a trolley of mass 200kg is travelling north at 2m\s. It collides head on with a second trolley of mass 500kg which is travelling south with a velocity of 5 m\s and they remain coupled together.
a)calculate the velocity of the two trolleys after collision.
b)what is the direction of motion of the trolley after collison?
conservation of momentum
200*2N+500*5S=(700)V
400N-2500N=700V
solve for V. A negative N means S
To calculate the velocity of the two trolleys after the collision, we can use the principle of conservation of momentum.
a) The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces are involved.
The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, we have:
Initial momentum of the first trolley = mass of the first trolley * velocity of the first trolley
= 200 kg * 2 m/s
= 400 kg·m/s (northward)
Initial momentum of the second trolley = mass of the second trolley * velocity of the second trolley
= 500 kg * (-5 m/s)
= -2500 kg·m/s (southward)
Total initial momentum = 400 kg·m/s + (-2500 kg·m/s)
= -2100 kg·m/s
Since there are no external forces acting on the system, the total momentum after the collision is also -2100 kg·m/s.
We can express the final velocity of the coupled trolleys as V (unknown).
Final momentum of the coupled trolleys = (mass of the first trolley + mass of the second trolley) * V
= (200 kg + 500 kg) * V
= 700 kg * V
So, the equation for the conservation of momentum is:
-2100 kg·m/s = 700 kg * V
Simplifying the equation, we find:
V = -2100 kg·m/s / 700 kg
V = -3 m/s
Therefore, the velocity of the two trolleys after the collision is -3 m/s, indicating that they are moving northward.
b) Since the velocity is negative, the negative sign represents the opposite direction of the initial velocity of the second trolley (southward). Therefore, the direction of motion of both trolleys after the collision is northward.
To solve this problem, we can apply the principle of conservation of momentum.
a) The momentum before the collision is equal to the momentum after the collision. Mathematically, we can write:
(m1 * v1) + (m2 * v2) = (m1 * v1') + (m2 * v2')
Where:
m1 = mass of the first trolley (200 kg)
v1 = velocity of the first trolley before the collision (2 m/s)
m2 = mass of the second trolley (500 kg)
v2 = velocity of the second trolley before the collision (-5 m/s)
v1' = velocity of the first trolley after the collision (unknown)
v2' = velocity of the second trolley after the collision (unknown)
Plugging in the values:
(200 kg * 2 m/s) + (500 kg * -5 m/s) = (200 kg * v1') + (500 kg * v2')
400 kg·m/s - 2500 kg·m/s = 200 kg·v1' + 500 kg·v2'
-2100 kg·m/s = 200 kg·v1' + 500 kg·v2' ---- (Equation 1)
Since the trolleys remain coupled together after the collision, their velocities will be the same, so v1' = v2'.
Substituting v1' = v2' into Equation 1:
-2100 kg·m/s = 200 kg·v1' + 500 kg·v1'
Combining the masses:
-2100 kg·m/s = (200 kg + 500 kg)·v1'
-2100 kg·m/s = 700 kg·v1'
Dividing both sides by 700 kg:
v1' = -2100 kg·m/s / 700 kg
v1' = -3 m/s
Therefore, the velocity of both trolleys after the collision is -3 m/s.
b) The negative sign indicates the direction of motion. Since the velocity is negative, the direction of motion of the trolley after the collision is south.