A laden lorry of mass 3000kg travelling due east at 40 m.s -1 collides head on with a large truck of mass 2000kg travelling at 30 m.s -1. the two vehicles combine during the collision. Calculate the velocity with which the two wrecks move after collision.]
To calculate the velocity with which the two wrecks move after the collision, we can use the principle of conservation of momentum.
The momentum before the collision is equal to the momentum after the collision.
Momentum (p) is calculated by multiplying mass (m) by velocity (v).
For the laden lorry:
Initial momentum = mass x velocity
p1 = 3000 kg x 40 m/s
p1 = 120,000 kg.m/s
For the large truck:
Initial momentum = mass x velocity
p2 = 2000 kg x (-30 m/s) (we use a negative sign because the truck is travelling in the opposite direction)
p2 = -60,000 kg.m/s
Summing up the initial momentum:
Total initial momentum = p1 + p2
Total initial momentum = 120,000 kg.m/s + (-60,000 kg.m/s)
Total initial momentum = 60,000 kg.m/s
Now, after the collision, the two vehicles combine, so we have a new combined mass (m_combined) and a final velocity (v_combined).
Total final momentum = m_combined x v_combined
Since the two vehicles combine, the new combined mass is the sum of the masses of the laden lorry and the large truck:
m_combined = 3000 kg + 2000 kg
m_combined = 5000 kg
Now, we can calculate the final velocity using the equation for momentum:
Total final momentum = m_combined x v_combined
Total final momentum = 5000 kg x v_combined (equation 1)
Since momentum is conserved, the total final momentum is equal to the total initial momentum:
Total final momentum = Total initial momentum (equation 2)
Setting equation 1 equal to equation 2, we have:
5000 kg x v_combined = 60,000 kg.m/s
Now, we can solve for v_combined:
v_combined = (60,000 kg.m/s) / 5000 kg
v_combined = 12 m/s
Therefore, the velocity with which the two wrecks move after the collision is 12 m/s.
To calculate the velocity with which the two wrecks move 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 defined as the product of its mass and velocity. Mathematically, momentum (p) is given by:
p = m * v
where p is the momentum, m is the mass, and v is the velocity.
In this scenario, we have two vehicles colliding head-on. Let's denote the velocity of the laden lorry as v1 and the velocity of the large truck as v2. Since the two vehicles combine and move as one after the collision, we need to calculate their velocity after the collision (v).
According to the conservation of momentum, the total momentum before the collision (p_initial) is equal to the total momentum after the collision (p_final). Mathematically, we can express this as:
p_initial = p_final
The total momentum before the collision (p_initial) can be calculated as the sum of the individual momenta of the laden lorry and the large truck before the collision:
p_initial = (m1 * v1) + (m2 * v2)
Similarly, the total momentum after the collision (p_final) is the combined momentum of the two wrecks:
p_final = (m1 + m2) * v
Since p_initial = p_final, we can write the equation as:
(m1 * v1) + (m2 * v2) = (m1 + m2) * v
Substituting the given values:
m1 = 3000 kg (mass of the laden lorry)
v1 = 40 m/s (velocity of the laden lorry)
m2 = 2000 kg (mass of the large truck)
v2 = 30 m/s (velocity of the large truck)
(3000 kg * 40 m/s) + (2000 kg * 30 m/s) = (3000 kg + 2000 kg) * v
Simplifying the equation gives:
120000 kgm/s + 60000 kgm/s = 5000 kg * v
Now, add the momenta on the left side of the equation:
180000 kgm/s = 5000 kg * v
Divide both sides of the equation by 5000 kg to isolate v:
v = 180000 kgm/s รท 5000 kg
v = 36 m/s
Therefore, the velocity with which the two wrecks move after the collision is 36 m/s.