A truck of mass 3000kg moving at 3m/s collides head on with a car of mass 600kg.the two stop dead on collision.at what velocity was the car travelling?
conserve momentum.
3000*3 = 600v
To find the velocity of the car before the collision, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces are present.
Let's denote the initial velocity of the car as Vc and the final velocity of both the truck and the car as 0 m/s (since they stop after the collision). The final velocity of the truck will also be 0 m/s.
Using the conservation of momentum equation, where the total initial momentum is equal to the total final momentum:
(Mass of truck * Initial velocity of truck) + (Mass of car * Initial velocity of car) = (Mass of truck * Final velocity of truck) + (Mass of car * Final velocity of car)
(3000 kg * 3 m/s) + (600 kg * Vc) = (3000 kg * 0 m/s) + (600 kg * 0 m/s)
9000 kg m/s + 600 kg * Vc = 0 kg m/s
600 kg * Vc = -9000 kg m/s
Now, solve for the initial velocity of the car:
Vc = (-9000 kg m/s) / (600 kg)
Vc = -15 m/s
Therefore, the car was traveling at a velocity of -15 m/s before the collision. The negative sign indicates that the car was moving in the opposite direction as the truck.
To find the velocity of the car before the collision, we can apply the principle of conservation of momentum.
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). The law of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, assuming there are no external forces acting on the system.
Mathematically, we can express this principle as:
Total momentum before collision = Total momentum after collision
Now let's calculate the total momentum before the collision:
Momentum of the truck before collision:
Momentum of the truck (p1) = Mass of the truck (m1) × Velocity of the truck (v1)
Given :
Mass of the truck (m1) = 3000 kg
Velocity of the truck (v1) = 3 m/s
p1 = m1 × v1
= 3000 kg × 3 m/s
= 9000 kg⋅m/s
Since the car is at rest initially, its momentum is zero.
Now, let's calculate the total momentum after the collision:
Total momentum after collision:
The truck and the car come to a stop after the collision. Therefore, the final velocity of both the truck and the car is zero.
Momentum of the truck after collision (p2) = Mass of the truck (m1) × Velocity of the truck (v2)
Given:
Mass of the truck (m1) = 3000 kg
Velocity of the truck (v2) = 0 m/s
p2 = m1 × v2
= 3000 kg × 0 m/s
= 0 kg⋅m/s
Using the principle of conservation of momentum:
Total momentum before collision = Total momentum after collision
p1 + p2 = 0
9000 kg⋅m/s + 0 = 0
Therefore, the car's velocity before the collision would be the value that makes the equation true. If the car has a velocity of 15 m/s, for instance, then the equation would be:
9000 kg⋅m/s + (600 kg × 15 m/s) = 0
Simplifying this equation would yield a true statement, indicating that the car's initial velocity was 15 m/s.
Hence, the car was traveling at 15 m/s before the collision.