high-speed stroboscopic photographs show that the head of a 215 kg golf club traveling at 55.0 m/s just before it strikes a 0.046 kg golf ball at rest on a tree. after the collision, the club travels (in the same direction) at 42.0 m/s. Use the law of conservation of momentum to find the speed of the golf ball just after impact.
To find the speed of the golf ball just after impact, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity, often represented by the equation:
momentum = mass × velocity
Before the collision:
Mass of the golf club = 215 kg
Velocity of the golf club = 55.0 m/s
Mass of the golf ball = 0.046 kg
Velocity of the golf ball = 0 m/s (since it is at rest)
The total momentum before the collision can be calculated by adding the momentum of the golf club and the golf ball:
Total momentum before = (Mass of golf club × Velocity of golf club) + (Mass of golf ball × Velocity of golf ball)
Total momentum before = (215 kg × 55.0 m/s) + (0.046 kg × 0 m/s)
Now, let's calculate it:
Total momentum before = 11,825 kg·m/s
After the collision:
Velocity of the golf club = 42.0 m/s
Now, since we know that the total momentum before the collision is equal to the total momentum after the collision, we can set up the equation:
Total momentum before = Total momentum after
11,825 kg·m/s = (215 kg × 42.0 m/s) + (0.046 kg × Velocity of golf ball)
We can now solve this equation to find the velocity of the golf ball after impact:
11,825 kg·m/s = 9,030 kg·m/s + (0.046 kg × Velocity of golf ball)
Subtracting 9,030 kg·m/s from both sides of the equation gives:
2,795 kg·m/s = (0.046 kg × Velocity of golf ball)
Now, divide both sides by 0.046 kg to isolate the velocity of the golf ball:
(2,795 kg·m/s) / (0.046 kg) = Velocity of golf ball
Solving this gives:
Velocity of golf ball = 60,760 m/s
Therefore, the speed of the golf ball just after impact is approximately 60,760 m/s