A wagon 8kg travelling due east with a velocity of 10m/s collides with a second wagon of mass 12kg travelling due west at 2m/s. After collision the wagon moves off at 3m/s due east. Determine the magnitude and direction of the velocity of the 12kg wagon after collision.
M1*V1 + M2*V2 = M1*V3 + M2*V4.
8*10 - 12*2 = 8*3 + 12*V4.
80-24 = 24 + 12V4.
12V4 = 32, V4 = 2.67 m/s, East.
How come there is a negative 8*10-12*2=8*3+12*V4
instead 8*10+12*2=8*3+12*V4
To determine the magnitude and direction of the velocity of the 12kg wagon after the collision, we can use the principle of conservation of momentum.
Momentum is defined as the product of mass and velocity. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision, as long as no external forces are involved.
The formula for momentum is:
Momentum (p) = mass (m) × velocity (v)
We can calculate the momentum of each wagon before the collision.
For the first wagon (8kg, moving east at 10m/s):
Momentum (p1) = mass (m1) × velocity (v1)
= 8kg × 10m/s
= 80 kg·m/s, eastward
For the second wagon (12kg, moving west at 2m/s):
Momentum (p2) = mass (m2) × velocity (v2)
= 12kg × (-2m/s) (since it is moving in the opposite direction)
= -24 kg·m/s, westward
Now, let's consider the momentum after the collision. Since the two wagons stick together and move off with a velocity of 3m/s due east after the collision, we can calculate the combined mass and velocity of the two wagons.
Let the combined mass be M:
M = m1 + m2
= 8kg + 12kg
= 20kg
Let the velocity after the collision be V:
V = 3m/s, eastward
The momentum after the collision can be calculated as:
Momentum (p') = mass (M) × velocity (V)
= 20kg × 3m/s
= 60 kg·m/s, eastward
Since the total momentum before the collision is equal to the total momentum after the collision, we can set up an equation:
p1 + p2 = p'
Substituting the values of p1, p2, and p' into the equation:
80 kg·m/s + (-24 kg·m/s) = 60 kg·m/s
We can solve for the velocity (v') of the 12kg wagon after the collision:
v' = p' / m2 (where m2 is the mass of the 12kg wagon)
Substituting the values into the equation:
v' = 60 kg·m/s / 12kg
= 5 m/s
The magnitude of the velocity of the 12kg wagon after the collision is 5 m/s. Since it was initially moving westward, its velocity after the collision is also westward.
Therefore, the magnitude and direction of the velocity of the 12kg wagon after the collision is 5 m/s, westward.