
Car 1 (initial momentum):
Mass of car 1 (m1) = 328 kg
Velocity of car 1 (v1) = 19.1 m/s
Initial momentum of car 1 (p1_initial) = m1 * v1
Car 2 (initial momentum):
Mass of car 2 (m2) = 790 kg
Velocity of car 2 (v2) = 13.0 m/s
Initial momentum of car 2 (p2_initial) = m2 * v2
Total initial momentum before the collision:
Initial total momentum (p_total_initial) = p1_initial + p2_initial
Next, let's calculate the momentum of each car after the collision:
Car 1 (final momentum):
Velocity of car 1 after the collision (v1_final) = ?
Mass of car 1 (m1) = 328 kg
Final momentum of car 1 (p1_final) = m1 * v1_final
Car 2 (final momentum):
Velocity of car 2 after the collision (v2_final) = 15.1 m/s
Mass of car 2 (m2) = 790 kg
Final momentum of car 2 (p2_final) = m2 * v2_final
Since the total momentum before the collision is equal to the total momentum after the collision, we have:
p_total_initial = p_total_final
p1_initial + p2_initial = p1_final + p2_final
m1 * v1_initial + m2 * v2_initial = m1 * v1_final + m2 * v2_final
Now we can substitute the given values into the equation:
(328 kg * 19.1 m/s) + (790 kg * 13.0 m/s) = (328 kg * v1_final) + (790 kg * 15.1 m/s)
Simplifying the equation:
6268.8 kg*m/s + 10270 kg*m/s = 328 kg * v1_final + 11909 kg*m/s
Now let's isolate v1_final:
v1_final = (6268.8 kg*m/s + 10270 kg*m/s - 11909 kg*m/s) / 328 kg
v1_final = 1907.8 kg*m/s / 328 kg
v1_final = 5.82 m/s
Therefore, the velocity of the first car after the collision is approximately 5.82 m/s