. A 1030-kg car going 3.4 m/s through a parking lot hits and sticks to the bumper of a stationary 1140-kg car. Find the speed of the joined cars immediately after the collision.
M1*V1 + M2*V2 = M1*V + M2*V
1030*3.4 + 1140*0 = 1030V + 1140V
V = ?
To find the speed of the joined cars immediately after the collision, we can use the principle of conservation of momentum.
According to the principle of conservation of momentum, 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 (p = m * v).
Let's calculate the momentum of each car before the collision:
Momentum of the first car (car 1) before the collision: p1 = m1 * v1
Mass of car 1 (m1) = 1030 kg
Velocity of car 1 (v1) = 3.4 m/s
Momentum of car 1 before the collision: p1 = 1030 kg * 3.4 m/s
Momentum of the second car (car 2) before the collision: p2 = m2 * v2
Mass of car 2 (m2) = 1140 kg
Velocity of car 2 (v2) = 0 m/s (since it is stationary)
Momentum of car 2 before the collision: p2 = 1140 kg * 0 m/s
Since car 2 is stationary, its momentum before the collision is zero.
According to the principle of conservation of momentum, the total momentum before and after the collision is equal. Therefore:
Total momentum before the collision = Total momentum after the collision
(p1 + p2) before the collision = (p1 + p2) after the collision
1030 kg * 3.4 m/s + 1140 kg * 0 m/s = (1030 kg + 1140 kg) * v (after the collision)
By solving the equation, we can find the value of v (after the collision):
3502 kg * m/s + 0 kg * m/s = 2170 kg * v
3502 kg * m/s = 2170 kg * v
v = (3502 kg * m/s) / 2170 kg
v ≈ 1.61 m/s
Therefore, the speed of the joined cars immediately after the collision is approximately 1.61 m/s.
To find the speed of the joined cars immediately after the collision, we can use the principle of conservation of linear momentum.
The principle of conservation of linear momentum states that the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.
Mathematically, this can be expressed as:
m1 * v1 + m2 * v2 = (m1 + m2) * vf
where:
m1 and m2 are the masses of the two cars (in kg),
v1 and v2 are the initial velocities of the two cars (in m/s),
and vf is the final velocity of the joined cars after the collision (in m/s).
In this case, we have:
m1 = 1030 kg (mass of the first car)
v1 = 3.4 m/s (initial velocity of the first car)
m2 = 1140 kg (mass of the second car)
v2 = 0 m/s (initial velocity of the second car since it is stationary)
Substituting these values into the equation, we get:
(1030 kg * 3.4 m/s) + (1140 kg * 0 m/s) = (1030 kg + 1140 kg) * vf
Simplifying further:
(1030 kg * 3.4 m/s) = (1030 kg + 1140 kg) * vf
3502 kg·m/s = 2170 kg * vf
Dividing both sides by 2170 kg to solve for vf:
vf = 3502 kg·m/s / 2170 kg ≈ 1.612 m/s
Therefore, the speed of the joined cars immediately after the collision is approximately 1.612 m/s.