A truck of mass 1.0 tonne moving at 4.0 m/s catches up and collides with a truck of mass 2.0 tonne moving at 3.0m/s in the same direction. The trucks become coupled together. Calculate their common velocity
use the conservation of momentum
m1v1+m2v2=(m1+m2)vfinal
17m/s
To calculate the common velocity of the two trucks after the collision, we need to apply 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.
Momentum (p) is defined as the product of an object's mass and its velocity. So, the momentum formula can be written as:
p = m * v
Where:
p = momentum
m = mass
v = velocity
Before the collision, the momentum of the first truck (Truck 1) is given by:
p1 = m1 * v1
After the collision, the two trucks become coupled together, so their final velocity can be denoted as v_f.
The momentum of the second truck (Truck 2) is given by:
p2 = m2 * v2
According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision:
p1 + p2 = (m1 + m2) * v_f
Now let's plug in the values given in the problem:
m1 = 1.0 tonne = 1000 kg (since 1 tonne = 1000 kg)
v1 = 4.0 m/s
m2 = 2.0 tonne = 2000 kg
v2 = 3.0 m/s
Substituting these values into the equation, we get:
(1000 kg * 4.0 m/s) + (2000 kg * 3.0 m/s) = (1000 kg + 2000 kg) * v_f
Simplifying further:
(4000 kg*m/s) + (6000 kg*m/s) = (3000 kg) * v_f
Combining the terms:
10000 kg*m/s = 3000 kg * v_f
Finally, we can solve for v_f by dividing both sides of the equation by 3000 kg:
v_f = (10000 kg*m/s) / (3000 kg)
v_f = 3.33 m/s
Therefore, the common velocity of the two trucks after the collision is approximately 3.33 m/s.