An object A of mass 20kg moving with an initial velocity of 3m/s makes a head on collision with object B mass 10kg moving with a velocity of 2m/s in opposite direction if A and B stick together after collision calculate their common velocity
M1V1–(M2V2)=V(M1+M2)
20*3–(10*2)=V(20+10)
60–20=V(30)
40/30=30V/30
V=1.3ms–1.
final momentum = initial momentum
(20+10) v = 20 * 3 - 10 * 2
30 v = 60 - 20
Well, when two objects collide, you can say they really "stick together" just like best friends. In this case, object A is like that friend who weighs 20kg and has an initial velocity of 3m/s. And object B, well, it's the cool kid weighing 10kg with a velocity of 2m/s in the opposite direction.
When these two friends collide, they decide to stick together and form a new friendship. So, we can combine their masses to get a total mass of 30kg.
Now let's calculate their common velocity, shall we? To do that, we need to apply the principle of conservation of momentum, which says that the total momentum before the collision is equal to the total momentum after the collision.
Before the collision, the momentum of object A can be calculated as mass A times its initial velocity: (20kg) x (3m/s) = 60 kg*m/s. Similarly, the momentum of object B can be calculated as mass B times its initial velocity: (10kg) x (-2m/s) = -20 kg*m/s (negative because it's moving in the opposite direction).
Now, after the collision, these two friends stick together and we want to find the common velocity. Let's call it V. Using the conservation of momentum principle, the total momentum after the collision should be equal to the total momentum before the collision, which gives us:
(30kg) x (V) = 60 kg*m/s - 20 kg*m/s
30V = 40 kg*m/s
V = 40 kg*m/s / 30kg
V ≈ 1.33 m/s
So, the common velocity of object A and B after the collision is approximately 1.33 m/s. They've decided to stick together and go forward with the new friendship they've formed during the collision.
To calculate the common velocity of the two objects after the collision, we can use the principle of conservation of momentum. This principle states that the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v), i.e., p = mv.
Given:
Mass of object A (m1) = 20 kg
Initial velocity of object A (v1) = 3 m/s
Mass of object B (m2) = 10 kg
Velocity of object B (v2) = -2 m/s (negative sign indicates opposite direction)
To find the common velocity after the collision (v):
Total initial momentum before the collision (p_initial) = p1_initial + p2_initial
Total final momentum after the collision (p_final) = p1_final + p2_final
According to the conservation of momentum:
p_initial = p_final
Therefore,
(m1 * v1) + (m2 * v2) = (m1 + m2) * v
Substituting the given values:
(20 kg * 3 m/s) + (10 kg * -2 m/s) = (20 kg + 10 kg) * v
Simplifying the equation:
60 kg m/s - 20 kg m/s = 30 kg * v
40 kg m/s = 30 kg * v
Finally, calculating the common velocity:
v = (40 kg m/s) / (30 kg)
v ≈ 1.33 m/s
Therefore, the common velocity of the two objects after the collision is approximately 1.33 m/s.
To calculate the common velocity of the objects after the collision, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity:
Momentum = mass × velocity
Before the collision, the momentum of object A is given by:
Momentum A = mass A × velocity A = 20 kg × 3 m/s = 60 kg·m/s (to the right)
And the momentum of object B is given by:
Momentum B = mass B × velocity B = 10 kg × (-2 m/s) = -20 kg·m/s (to the left)
Since these two objects are moving in opposite directions, we consider their velocities as negative for object B.
Now, let's calculate the total momentum before the collision:
Total momentum before collision = Momentum A + Momentum B
= 60 kg·m/s + (-20 kg·m/s)
= 40 kg·m/s (to the right)
According to the principle of conservation of linear momentum, this total momentum should be equal to the total momentum after the collision when the objects are stuck together.
Let's represent the common velocity of object A and B after the collision as V (to the right). The total momentum after the collision is given by:
Total momentum after collision = (20 kg + 10 kg) × V
= 30 kg × V
Equating the total momentum before and after the collision, we have:
40 kg·m/s = 30 kg × V
Now, let's solve for V:
V = 40 kg·m/s / 30 kg
V = 4/3 m/s
Therefore, the common velocity of objects A and B after the collision is 4/3 m/s to the right.