High-speed stroboscopic photographs show that the head of a golf club of mass 230g is traveling at 56.1m/s just before it strikes a 44.6g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 41.4m/s. Calculate the speed of the golf ball just after impact.
momentum is conserved.
massclub*velocityinitial=massball*speedball+mass club*speedfinal club
massclub(vi-vf)=massball*speedball
speedball=massclub/massball * (56.1-44.6)
To solve this problem, we can use the principle of conservation of momentum. Before the collision, the total momentum of the system (the golf club head and the golf ball) is equal to the momentum after the collision.
First, let's find the initial momentum of the golf club head:
Initial momentum of the golf club head (before the collision) = mass of the golf club head × velocity of the golf club head
= 0.230 kg × 56.1 m/s
Next, let's find the final momentum of the golf club head:
Final momentum of the golf club head (after the collision) = mass of the golf club head × velocity of the golf club head after the collision
= 0.230 kg × 41.4 m/s
Now, let's calculate the initial momentum of the golf ball. Since the golf ball is at rest before the collision, its initial velocity is 0:
Initial momentum of the golf ball (before the collision) = mass of the golf ball × velocity of the golf ball
= 0.0446 kg × 0 m/s
Finally, let's find the final momentum of the golf ball. We can assume it travels in the same direction as the golf club head:
Final momentum of the golf ball (after the collision) = mass of the golf ball × velocity of the golf ball after the collision
Now, we need to apply the conservation of momentum principle:
Initial momentum of the golf club head + Initial momentum of the golf ball = Final momentum of the golf club head + Final momentum of the golf ball
0.230 kg × 56.1 m/s + 0.0446 kg × 0 m/s = 0.230 kg × 41.4 m/s + 0.0446 kg × velocity of the golf ball after the collision
Simplifying the equation:
12.654 kg·m/s = 9.534 kg·m/s + 0.0446 kg × velocity of the golf ball after the collision
Subtracting 9.534 kg·m/s from both sides:
3.12 kg·m/s = 0.0446 kg × velocity of the golf ball after the collision
Now, we can solve for the velocity of the golf ball after the collision:
velocity of the golf ball after the collision = 3.12 kg·m/s ÷ 0.0446 kg
velocity of the golf ball after the collision ≈ 69.97 m/s
Therefore, the speed of the golf ball just after impact is approximately 69.97 m/s.