A body of mass 3kg moving at 15m/s collides with another body of mass 5kg moving at 26 m/s in the same direction. After collision the 5kg body moves at 39.8m/s in the same direction. Find the velocity of the 3kg body after collision
total momentum is constant in the system
the sum of the initial momenta equals the sum of the final momenta
find the total and subtract the larger mass after the collision
To find the velocity of the 3kg body after the collision, we can use the principle of conservation of linear momentum.
The principle of conservation of linear momentum states that the total linear momentum of an isolated system remains constant before and after the collision.
In mathematical form, the linear momentum before the collision is equal to the linear momentum after the collision.
Let's denote the velocity of the 3kg body after the collision as v₁ and the velocity of the 5kg body after the collision as v₂.
The linear momentum before the collision is given by the sum of the products of the masses and velocities of the two bodies:
Linear momentum before = (mass₁ * velocity₁) + (mass₂ * velocity₂)
Linear momentum before = (3kg * 15m/s) + (5kg * 26m/s)
Linear momentum before = 45kg·m/s + 130kg·m/s
Linear momentum before = 175kg·m/s
Similarly, the linear momentum after the collision is given by:
Linear momentum after = (mass₁ * velocity₁) + (mass₂ * velocity₂)
Linear momentum after = (3kg * v₁) + (5kg * 39.8m/s)
Linear momentum after = 3kg·v₁ + 199kg·m/s
Since linear momentum is conserved, we can equate the linear momentum before and after the collision:
175kg·m/s = 3kg·v₁ + 199kg·m/s
Rearranging the equation, we get:
3kg·v₁ = 175kg·m/s - 199kg·m/s
3kg·v₁ = -24kg·m/s
Dividing both sides by 3kg, we find:
v₁ = -8m/s
Therefore, the velocity of the 3kg body after the collision is -8m/s, indicating that it moves in the opposite direction of its initial motion.