Two moving balls collide together. Determine the magnitude of their common final velocity. The first ball of mass o.5 kg and a velocity va = 3i+5j m/s. The second ball B has a mass of 1 kg and a velocity vb = 1.2i-j+1.8k m/s
total x momentum = .5*3 + 1*1.2 = 2.7
total y momentum = .5*5 + 1*1.8 = 4.3
sqrt (2.7^2+4.3^2) = 5.1 = mag of total momentum
mass = 1.5
so
v = 5.1/1.5 = 3.4 m/s
To determine the magnitude of their common final velocity after the collision, you can use the principles of conservation of momentum and kinetic energy.
1. Calculate the initial momentum of each ball:
- The momentum of ball A (pA) is given by its mass (mA) multiplied by its initial velocity (vA):
pA = mA * vA
- Substitute the mass and velocity values for ball A to calculate its initial momentum.
- Similarly, calculate the initial momentum of ball B (pB) using its mass (mB) and initial velocity (vB).
2. Calculate the total initial momentum (pInitial) of the system:
- Since momentum is a vector quantity, you need to add the momenta of the two balls using vector addition.
- Add pA and pB to obtain the initial momentum of the system.
3. Apply the principle of conservation of momentum:
- According to the conservation of momentum, the total momentum of the system before the collision should be equal to the total momentum after the collision.
- Since the balls collide and stick together, the final momentum (pFinal) of the system will be the sum of their masses multiplied by their common final velocity (vFinal).
- Set pInitial equal to pFinal and solve for vFinal.
4. Calculate the magnitude of the common final velocity:
- Once you have the value of vFinal, you can calculate its magnitude using the formula:
|vFinal| = √(vFinal · vFinal)
- Compute the dot product of vFinal with itself, take the square root of the result, and you'll have the magnitude of the common final velocity.
By following these steps, you can determine the magnitude of their common final velocity after the collision.