A body of mass 1 kg and velovity 10 m/s collides with another body if mass 3 kg and velocity 2 m/s comming from the exactly opposite direction. if on collision the body's much into one find the magnitude and direction of common velocity
Momentum = m1*V1 - m2*V2= 1*10-3*2=4 in
the direction of m1.
m*V = 4
V = 4/m = 4/(1+3) = 1 m/s. in the direction of m1.
Momentum = m1*V1 - m2*V2= 1*10-3*2=4 in
the direction of m1.
m*V = 4
V = 4/m = 4/(1+3) = 1 m/s. in the direction of m1.
To find the magnitude and direction of the common velocity after the collision, we can use the principles of conservation of momentum and kinetic energy.
Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Mathematically, it can be written as:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Where:
- m1 and m2 are the masses of the two bodies
- v1 and v2 are their respective velocities before the collision
- vf is the common final velocity after the collision
Using the given values:
m1 = 1 kg
v1 = 10 m/s
m2 = 3 kg
v2 = -2 m/s (since it is opposite direction, the velocity is negative)
Substituting the values into the equation gives us:
(1 kg * 10 m/s) + (3 kg * -2 m/s) = (1 kg + 3 kg) * vf
Simplifying the equation gives us:
10 kg*m/s - 6 kg*m/s = 4 kg * vf
4 kg * vf = 4 kg*m/s
vf = (4 kg*m/s) / 4 kg
vf = 1 m/s
The magnitude of the common velocity after the collision is 1 m/s. But we still need to determine the direction.
Since the first body has a positive velocity (moving to the right) and the second body has a negative velocity (moving to the left), the direction of the common velocity will depend on which side is positive.
If we assume the right side is the positive side, then the common velocity will have a positive direction, meaning the bodies will move to the right together.
Therefore, the magnitude of the common velocity is 1 m/s, and the direction is to the right.