A body of mass 4kg moving with a velocity of 10meter per second collide with a stationary body of mass 6kg. If the two body move together after the collision, calculate their common veoocity
To solve this problem, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. It is conserved in a closed system, which means that the total momentum before the collision is equal to the total momentum after the collision.
The momentum before the collision can be calculated as:
Momentum1 = mass1 * velocity1 = 4 kg * 10 m/s = 40 kg·m/s
Since the second body is stationary, its initial velocity is 0, so its momentum is:
Momentum2 = mass2 * velocity2 = 6 kg * 0 m/s = 0 kg·m/s
The total momentum before the collision is the sum of the momenta of the two bodies:
Total momentum before = Momentum1 + Momentum2 = 40 kg·m/s + 0 kg·m/s = 40 kg·m/s
After the collision, the two bodies move together with a common velocity, which we'll call V.
The total mass after the collision is the sum of the masses of the two bodies:
Total mass = mass1 + mass2 = 4 kg + 6 kg = 10 kg
The total momentum after the collision is the product of the total mass and the common velocity:
Total momentum after = Total mass * Common velocity = 10 kg * V
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore,
Total momentum before = Total momentum after
40 kg·m/s = 10 kg * V
Divide both sides of the equation by 10 kg:
40 kg·m/s / 10 kg = V
4 m/s = V
Therefore, the common velocity of the two bodies after the collision is 4 m/s.
To calculate the common velocity of the two bodies 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:
momentum = mass * velocity
Before the collision, the first body of mass 4 kg is moving with a velocity of 10 m/s, and the second body of mass 6 kg is stationary. Therefore, the total momentum before the collision is:
momentum_before = (mass1 * velocity1) + (mass2 * velocity2)
= (4 kg * 10 m/s) + (6 kg * 0 m/s)
= 40 kg*m/s
After the collision, the two bodies move together with a common velocity. Let's call this common velocity v.
The total momentum after the collision is:
momentum_after = (mass1 + mass2) * v
= (4 kg + 6 kg) * v
= 10 kg * v
According to the principle of conservation of momentum, momentum_before = momentum_after. Therefore:
40 kg*m/s = 10 kg * v
To find the common velocity v, we can rearrange the equation:
v = 40 kg*m/s / 10 kg
= 4 m/s
Hence, the common velocity of the two bodies after the collision is 4 m/s.
To calculate the final common velocity after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision, we need to find the momentum of each body:
Momentum (p) = mass (m) x velocity (v)
For the first body with a mass of 4kg and velocity of 10m/s:
Momentum of first body = 4kg x 10m/s = 40 kg m/s
For the second body with a mass of 6kg and is stationary (velocity = 0):
Momentum of second body = 6kg x 0m/s = 0 kg m/s
Total momentum before the collision = 40 kg m/s + 0 kg m/s = 40 kg m/s
After the collision, the two bodies move together with the same common velocity (let's call it V). Since they are now moving together, their masses can be added up:
Total mass after the collision = 4kg + 6kg = 10kg
Using the law of conservation of momentum, we equate the total momentum before the collision to the total momentum after the collision:
Total momentum before collision = Total momentum after collision
40 kg m/s = 10kg x V
Now we can solve for the common velocity (V):
V = (40 kg m/s) / 10kg
V = 4 m/s
Therefore, the common velocity of the two bodies after the collision is 4 m/s.