Lecture Week 5 Motion in Sport, Projectiles, Friction, COR

1. Lecture Week 5 Motion in Sport, Projectiles, Friction, COR

2. Motion Linear Motion . (Translatory motion) The sprinter runs from A to B. Curvilinear Motion • Most jumps are along a curved line.

3. Projectile Motion • The thrown object is called the projectile. Its path is called the trajectory. We will not consider air resistance. Without air resistance, the projectile will follow a parabolic trajectory. • This is a two dimensional problem. Therefore, we will consider x and y directed displacements, velocities, and accelerations.

4. There are many examples of projectile motion is sport. • Golf ball • Basketballs • Javelin • Ski jumping • Diving • Trampoline • Archery • Soccer • Football • Cricket

5. The following factors influence the projectiles trajectory • Angle of release • Speed of release • Height of release • Gravity • Spin • Air resistance See java demo

7. Throughout the path of the projectile, change occurs only in the vertical direction due to the influence of gravity, while the horizontal component of the velocity will not change. (This is not quite true, there will be a very small slowdown in the horizontal direction due to air resistance).

8. Original or initial conditions The original conditions are the size of the velocity and the angle above the horizontal with which the projectile is thrown. Velocity = 40 m/s 35 degrees Velocity = 40 m/s Angle = 35 degrees

9. Calculate the components of the original velocity Horizontal component Vertical component V (vert) V (horiz)

10. What are the horizontal and vertical components of acceleration a (horiz) = 0 There is no force acting in the horizontal direction once the projectile has been launched. a (vert) = g or 9.8 m/s2 Gravity is a force acting on the projectile. The projectile will accelerate under the influence of gravity, so its vertical (x) acceleration will be downward, or negative, and will be equal in size to the acceleration due to gravity on Earth. There will be no acceleration in the horizontal (x) direction since the force of gravity does not act along this axis.

11. A: What is the time to the top of the trajectory At the top of the trajectory the y, or upward, velocity of the projectile will be 0 m/s. The object is still moving at this moment, but its velocity is purely horizontal. At the top it is not moving up or down, only across. velocity (final) = velocity (initial) + at In the vertical direction. velocity(final) = 0 velocity(initial) = 22.9 a = -9.8 t = ? velocity (final) = velocity (initial) + at

12. B: How high does the projectile rise. Here you need to find the displacement (D) in the y direction at the time when the projectile is at the top of its flight. D = vt + ½ a t2 V = 22.9 m/s T = 2.33 sec A = -9.8 m/s2 D = vt + ½ a t2

13. C: How far away does the projectile land from its starting point D = vt + ½ a t2 This time we are working in the horizontal direction V = 32.8 m/s a = 0 m/s2 t = 2.33 sec (X 2 for total journey) D = vt + ½ a t2

14. Friction

15. Friction In field hockey, a sport which is played on grass, moving the ball from one side of the field is much harder than moving an ice hockey puck across an ice rink due to a force called friction There is more friction on a coarse, grassy surface than on the slick surface of an ice rink due to the amount of resistance. Field hockey player, therefore, must hit the ball with a great amount of force to send it across the field, whereas ice hockey players can easily send a puck gliding across the rink.

16. Newton's first law states that an object in motion will remain in motion unless acted on by an outside force; an object at rest will remain at rest unless acted on by an outside force.What does bowling have to do with Newton's 1st law? • If you have ever bowled, you know that after rolling the ball it continues to move across the alley until it comes into contact with the pins. After being put into motion, the bowling ball will remain in motion until friction eventually slows it down.If the bowling alley never ended would the ball keep rolling forever? • No! As a result of friction (an outside force) the ball will eventually stop.

17. Drag Force • Drag force is a resistance force - • Sportsmen reduce drag by using specialised techniques, equipment or clothing. • Streamlining reduces form drag.

18. Lift Force Direction of fluid flow Lift force

19. COR Coefficient of Restitution To find the coefficient of restitution in the case of a falling object bouncing off the floor, or off a racquet on the floor, use the following formula: c = coefficient of restitution (dimensionless) h = bounce height H = drop height

20. The coefficient of restitution merely tells you how much of the original kinetic energy remains after a collision . It can also be calculated this way using kinetic energy if we know the velocities before and after collision. M = mass V = velocity V = 4 m/s M = 0.3 kg KE = _____________ V = 5 m/s M = 0.3 kg KE = _____________

21. The coefficient of restitution merely tells you how much of the original kinetic energy remains after a collision of the clubhead with the golf ball. The higher the coefficient of restitution, the faster the ball will be propelled by the clubhead for a given impact speed. So why all the fuss over this figure? It's because the USGA is trying its best to limit the influence of technology in golf. The USGA has adopted limits of 0.830 on the coefficient of restitution a given clubface may have as part of its effort to define the boundaries of technology in the game.