Three carts are moving on a frictionless horizontal track as shown in the figure. The 4.00 kg cart is moving to the right with a speed of 7.0 m/s, the 10.0 kg cart is also moving to the right with a speed of 6.0 m/s while the 3.00 kg cart moves to the left with a speed of 5 m/s. Find the final speed of the carts when they are all stuck together. Hint: The order at which the carts stick together does not matter. Can you see why?
Been stuck on this for a while, i've used my inelastic equation but i just dont get the correct answer.
add the momentums, set them equal to the final momentum.
mass1*V1+mass2*V2+mass3*V3=(mass1+mass2+mass3)Vfinal
make certain you use right as + speed, left as - speed.
Thank you!!! I didn't make the velocity negative for the cart going left! That was all i was doing wrong. I'm kicking myself.
To find the final speed of the carts when they are stuck together, you can use the principle of conservation of momentum. According to this principle, the total momentum before the carts stick together is equal to the total momentum after the carts stick together.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) is given by the equation: p = m * v, where m is the mass of the object and v is its velocity.
Let's assign a positive direction as to the right and a negative direction as to the left. We can write the initial and final momenta equations as follows:
Initial momentum:
m1 * v1 + m2 * v2 + m3 * v3 = (m1 + m2 + m3) * vf
where m1, m2, and m3 are the masses of the carts, and v1, v2, and v3 are their respective velocities, and vf is the final velocity of the three carts together.
Substituting the known values, we have:
(4.00 kg * 7.0 m/s) + (10.0 kg * 6.0 m/s) + (3.00 kg * -5 m/s) = (4.00 kg + 10.0 kg + 3.00 kg) * vf
Simplifying the equation:
28.00 kg·m/s + 60.00 kg·m/s - 15.00 kg·m/s = 17.00 kg * vf
Combining the terms on both sides:
73.00 kg·m/s = 17.00 kg * vf
Now, we can solve for vf by dividing both sides of the equation by 17.00 kg:
vf = (73.00 kg·m/s) / 17.00 kg
Calculating the final speed:
vf = 4.29 m/s (rounded to two decimal places)
Therefore, the final speed of the three carts when they are stuck together is approximately 4.29 m/s.
Now, regarding the hint, the order at which the carts stick together does not matter because momentum is a vector quantity. The sum of momenta before and after the carts stick together will be the same regardless of the order in which they are stuck. This is due to the conservation of momentum principle, which states that the total momentum of a closed system remains constant if no external forces act on the system.