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
conservation of momentum
masshead*speehead=massclub*speedclub+massball*speedball
solve for speedball
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The formula for momentum is given by:
Momentum = mass * velocity
Let's assume that the speed of the golf ball immediately after the impact is "v".
Before the collision:
The momentum of the golf club head (197 g) is given by:
Momentum of club head = (197 g) * (36.8 m/s)
The momentum of the golf ball (45.9 g) is zero since it's at rest:
Momentum of golf ball = (45.9 g) * (0 m/s) = 0
The total momentum before the collision is the sum of the individual momenta:
Total momentum before collision = Momentum of club head + Momentum of golf ball
After the collision:
The momentum of the golf club head is given by:
Momentum of club head = (197 g) * (25.9 m/s)
The momentum of the golf ball is given by:
Momentum of golf ball = (45.9 g) * (v m/s)
The total momentum after the collision is the sum of the individual momenta:
Total momentum after collision = Momentum of club head + Momentum of golf ball
According to the conservation of momentum principle, we can equate the total momentum before and after the collision:
Total momentum before collision = Total momentum after collision
(197 g) * (36.8 m/s) = (197 g) * (25.9 m/s) + (45.9 g) * (v m/s)
Now we can solve this equation to find the value of "v", which represents the speed of the golf ball immediately after impact.
By canceling out the mass term (197 g) from both sides of the equation, we get:
36.8 m/s = 25.9 m/s + (45.9 g / 197 g) * (v m/s)
Simplifying further:
10.9 m/s = (45.9 g / 197 g) * (v m/s)
Now we solve for "v":
v m/s = (10.9 m/s) * (197 g / 45.9 g)
Calculating this expression:
v ≈ 47.092 m/s
Therefore, the speed of the golf ball immediately after impact is approximately 47.092 m/s.