Driving it home
At the driving range an experiment was set up with the local pro golfer. Four identical looking golf balls where teed up. Only one of the balls is an official regulation golf ball of high quality. Each of these balls have the same mass but vastly different physical characteristics. The golfer is asked to drive each of the four ball one after the other with four identical swings. The golfer is renowned for his ability to produce a very consistent and long drives on every drive attempt.
Drive #1 the ball sails off. The first contact with the ground was 300 yards out on the flat driving range. A beautiful drive.
Drive #2 the ball sails off. The first contact with the ground was 25 yards out on the flat driving range. The ball ends up about 30 yards from the tee. A disappointing drive.
Drive #3 the ball deforms drastically with the impact of the club and ends up stuck to the face of the club like a sticky blob of bubble gum. The golfer has to clean the remnants of the ball off his club for the last shot.
Drive #4 the ball is made up of a very fragile and brittle material. At the first contact with the club the ball disintegrated into a fine powder that was scattered out in every direction in a more or less uniform cloud of dust. (This may not actually be possible in real life but let’s say that is what happened for this problem)
The speed of the golf club head was measure at a point that was 10 cm, of head travel, after impact on each drive.
Assumptions:
The golfer completely relaxes his swing the instant the club strikes each ball, any movement of the club after the impact is strictly do to the momentum of the club. (Again: this may not actually be possible in real life but let’s say that is what happened for this problem)
The club head speed, club direction of travel, club orientation and the point of impact of all the balls on the club face are identical in each drive.
The golfer is using the same regulation driver for all four shots. The mass of the head of the driver is about four times the mass of a golf ball.
Which one of the four drives had the highest club speed at the time of the measurements?
A: The measured club head speeds would all be the same for all four shots.
B: There is insufficient information given to determine an answer.
C: Drive #1
D: Drive #2
E: Drive #3
F: Drive #4
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1 solution
Considering the ball + the club as a closed system and the tee as the frame of reference. Momentum must be conserved with each drive. With each drive the instant just before impact the ball has 0 velocity and therefor 0 momentum.
p=mv
At impact the club head has some value of velocity towards the ball. In drive #1, drive #2 and drive #3 the mass of the ball is set into motion by the club head impact. After impact the mass of the ball is moving (has velocity). The total mass of the system remains constant and the total momentum of the system remains constant. If the ball has velocity it has momentum. Any momentum in the ball after impact must have come from a transfer of momentum from the club, because in a closed system momentum is conserved. If the club lost momentum to the ball it lost velocity because the club mass is constant.
With the fourth drive the ball’s mass was distributed evenly in all directions. Since the distribution was even there is no net velocity of the mass of the ball. The particles of dust moving backwards cancel out the particles moving forwards. The net velocity of the mass of the ball remains at 0. The club head speed in not effected by the impact with the disintegrating ball.
The club speed will be the highest after drive #4.