ESPN has a new show called Super Smack: When Giants Collide! On the first episode, the World's largest bowling ball (Mbb=1200 kg) moving to the right with a speed of 3.0 m/s, collides head-on (in a perfectly inelastic collision) with the World's Largest Ball of Wax (Mwax=240 kg) which is moving to the left with a speed of 5.0 m/s. Determine the motions of the two balls after the collision (Assume both balls are moving horizontally without air resistance; also, this problem does not involve rolling.)
PLEASE HELP and show all work physics is my worst subject
conservation of momentum
Mbb*Vbb + Mwax*Vwax= (Mwax+Mbb)*Vfinal solve for Vfinal.
Note velocity signs: if to the right is +, then to the left is -
Given: M1 = 1200 kg, V1 = 3 m/s,
M2 = 240kg, V2 = -5 m/s.
V3 = Velocity of M1 and M2 after collision.
Momentum before = Momentum after,
M1*V1 + M2*V2 = M1*V3 + M2*V3,
1200*3 + 240*(-5) = 1200V3 + 240*V3,
V3 = ?.
To determine the motions of the two balls after the collision, we can use the principles of conservation of momentum and energy.
Step 1: Calculate the total momentum before the collision.
The momentum of an object is equal to its mass multiplied by its velocity.
For the bowling ball (Mbb = 1200 kg) moving to the right:
Momentum of the bowling ball = mass x velocity
Pbb = Mbb * Vbb = 1200 kg * 3.0 m/s = 3600 kg·m/s (to the right)
For the ball of wax (Mwax = 240 kg) moving to the left:
Momentum of the ball of wax = mass x velocity
Pwax = Mwax * Vwax = 240 kg * (-5.0 m/s) = -1200 kg·m/s (to the left, since its velocity is negative)
The total momentum before the collision is the sum of the momenta of the two balls:
Total momentum before = Pbb + Pwax = 3600 kg·m/s - 1200 kg·m/s = 2400 kg·m/s (to the right)
Step 2: Apply conservation of momentum.
In a perfectly inelastic collision, the objects stick together after the collision. Therefore, the total momentum before the collision is equal to the total momentum after the collision.
Total momentum before = Total momentum after
Let's assume the final velocity of the combined objects (merged ball) after the collision is Vfinal.
Total momentum before = total momentum after
2400 kg·m/s = (Mbb + Mwax) * Vfinal
Step 3: Solve for the final velocity.
Substituting the given masses into the equation:
2400 kg·m/s = (1200 kg + 240 kg) * Vfinal
2400 kg·m/s = 1440 kg * Vfinal
Dividing both sides of the equation by 1440 kg:
Vfinal = 2400 kg·m/s / 1440 kg = 1.67 m/s
Therefore, the final velocity of the combined objects after the collision is 1.67 m/s to the right.
Step 4: Determine the individual motions of the balls after the collision.
Since the objects stick together after the collision, both the bowling ball and the ball of wax will move with the same final velocity, 1.67 m/s to the right.
So, the motion of the bowling ball after the collision is to the right with a speed of 1.67 m/s.
And the motion of the ball of wax after the collision is also to the right with a speed of 1.67 m/s.