On a single straight track, a vehicle of mass 500 kg moving with a vel...
Given:- Mass of the first vehicle (m1) = 500 kg
- Initial velocity of the first vehicle (u1) = 25 m/s
- Mass of the second vehicle (m2) = 250 kg
- Initial velocity of the second vehicle (u2) = 10 m/s
To find:- Common velocity (v) with which both vehicles will move together after the impact
Explanation:
Momentum:Momentum is the product of mass and velocity of an object. It is given by the equation:
Momentum (p) = mass (m) × velocity (v)
Conservation of Momentum:According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision, provided no external forces act on the system.
Mathematically, it can be expressed as:
Total momentum before collision = Total momentum after collision
(m1 × u1) + (m2 × u2) = (m1 + m2) × v
Substituting the given values:
(500 kg × 25 m/s) + (250 kg × 10 m/s) = (500 kg + 250 kg) × v
Simplifying the equation:
12500 kg·m/s + 2500 kg·m/s = 750 kg × v
15000 kg·m/s = 750 kg × v
Dividing both sides of the equation by 750 kg:
v = 15000 kg·m/s / 750 kg
v = 20 m/s
Therefore, the common velocity with which both vehicles will move together after the impact is 20 m/s.