An object with a mass of 5kg collides witn an object with a mass of 3kg that is stationary.the two objects stick together and move on with a velocity of 6m.-1 .what was the velocity of the 5kg mass before the collision took place?
To determine the velocity of the 5kg mass before the collision, we can use the law of conservation of momentum. This law states that the total momentum before a collision is equal to the total momentum after the collision.
The formula for momentum is:
momentum = mass × velocity
Let's denote the velocity of the 5kg mass before the collision as V1.
The total momentum before the collision can be calculated as:
momentum_before = (mass1 × V1) + (mass2 × 0)
Since the 3kg mass is stationary, its velocity is 0.
The total momentum after the collision is given by:
momentum_after = (mass1 + mass2) × velocity
Given that the total mass after the collision is (5kg + 3kg) = 8kg, and the velocity after the collision is 6m/s, we can write:
momentum_after = 8kg × 6m/s = 48 kg·m/s
According to the law of conservation of momentum, momentum_before = momentum_after. Therefore:
(mass1 × V1) + (mass2 × 0) = 48 kg·m/s
Substituting the given values, we have:
(5kg × V1) + (3kg × 0) = 48 kg·m/s
5kg × V1 = 48 kg·m/s
Dividing both sides by 5kg, we find:
V1 = 48 kg·m/s / 5kg
V1 = 9.6 m/s
Therefore, the velocity of the 5kg mass before the collision took place was 9.6 m/s.
To find the velocity of the 5kg mass before the collision took place, we can use the principle of conservation of momentum.
Momentum is defined as the product of an object's mass and its velocity. The law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, provided no external forces are involved.
Given:
Mass of object 1 = 5kg
Mass of object 2 = 3kg
Velocity after collision (combined velocity) = 6 m/s
Let's denote the velocity of the 5kg mass before the collision as V1 and the velocity of the 3kg mass as V2.
Using the conservation of momentum, we have:
(Mass of object 1 * Velocity of object 1 before collision) + (Mass of object 2 * Velocity of object 2 before collision) = (Mass of object 1 + Mass of object 2) * Velocity after collision
Substituting the given values, we get:
(5kg * V1) + (3kg * 0) = (5kg + 3kg) * 6 m/s
Since object 2 is initially stationary (V2 = 0), its momentum before the collision is zero.
Simplifying the equation, we have:
5kg * V1 = 8kg * 6 m/s
Now we can solve for V1:
5kg * V1 = 48kg m/s
V1 = 48kg m/s / 5kg
So the velocity of the 5kg mass before the collision took place is:
V1 = 9.6 m/s