Scenario :
A truck has a mass of 2000kg and is moving at 50m/s and collides with another truck that has a mass of 2000kg moving at a speed of -20m/s.
1)Is this a sticky or springy collision?
2)What is the total momentum after the collision?
3)If both trucks stick together and begin to move off after this Collison , at what speed will they move off at?
It probably will be inelastic.
total momentum after=2000*50+2000*(-20)
3) momentum after=(4000)V=2000*30
V=15m/s
To determine the answers to the scenarios, we need to apply the principles of conservation of momentum and kinetic energy. Let's go through each question step by step:
1) Is this a sticky or springy collision?
To answer this question, we need to consider whether the two trucks stick together after the collision or rebound away from each other.
If the trucks stick together, it is a sticky collision. In a sticky collision, the two objects merge and move together as a single object after the collision.
If the trucks rebound away from each other, it is a springy collision. In a springy collision, the objects separate and move off in opposite directions after the collision.
In the given scenario, it is mentioned that both trucks stick together after the collision. Therefore, it is a sticky collision.
2) What is the total momentum after the collision?
Momentum is defined as the product of an object's mass and its velocity. According to the principle of conservation of momentum, the total momentum before and after the collision remains the same.
The formula for momentum is:
Momentum = mass × velocity
For the first truck:
Mass (m1) = 2000 kg
Velocity (v1) = 50 m/s
For the second truck:
Mass (m2) = 2000 kg
Velocity (v2) = -20 m/s (negative sign indicates the opposite direction)
To calculate the total momentum after the collision, add the individual momentum vectors:
Total momentum after the collision = (m1 × v1) + (m2 × v2)
Total momentum after the collision = (2000 kg × 50 m/s) + (2000 kg × -20 m/s)
Solve the equation:
Total momentum after the collision = 100000 kg·m/s + (-40000 kg·m/s)
Total momentum after the collision = 60000 kg·m/s
Therefore, the total momentum after the collision is 60000 kg·m/s.
3) If both trucks stick together and begin to move off after this collision, at what speed will they move off at?
Since both trucks stick together and move as one object after the collision, we can consider them as a single system.
The total mass of both trucks combined is:
Total mass (m_total) = m1 + m2
Total mass (m_total) = 2000 kg + 2000 kg
Total mass (m_total) = 4000 kg
To find the final velocity of the combined system, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Total momentum before = Total momentum after
For the initial momentum:
Initial momentum = (m1 × v1) + (m2 × v2)
For the final momentum:
Final momentum = (m_total × v_final)
Setting the two equations equal to each other:
Initial momentum = Final momentum
(m1 × v1) + (m2 × v2) = m_total × v_final
Substituting the given values:
(2000 kg × 50 m/s) + (2000 kg × -20 m/s) = 4000 kg × v_final
Solve the equation:
100000 kg·m/s - 40000 kg·m/s = 4000 kg × v_final
60000 kg·m/s = 4000 kg × v_final
Divide both sides by 4000 kg:
60000 kg·m/s / 4000 kg = v_final
v_final = 15 m/s
Therefore, if both trucks stick together and move off after the collision, they will have a speed of 15 m/s.