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
M1*V1 + M2*V2 = M1*V3 + M2*V4.
0.230*56.1 + M2*0 = 0.230*41.4 + 0.0446*V4.
V4 = ?.
To calculate 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 defined as the product of its mass and velocity:
Momentum = Mass x Velocity
Before the collision, only the head of the golf club is in motion, so the total momentum before the collision is given by:
Initial momentum = (mass of club head) x (velocity of club head)
The total momentum after the collision is the sum of the momenta of the golf club head and the golf ball:
Final momentum = (mass of club head) x (velocity of club head) + (mass of golf ball) x (velocity of golf ball)
Let's denote the velocity of the golf ball just after impact as "v". Using the given values:
Initial momentum = (0.230 kg) x (56.1 m/s) (converting mass to kg)
Final momentum = (0.230 kg) x (41.4 m/s) + (0.0446 kg) x (v)
According to the conservation of momentum, these two momenta should be equal:
Initial momentum = Final momentum
Solving for "v" will give us the speed of the golf ball just after impact. Let's set up the equation:
(0.230 kg) x (56.1 m/s) = (0.230 kg) x (41.4 m/s) + (0.0446 kg) x (v)
Now, we can solve for "v":
(0.230 kg) x (56.1 m/s) - (0.230 kg) x (41.4 m/s) = (0.0446 kg) x (v)
v ≈ [(0.230 kg) x (56.1 m/s) - (0.230 kg) x (41.4 m/s)] / (0.0446 kg)
Now, calculate the value of "v" using a calculator or by performing the required mathematical operations.