A body of mass 4kg moving with a velocity of 10 meter per second collide with a stationary body of mass 6kg. If the two body move together after the collision, calculate their common velocity
To solve this problem, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the initial velocity of the stationary body as v2 (since it is stationary, its initial velocity is 0). Let's also denote the final common velocity of both bodies after the collision as v_f.
The total momentum before the collision is given by:
Initial momentum = (mass1 * velocity1) + (mass2 * velocity2)
= (4 kg * 10 m/s) + (6 kg * 0 m/s)
= 40 kg m/s + 0 kg m/s
= 40 kg m/s
The total momentum after the collision is given by:
Final momentum = (mass1 + mass2) * velocity_f
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can write:
40 kg m/s = (4 kg + 6 kg) * velocity_f
Now we can solve for the final common velocity (velocity_f):
40 kg m/s = 10 kg * velocity_f
Dividing both sides of the equation by 10 kg gives:
velocity_f = 40 kg m/s / 10 kg
= 4 m/s
Therefore, the common velocity of the two bodies after the collision is 4 m/s.
To find the common velocity of the two bodies after the collision, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. The total momentum before the collision is equal to the total momentum after the collision.
Let's denote the initial velocity of the 4kg body as v1 and the initial velocity of the 6kg body as v2. Since the second body is initially stationary, v2 is equal to 0.
Using the principle of conservation of momentum, we have:
Total momentum before collision = Total momentum after collision
(mass1 * velocity1) + (mass2 * velocity2) = (mass1 + mass2) * common velocity
(4kg * 10m/s) + (6kg * 0m/s) = (4kg + 6kg) * common velocity
40kg m/s = 10kg * common velocity
Dividing both sides by 10kg, we get:
4m/s = common velocity
So, 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 calculated by multiplying its mass by its velocity. So, let's calculate the initial momentum and the final momentum for the two bodies.
Initial momentum before the collision:
Body 1 momentum = mass of body 1 × velocity of body 1
= 4 kg × 10 m/s
= 40 kg⋅m/s
Body 2 is stationary, so its initial momentum is 0 kg⋅m/s.
Total initial momentum = Body 1 momentum + Body 2 momentum
= 40 kg⋅m/s + 0 kg⋅m/s
= 40 kg⋅m/s
Final momentum after the collision:
Since the two bodies move together after the collision, their final velocity will be the same. Let's denote it as Vf.
Body 1 final momentum = mass of body 1 × final velocity = 4 kg × Vf
Body 2 final momentum = mass of body 2 × final velocity = 6 kg × Vf
Total final momentum = Body 1 final momentum + Body 2 final momentum
According to the principle of conservation of momentum,
Total initial momentum = Total final momentum
40 kg⋅m/s = 4 kg × Vf + 6 kg × Vf
40 kg⋅m/s = 10 kg × Vf
Dividing both sides by 10 kg:
4 m/s = Vf
Therefore, the common velocity of the two bodies after the collision is 4 m/s.