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The red line represents a pitching wedge, the black line a 9-iron and the blue line a driver. This graph represents how the horizontal and vertical displacement differs from each type of golf club. The pitching wedge is a club that goes for an accuracy approach, while a driver is aimed at achieving horizontal displacement. From the table of results and the accompanying graph, a summary of the results can be identified. The results show that generally each change of the golf ball results in a consistent increase in distance hit produced by each individual.
Bar from James, the results are almost identical when averages are calculated. James was inconsistent with his practice and golf ball shots, which is why his line is very identifiable to the viewer at first glance of the averages graph. Due to the results obtained it is safe to say generally with the induction of a different ball, the distance hit by each individual is vastly changed and increased from the air ball through the practice ball and finally finishing with the golf ball.
Question 2) In theory the driver should project the three balls with a greater horizontal displacement compared to the 9-iron and a greater acceleration, while the 9-iron would produce a greater vertical displacement. These results would occur due to many biomedical principles. The main biomedical principles that would cause these results to be evident would be angular velocity, the weight of the driver being lighter, moment of inertia, coefficient of restitution, angle of release, impulse-momentum relationship and the conservation of momentum.
The results would show, if a driver were to be used, that the horizontal displacement would increase compared to the nine iron, the 9-iron would have a greater horizontal displacement, the trajectory of the ball would greatly differ and the acceleration of the ball would increase due to the many biomedical principles later discussed. The yellow line represents a nine iron, while the blue line is the driver. Question 3) Part 1: Accounting for Results The results showed that generally the golf ball had a much greater horizontal displacement compared to the practice ball and air ball.
Although the practice ball had a less horizontal displacement compared to the golf ball, the horizontal displacement of the practice ball was far greater than the air ball. Linear momentum is the product of mass and velocity. The mass of the golf all was greater than the practice ball and the practice ball’s mass was greater than the air ball. The velocity of the golf ball was much greater than the other two balls due to the distance covered by the ball divided by the time, which is shown in the equation v=s/t.
Due to the velocity and mass being greater in the golf ball compared to the other two balls, the linear momentum of the golf ball was far greater than the practice ball and air ball. Air resistance and drag had a major influence in the results obtained in question 1. In fluid dynamics, drag (sometimes called air resistance or fluid resistance) refers o forces which act on a solid object in the direction of the relative fluid flow velocity (Wisped). Drag on the air ball would have affected it the most out of all balls, due to its hollow structure and big air holes around the ball.
Drag forces always decrease fluid velocity relative to the solid object in the fluid’s path. As the fluid was continuously going through and acting against the air ball, this caused the ball to decrease in velocity only after a few seconds of being hit. The drag forces placed upon the practice ball were significantly reduced due to the practice ball containing no air holes. The structure of the practice ball was still hollow inside, which caused the ball to still be affected by drag. Lastly the golf ball obtained the least amount of drag due to the solid structure of the ball.
Overall drag was a key factor in influencing the distances covered by each respective ball. The coefficient of restitution is a value representing the ratio of the velocity after an impact compared with the velocity before the impact. Basically the CORE measures the bounciness of an object. A perfect elastic collision is when no energy is lost during the collision and there’s full inspiration of linear momentum, CORE = 1. An imperfectly elastic collision is where energy is lost during collision and conservation of linear momentum doesn’t occur, CORE < 1.
The three factors influencing the coefficient of restitution are the materials of the interacting bodies, the velocity of the collision and the temperature of the materials involved. The temperature of the materials involved does not affect this experiment. If all three balls were to be dropped at the same height onto the concrete ground, the golf ball would be much more bouncy compared to the practice ball and air ball. The practice all would then be the second most bouncy, followed by the air ball.
This is due to the materials of the interacting bodies, as the golf ball has materials that enable it to have a coefficient of restitution closer to one. By the golf ball having a coefficient of close to one, the ball is able to produce a greater horizontal displacement compared to the other two balls. Newton’s 2nd Law (F=m. A) relates to the behavior of objects when all forces are unbalanced, resulting in the development of acceleration. To increase acceleration, force must be applied, assuming the mass is held constant. In this experiment the mass of the balls ray from the air ball being the lightest to the golf ball being the heaviest.
Due to the force applied on each ball by the golf club remained the same, the initial acceleration on the air ball was greater than the golf ball. This initial acceleration being greater only lasted less than a second, due to external factors such as drag. This is also due to the air ball having a very low inertia compared to the heavier golf ball The Law of Conservation of Linear Momentum states that when two bodies collide, the momentum into the collision remains the same as the momentum after the collision and therefore momentum is covered (baby codebook).
During a golf swing, the total system momentum is not conserved and some energy is ‘lost’ to the collision. This is caused by the club striking the ball where energy is lost through sound, heat and friction. The difference between each ball is that the air ball loses the most energy as the momentum of the ball doesn’t equal the momentum of the club during the swing. This is caused by the structure of the ball and also external forces such as drag affecting the ball through the air. With the practice ball some momentum is lost through the striking of the ball as the ball changes shape when hit due to the materials of the all.
In comparison when the club is swung and hits the golf ball less momentum is lost as the momentum of the ball stays relatively similar to the club, but some is lost through external factors like drag. Although the golf ball has the smallest instantaneous velocity once hit, the external effects like drag affect the practice and air ball significantly more than the golf ball. The momentum lost during the golf ball is significantly less than the momentum lost with the practice and all balls.
The Magnums effect explains the change in flight path of a projectile and particularly relates to a ball that is spinning. It is the curving effect of spin on the flight off ball. As the ball spins it pulls around with it a boundary layer of air. The differences in pressure between the particles in the boundary layer above- and-below or side-to-side, depending on the direction of spin of the ball. In this experiment the pressure was above and below (back spin) the boundary layer which enabled the balls to have a horizontal displacement.
The Magnums effect affected the air ball least, due to the structure of the air ball containing holes around the structure and having a hollow mid section. Bernoulli principle states that an increase in the speed of fluid occurs simultaneously with a decrease in pressure. Bernoulli principle was the most effective with the golf ball due to its solid structure and dimples around the circumference of the ball. Bernoulli principle was least effective With the air ball as it is a hollow structure; therefore air resistance was able to move through the ball.
Bernoulli principle applied to the practice ball to a certain extent due to the non hollow circumference but was not as effective due to its hollow mid section. Part 2: Accounting for Predictions The predictions stated in question 2 were that a driver would cause each ball to have greater horizontal displacement and acceleration compared to a nine iron due to many biomedical principles. Moment of inertia is equal to the sum of the mass multiplied by the distance from mass concentration to the axis of rotation, shown in the equation l=imams x ray.
The critical factor in being able to swing the golf club is the distribution of the objects mass about the point that is used to rotate the object. The difference of the distance from mass concentration to the axis of rotation is showed in the following diagrams: Driver 9_iron From the diagram above, it is clearly shown that the 9-irons point where mass is equally distributed (r) is far greater than the iron. This causes the 9-iron to have a greater moment of inertia and therefore more force is required to swing the club.
This assumption suits what each clubs purpose is, as the driver is looking for maximum distance whilst the 9-iron for accuracy. The purpose of the driver having a lower moment of inertia is that the club can be swung with greater velocity, acceleration and hence more momentum is being placed onto the golf ball. Question two states that the angular acceleration of the movements of the layer’s body will be the same for all shots. With this said, the driver has a longer shaft and must hit the ball at the same time as the 9-iron due to the angular acceleration remaining constant.
For this to be able to occur, the diver must contain greater club head velocity due to the driver covering a greater distance through the swing because of the length of the club being greater. Again this supports the prediction that the balls will be hit a greater horizontal displacement with a driver as the club has greater velocity when impacting with the ball compared to the 9-iron. Newton’s 2nd law relates to the behavior of all objects when all forces are unbalanced, resulting in the development of acceleration and can be represented by the equation F=m. Acceleration is equal the the final velocity take away the initial velocity divided by time, which is represented by a=v-u/t Due to the club head of the driver having greater velocity, as stated above, the force of the driver onto the ball must be greater than the force of the 9-iron onto the ball. F=m. A can be changed into F=m(vi-vi)/t which shows acceleration is made up of the final velocity take away the initial divided by time. This then can be arranged to show Ft=m(vi-vi) which is basically impulse is equal to force multiplied by time.
The greater the acceleration, the grater the force, the greater the impulse which leads on to the greater the change in momentum. Again this biomedical principle reiterates the velocity approach obtained by the driver and the accuracy approach needed for the 9-iron. The coefficient of restitution is a key factor in influencing the hypothesis stated in question 2. The CORE on the club face of the driver is closer to 1 compared to the 9-iron. Drivers are now days made out of the lightweight material titanium which has a CORE of around 0. . 9-irons are made out of iron, a material that has a much less CORE. Again this supports the driver pursuing the maximum velocity approach while the iron is after a more accurate approach. With a higher CORE, the ball is able to spring off the club face without as much energy being lost from the collision, hence a higher chance of a greater distance being covered. The lower CORE suits the iron as the ball will not spring off the club as much as the driver which enables the club to contain a more accuracy approach.
Angle of release refers to the angle at which a projectile leaves the round to gain maximum horizontal displacement. When the height of release and landing are the same, assuming no external factors such as air resistance act on the projectile, the theoretical optimal angle of release is 45 degrees. The difference between the driver and 9-iron is that the iron has a much greater angle of release, which is paramount for an accuracy approach. The greater the angle of release, the higher the vertical displacement and the less horizontal displacement would occur.
The 9-iron has a similar angle of release to that of a pitching wedge, which needs an angle of release greater than 45 degrees to be blew to project the ball out the bunker and onto the green or fairway. Question 4) The biggest gains in distance with today’s drivers most relates to club lengths which are 1 1/2″ to 2″ longer, head weights that are lighter because of graphite shafts which are much lighter than steel and a total club weight which is also lighter. This means that longer, lighter drivers can be swung faster. (http://www. Relatable. Mom/263) Shaft Length: Longer shafted drivers have the potential for greater distance via fast club head speed with the same angular acceleration off given individual due to increased shaft length. With the increased velocity of the club, the chances of a greater horizontal displacement are significantly enhanced. A driver with a longer shaft produces a greater impulse on the ball as the driver has the cover more distance when swung hence travel fast therefore greater impulse therefore greater change in momentum therefore greater horizontal displacement.
To use the effect of the longer shaft even more, a greater range of motion (flexibility) about the shoulder and hips, will help gain a greater horizontal displacement which is essential for a driver. As mentioned before the head of the drivers are lighter due to the titanium the ewer larger driver heads have higher moments of inertia and as a result have bigger sweet spots, which allows greater distance to be achieved even if the impact is not in the middle of the face. Head: Modern drivers employ similar concepts to optimize the club-head design by using lightweight titanium alloys – one of the lightest metals used for golf club making.
These materials allow designers to become more creative with, and creating bigger and more forgiving club-heads. Such design concepts, together with the advanced shaft technology, have enabled designers to take advantage of benefits from longer shaft length, egger sweet-area, lower and deeper centre of gravity (CGI), draw biased CGI and gravity angle as well as better gear effect. One of the most significant changes in golf equipment material may be the use of titanium. Pure titanium (It) is rather soft, as is iron, and not strong enough for golf club applications except for face inserts.
There are basically two types of titanium alloys used for golf clubs. 6-4 titanium which includes 6% of aluminum (AAA), and 4% of vanadium (Va) are used exclusively for cast clubs, while beta titanium (15% Va, 3% Car, 3% AAA, 3% In) are useful for forging. Some models utilize heavy tungsten inserts with titanium. Lightweight materials and thin metal wall forming technology allow designers to distribute more weight to the perimeter, which in turn creates a larger sweet area and provides more forgiveness on off-centre hits.
Keep in mind that larger sweet spots do not necessarily correlate to larger C. O. R. (spring face) impact areas. Once again, it is a very small impact area that achieves maximum spring face effect. The larger sweet spot on its own merits means that you will achieve greater distance and a much better solidness of feel on off-centre hits s. A smaller sweet spot. The purpose of using titanium drivers is to make the most of the biomedical principles that can be used in golf. Titanium alloys is a very light metal, much lighter than drivers made in the past with materials such as wood.
This allows the club to have a lower moment of inertia, which then enables the club to the swung with a greater acceleration, hence a greater velocity which places a greater impulse on the ball which therefore gives the ball a greater horizontal displacement, which is the ultimate purpose of a driver. Relate to biomedical principles in more detail Golf Balls: Golf, as we know it, was first played with a leather-covered ball stuffed with goose or chicken feathers. Several pieces of stout leather were tightly stitched, leaving a small opening.