A body of mass 5 kg moving with a velocity of 20meter per second square hits stationary body of mass 3kg. If they move together after collisions with a velocity v, find the velocity v
To find the velocity v after the collision, we can use the principle of conservation of momentum.
Before the collision, the momentum of the 5 kg body is given by:
momentum1 = mass1 * velocity1 = 5 kg * 20 m/s = 100 kg m/s
Since the other body is stationary, its momentum before the collision is zero:
momentum2 = mass2 * velocity2 = 0
The total momentum before the collision is given by the sum of the momenta of the two bodies:
total momentum before = momentum1 + momentum2 = 100 kg m/s + 0 = 100 kg m/s
After the collision, the two bodies move together as one object with mass m = mass1 + mass2:
m = 5 kg + 3 kg = 8 kg
Let v be the velocity of the two bodies after the collision.
The total momentum after the collision is given by the mass of the combined bodies multiplied by the velocity:
total momentum after = m * v
According to the conservation of momentum principle, the total momentum before and after the collision should be equal:
total momentum before = total momentum after
100 kg m/s = 8 kg * v
v = 100 kg m/s / 8 kg
v = 12.5 m/s
Therefore, the velocity v after the collision is 12.5 m/s.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces are present.
The momentum of an object is given by the product of its mass and velocity. So, for the first body with a mass of 5 kg and a velocity of 20 m/s, its momentum before the collision is:
Momentum1 = mass1 * velocity1
= 5 kg * 20 m/s
= 100 kg m/s
For the second body, which is at rest and has a mass of 3 kg, its momentum before the collision is:
Momentum2 = mass2 * velocity2
= 3 kg * 0 m/s
= 0 kg m/s
Since there are no external forces acting on the system, the total momentum before the collision is equal to the total momentum after the collision. Therefore, the total momentum after the collision is also 100 kg m/s.
Now, let's assume the two bodies move together after the collision with a velocity of v. Therefore, the momentum after the collision is:
Momentum_after = (mass1 + mass2) * velocity_after
= (5 kg + 3 kg) * v
= 8 kg * v
Since the total momentum after the collision is equal to the total momentum before the collision:
Momentum_after = Momentum1 + Momentum2
8 kg * v = 100 kg m/s + 0 kg m/s
8 kg * v = 100 kg m/s
Now, we can solve for v:
v = (100 kg m/s) / 8 kg
v = 12.5 m/s
Therefore, the velocity after the collision, v, is 12.5 m/s.
To find the velocity, v, 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 (p) is given by the mass (m) multiplied by the velocity (v).
Initial momentum before the collision:
Momentum of the first body = mass of the first body (m1) × velocity of the first body (v1)
P1 = m1 × v1 = 5 kg × 20 m/s = 100 kg·m/s
The second body is stationary, so its initial momentum is 0.
Total initial momentum = P1 + P2 = 100 kg·m/s + 0 kg·m/s = 100 kg·m/s
Final momentum after the collision:
Momentum of the combined objects after the collision = total mass (m1 + m2) × final velocity (v)
Since the two objects move together after the collision, we can write:
Final momentum = (m1 + m2) × v
Total final momentum = (5 kg + 3 kg) × v = 8 kg × v
According to the principle of conservation of momentum, the initial momentum is equal to the final momentum:
Total initial momentum = Total final momentum
100 kg·m/s = 8 kg × v
To find v, we can divide both sides of the equation by 8 kg:
v = 100 kg·m/s ÷ 8 kg = 12.5 m/s
Therefore, the velocity v after the collision is 12.5 m/s.