A 3000-kg car bumps into a stationary, 5000-kg truck. The
velocity of the car before the collision was +4 m/s and
-1 m/s after the collision. What is the velocity of the truck
after the collision?
To find the velocity of the truck after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
Momentum (p) is calculated as the product of mass (m) and velocity (v): p = m * v.
Let's calculate the total momentum before the collision:
Momentum of the car before the collision = (mass of car) * (velocity of car before collision) = (3000 kg) * (4 m/s) = 12000 kg*m/s (since the velocity is positive)
Momentum of the truck before the collision = (mass of truck) * (velocity of truck before collision) = (5000 kg) * (0 m/s) = 0 kg*m/s (since the truck is stationary)
The total momentum before the collision is the sum of the individual momenta:
Total momentum before collision = Momentum of car before collision + Momentum of truck before collision = 12000 kg*m/s + 0 kg*m/s = 12000 kg*m/s.
The total momentum after the collision should also be equal to 12,000 kg*m/s.
Let's calculate the momentum of the car after the collision:
Momentum of the car after the collision = (mass of car) * (velocity of car after collision) = (3000 kg) * (-1 m/s) = -3000 kg*m/s (since the velocity is negative).
Now we can calculate the velocity of the truck after the collision:
Total momentum after the collision = Momentum of car after the collision + Momentum of truck after the collision = -3000 kg*m/s + Momentum of truck after the collision.
We can rewrite the equation:
12000 kg*m/s = -3000 kg*m/s + Momentum of truck after the collision.
To isolate Momentum of truck after the collision, we rearrange the equation:
Momentum of truck after the collision = 12000 kg*m/s + 3000 kg*m/s = 15000 kg*m/s.
Finally, we divide the momentum by the mass of the truck to find its velocity:
Velocity of the truck after the collision = Momentum of truck after collision / Mass of truck = 15000 kg*m/s / 5000 kg = 3 m/s.
Therefore, the velocity of the truck after the collision is 3 m/s.
To find the velocity of the truck 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. So, we can calculate the momentum of the car before the collision and after the collision, and then use the conservation of momentum to find the velocity of the truck.
Let's first calculate the momentum of the car before the collision:
Momentum of the car before = Mass of the car × Velocity of the car before
Momentum of the car before = (3000 kg) × (+4 m/s)
= +12,000 kg·m/s (taking the positive direction as the initial direction of the car)
Next, let's calculate the momentum of the car after the collision:
Momentum of the car after = Mass of the car × Velocity of the car after
Momentum of the car after = (3000 kg) × (-1 m/s)
= -3000 kg·m/s (taking the negative sign as the car's direction reversed after the collision)
Now, let's use the conservation of momentum to find the velocity of the truck after the collision:
Total momentum before = Total momentum after
Momentum of the car before = Momentum of the car after + Momentum of the truck after
+12,000 kg·m/s = -3000 kg·m/s + Momentum of the truck after
Momentum of the truck after = +12,000 kg·m/s - (-3000 kg·m/s)
= +12,000 kg·m/s + 3000 kg·m/s
= +15,000 kg·m/s
Finally, we can calculate the velocity of the truck after the collision using the equation:
Momentum of the truck after = Mass of the truck × Velocity of the truck after
Velocity of the truck after = Momentum of the truck after / Mass of the truck
Velocity of the truck after = (+15,000 kg·m/s) / (5000 kg)
= +3 m/s
Therefore, the velocity of the truck after the collision is +3 m/s in the same direction as the initial direction of the car.
v₁= {-2m₂v₂₀ +(m₁-m₂)v₁₀}/(m₁+m₂)
v₂={ 2m₁v₁₀ - (m₂-m₁)v₂₀}/(m₁+m₂)