High-speed stroboscopic photographs show
that the head of a 197 g golf club is traveling at 36.8 m/s just before it strikes a 45.9 g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 25.9 m/s. Find the speed of the golf ball immediately after impact.
Answer in units of m/s
To find the speed of the golf ball immediately after impact, 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.
The momentum of an object is given by the product of its mass and its velocity: momentum = mass × velocity.
Let's denote the initial velocity of the golf ball as Vi, and the final velocity of the golf ball as Vf. We can write the equation for conservation of momentum as:
(mass of club head × initial velocity of club head) + (mass of golf ball × initial velocity of golf ball) = (mass of club head × final velocity of club head) + (mass of golf ball × final velocity of golf ball)
Plugging in the given values:
(197 g × 36.8 m/s) + (45.9 g × 0 m/s) = (197 g × 25.9 m/s) + (45.9 g × Vf)
Converting the masses to kilograms and solving for Vf:
(0.197 kg × 36.8 m/s) + (0.0459 kg × 0 m/s) = (0.197 kg × 25.9 m/s) + (0.0459 kg × Vf)
7.2464 kg·m/s = 5.0763 kg·m/s + (0.0459 kg × Vf)
Subtracting 5.0763 kg·m/s from both sides:
2.1701 kg·m/s = 0.0459 kg × Vf
Dividing both sides by 0.0459 kg:
Vf = 2.1701 kg·m/s / 0.0459 kg
Vf ≈ 47.33 m/s
Therefore, the speed of the golf ball immediately after impact is approximately 47.33 m/s.
To find the speed of the golf ball immediately after impact, we need to apply the principle of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
First, let's calculate the initial momentum of the system, which includes the golf club head and the golf ball. The initial momentum is given by:
Initial momentum = mass of golf club head * velocity of golf club head + mass of golf ball * velocity of golf ball
Since the golf club head is traveling at 36.8 m/s and the golf ball is at rest, the initial momentum simplifies to:
Initial momentum = 197 g * 36.8 m/s + 45.9 g * 0 m/s
Now, let's convert the masses to kilograms:
Mass of golf club head = 197 g / 1000 g/kg = 0.197 kg
Mass of golf ball = 45.9 g / 1000 g/kg = 0.0459 kg
Substituting the values, we get:
Initial momentum = 0.197 kg * 36.8 m/s + 0.0459 kg * 0 m/s
Initial momentum = 7.2456 kg m/s
After the collision, the final momentum is given by:
Final momentum = mass of golf club head * velocity of golf club head + mass of golf ball * velocity of golf ball
We're given that the golf club head is traveling at 25.9 m/s after the collision. Let's assume the velocity of the golf ball after the collision is v m/s.
Final momentum = 0.197 kg * 25.9 m/s + 0.0459 kg * v m/s
Final momentum = 5.0983 kg m/s + 0.0459 kg * v m/s
According to the principle of conservation of linear momentum, the initial momentum is equal to the final momentum:
7.2456 kg m/s = 5.0983 kg m/s + 0.0459 kg * v m/s
Rearranging the equation to solve for v:
0.0459 kg * v m/s = 7.2456 kg m/s - 5.0983 kg m/s
0.0459 kg * v m/s = 2.1473 kg m/s
Dividing both sides of the equation by 0.0459 kg:
v m/s = (2.1473 kg m/s) / (0.0459 kg)
v m/s ≈ 46.8 m/s
So, the speed of the golf ball immediately after impact is approximately 46.8 m/s.
momentum (m*v) is conserved:
197*36.8 + 45.9*0 = 197*25.9 + 45.9v
v = 46.78