Difficult momentum question need help please!!!?

Question

Two carts with masses of 4.84 kg and 2.34 kg move toward each other on a frictionless track with speed of 4.90 m/s and 3.12 m/s respectively. The carts stick together after colliding head - on. Find the final speed.

Answer 1

Mass of the heavier cart (M) = 4.84 Kg
The (initial)vel. of the heavier cart(V) = 4.90 m/s
Mass of the lighter cart(m) = 2.34 Kg
The (initial)vel. of the lighter cart(v) = - 3.12 m/s(Opp. Direction)
After collision as the bodies stick together, after collision their mass will be = (M+m) Kg
Let the final velocity be V' m/s
By law of conservation of momentum,
(M x V) + (m x -v) = (M + m) x V'
(4.84 x 4.9) + (2.34 x -3.12) = (7.18) x V'
(23.716) + (-7.3008) = 7.18 x V'
16.4152 = 7.18 x V'
V' = 16.4152 / 7.18 = 2.286 m/s
... .... .... ..... ===========
(as the vel. is +ve, it goes in the same direction as that of the larger cart)

Answer 2

Momentum = Mass x Velocity

Momentum is conserved (the total momentum is the same for the combined mass of the two carts after the collision as it was for each of them (total) before the collision.

So, the equation would be:

M1 x V1 + M2 x V2 = (M3 x V3)

(1) = mass and velocity of one of the carts
(2) = mass and velocity of the other cart
(3) = mass and velocity of the stuck together carts after the collision.

Just plug in the numbers and do the math.

Best wishes and good luck.

P.S. remember, because the carts are going in opposite directions, one of them has a "negative" velocity!

Answer 3

7.18 kg(x velocity)=(4.84 *4.90) - (2.34*3.12)
x=2.29 m/s
As you notice the inelastic collision conserved momentum. The combined mass (7.18 kg travels in the direction that is the same as the first cart (4.84 kg).

Answer 4

Because the carts stick together, the collision must be an inelastic collision, which means that energy is NOT conserved.

However, momentum is still conserved in this equation. If momentum is equal to mv, then the initial momentum of both carts should be equal to the final momentum of both carts.

Here is what your equation should look like:
(m1)(v1) + (m2)(v2) = (m1 + m2)(v final)

Remember that the carts are going in different directions, so make one initial velocity negative to reflect that.

Hope that helps!

Answer 5

2.29 m/s