Ball A, with a mass of 20 kg, is moving to the right at 20 m/s. At what velocity should Ball B, with a mass of 40 kg, move so that they both come to a standstill upon collision?
How do I solve this?
conserve momentum. After the collision, the total momentum is zero. So, it must also come out to zero while the balls were moving:
20*20 + 40v = 0
Note the sign of the velocity for B. What does that indicate?
Wait so I'm trying to solve for the V?
well, yeah - that was the question, wasn't it?
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision. In equation form:
Total momentum before = Total momentum after
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v):
p = mv
Given information:
Mass of Ball A (m1) = 20 kg
Initial velocity of Ball A (v1) = 20 m/s
Mass of Ball B (m2) = 40 kg
Velocity of Ball B (v2) = ? (what we need to find)
Step 1: Calculate the total momentum before the collision.
The total momentum before the collision equals the sum of the momenta of Ball A and Ball B:
Total momentum before = m1 * v1 + m2 * v2
Substituting the given values:
Total momentum before = (20 kg * 20 m/s) + (40 kg * v2)
Step 2: Calculate the total momentum after the collision.
After the collision, both balls come to a standstill. Therefore, the final velocity of both balls (vf) is 0 m/s. The total momentum after the collision is the sum of their momenta:
Total momentum after = 0 + 0 = 0
Step 3: Apply the principle of conservation of momentum.
Set the total momentum before the collision equal to the total momentum after the collision:
(20 kg * 20 m/s) + (40 kg * v2) = 0
Simplifying the equation:
400 kg·m/s + 40 kg·v2 = 0
Step 4: Solve for v2.
Rearrange the equation to solve for v2:
40 kg·v2 = -400 kg·m/s
Divide both sides by 40 kg:
v2 = -400 kg·m/s / 40 kg
v2 = -10 m/s
Therefore, to make both balls come to a standstill upon collision, Ball B should move to the left at a velocity of 10 m/s. The negative sign indicates the opposite direction of Ball A's initial velocity.