Week 3 - Linear Kinetics

Question 1

Who is Sir Isaac Newton? (6 points)

Answer 1

• 1642-1727
• English mathematician
• Student and later professor at Cambridge university
• Proposed fundamental laws that are the basis of modern mechanics, including:
  
  • 3 Laws of Motion
  • Law of Gravitation

Question 2

What is Newton’s 1st Law? (5 points)

Answer 2

• Also called the law of inertia
• Every body at rest or moving with constant velocity in a straight line will continue in that state unless compelled to change by an external force exerted on it
• For example, a soccer player kicks a ball, which was initially at rest.
• A passenger on a bus will travel at the same speed as the bus. If the bus suddenly reduces speed and passenger is not restrained, the passenger will continue to travel at the speed that they possessed before the bus braked and therefore be thrown forward
• Basis for the principle of conservation of momentum (if only objects whose mass is constant are considered)

Question 3

What is conservation of momentum? (3 points)

Answer 3

• The conservation of momentum states that,within some problem domain, the amount of momentum remains constant
• Momentum is neither created nor destroyed, but only changed through the action of forces as described by Newton’s laws of motion.
• In the absence of external forces, the total momentum of a given system is constant

Question 4

Describe Inertia (2 points)

Answer 4

• The reluctance of a body to change its state of rest or motion
• E.g. A striker kicking a free kick in soccer or a goalie stopping the ball from going into the goal. The soccer ball in both scenarios has a certain amount of inertia

Question 5

Describe Mass (3 points)

Answer 5

• The quantity of matter in a body (kg)
• A measure of inertia
• A body with a greater mass has a greater inertia and would be more difficult to move

Question 6

Describe linear momentum (7 points)

Answer 6

• Product of an object’s mass and linear velocity
• A way to quantify motion and inertia in one measure
• Vector
• A static object with zero velocity will have no momentum
• A change in the body’s momentum can be caused by a change in either mass or velocity. However, in most human movement situations, a change in momentum is caused by a change in velocity.
• The faster an object moves, the more momentum
• The larger a moving object’s mass, the more momentum

Question 7

What is the equation to describe the conservation of momentum? (7 points)

Answer 7

Total momentum before a collision = total momentum after a collision

maVia + mbVib = maVfa + mbvfb

m = mass
Vi = velocity before the impact
Vf = velocity after the impact
a = body 1
b = body 2

Question 8

Describe collision (4 points)

Answer 8

• An event in which two or more bodies exert relatively large forces on each other in a relatively short time
• During collision, bodies deform and reform
• The behaviour of two objects following a collision depends on their collective momentum and the nature of the impact
• A transfer of momentum and kinetic energy occurs

Question 9

Describe elastic collision (6 points)

Answer 9

• Objects collide and separate, but maintain original shape
• Momentum conserved
• Examples:
  
  • Kicking a soccer ball
  • Hitting a baseball with a bat
  • Pool and snooker

Question 10

Describe inelastic collision (2 points)

Answer 10

• Momentum is still conserved
• but rather than bouncing off each other, objects stay together and move together with the same velocity

Question 11

Describe perfectly inelastic collision (3 points)

Answer 11

• Often referred to as a plastic collision
• One of objects deforms and does not regain its original shape,
• Bodies do not separate afterward

Question 12

Describe coefficient of restitution (4 points)

Answer 12

• In sports, most collisions are neither perfectly elastic nor perfectly inelastic, but somewhere between the two
• Elasticity is the property of a body to return to its original shape after deformation
• The degree to which it can reform is described as its coefficient of elasticity or coefficient of restitution
• It has no units as it is a ratio (ranges between 0 and 1). The closer to 1, the more elastic. The closer to 0, the more plastic

Question 13

What is the equation for coefficient of restitution? (7 points)

Answer 13

e = Velocity of separation/Velocity of impact
= V1 - V2 / U1 - U2

• e = Coefficient of restitution (influenced by the nature of both bodies)
• V1= Velocity of body 1 after impact e.g. ball
• V2= Velocity of body 2 after impact e.g. floor
• U1= Velocity of body 1 before impact
• U2= Velocity of body 2 before impact

Question 14

What is the alternative formula for coefficient of restitution? When should it be used? (4 points)

Answer 14

e = √ hb / hd

• hb = height of bounce
• hd = height of drop
• If a ball is dropped from a specific height onto a fixed impact surface then height of drop and height of rebound is sufficient to calculate e

Question 15

What factors influence coefficient of restitution? (2 points)

Answer 15

• Elasticity is affected by material and temperature
• Reformation/rebound behaviour is affected by the nature of contacting surfaces and velocity of impact

Question 15

Describe oblique impacts (10 points)

Answer 15

• Collisions which takes placewhen one of the two bodies has a velocity at an angle with the line of collision
• After rebound, always some loss of velocity:
  
  • Vv due to e
  • Vh due to ground reaction forces and limiting friction
• Two angles created during this impact
  
  • Angle of incidence: the angle before the collision
  • Angle of reflection: the angle after the collision
• If loss of Vv & loss of Vh equal, Angle of Incidence = Angle of Reflection
• Angle of Reflection is greater than Angle of Incidence, ball bounces lower. Will have small coefficient of restitution and low amount of friction
• Angle of Reflection is less than Angle of Incidence, ball bounces higher. Will have high coefficient of restitution and high amount of friction

Question 16

What is Newton’s 2nd Law? (7 points)

Answer 16

• Also known as law of acceleration
• The acceleration of a body is proportional to the force causing it and takes place in the direction in which the force acts
• F = ma
• Expresses a cause-and-effect relationship
• Forces cause acceleration and acceleration is the effect of forces
• Any time an object starts, stops, speeds up, slows down, or changes direction it is accelerating
• A net external force is acting to cause the acceleration

Question 17

Define net force

Answer 17

a force not counteracted by another force

Question 18

Describe impulse (4 points)

Answer 18

• Force x time = change in momentum
• Impulse = F x t (Ns)
• Impulse = change in momentum
• The greater the Impulse, the greater the change in the object’s velocity (acceleration)

Question 19

How can impulse be used to increase momentum? (13 points)

Answer 19

• Maximising the impulses is the primary objective of many sports
• Accomplish this by exerting a large force against object for as long a time as possible.
• In many sports skills – aim is to cause a large change in velocity. For example, initial velocity is zero, final velocity is fast, so we increase its momentum
• Throwing events:
  
  • The object has no velocity at the beginning of the throw and the athlete aims to give it velocity at the end.
  • This is accomplished by the athlete exerting a large force for as long as possible
  • The length of time applied onto the force is typical dependent on the technique of the athlete
  • Sprinters
• Striking events:
  
  • Typically has no velocity at the beginning and athlete is required to provide a fast velocity just before impact
• Sprinters
  
  • Elite sprinters have an initial velocity of zero, but develop greater impulse against the starting blocks compared to well-trainer, but sub-elite sprinters
  • This allows the elite sprinter to have a greater final velocity
• Because there is a limit on the amount of force that humans can produce and apply, athletes must focus on maximizing the time the force is applied over to further increase the impulse

Question 20

What is a practical application of increasing impulse to increase post-impact velocity of an object, such as a tennis ball? (9 points)

Answer 20

• Increase ball velocity at impact or velocity of the striking apparatus (tennis racquet)
• Increase mass of ball or racquet
  
  • More force will be required to get ball to move at same velocity as with a lighter racquet
  • Want high momentum
  • Use racquet with more mass will require more strength from user
• Increase elasticity of the impact
  
  • Larger “sweet spot”
  • Equipment design. Example- string tension of tennis racquet
  • Technique. Example - firm grip on racket

Question 21

How can impulse be used to decrease momentum? (10 points)

Answer 21

• In other activities, fast initial velocity, we want to decrease this to slow or stop.
• Using impulse to decrease momentum is accomplished by increasing the impact time.
• Landing from a jump
  
  • Bending knees to cushion landing. Allows jumper to decrease momentum
  • If landing with straight knees, impact time is smaller and average impact force is greater.
  • Change in momentum would still be the same, but the impact force could be large enough to cause injury
• Catching an object, such as ball
  
  • “Give with the hands” to increase amount of impact time
• Landing on mats in high jump
  
  • Mat deforms over time, therefore slowing the jumper down over a longer time period

Question 22

Define ground reaction force (GRF)

Answer 22

the force exerted by the ground on a body in contact with it

Question 23

Describe the measurement of GRF (8 points)

Answer 23

• In a lab, measured with a force platform
• GRF can be separated into three force components:
  
  • Fz = vertical
  • Fy = antero-posterior (forward-backward)
  • Fx = medio-lateral (side to side)
• When traveling in straight line, the Fx will be relatively small
• When running at a constant velocity, there will be a relatively even Fy.
• Force platform can be used to measure impulse

Question 24

What is Newton’s 3rd Law? (10 points)

Answer 24

• Also known as law of reaction
• For every force that is exerted by one body on another, there is an equal & opposite force exerted by the 2nd body on the 1st.
• Simply, for every action (force), there is an equal & opposite reaction (force)
• Helps explain how forces act and what they act on
• Explains that forces come in pairs, and that each force in a pair acts on a separate object.
• For example:
  
  • When a soccer play kicks the ball, there is a period of time where the ball and the players foot are in contact. During contact, the player exerts a force onto the ball and simultaneously experiences a force exerted by the ball onto their foot.
  • The greater the force applied onto the ball, the greater the force exerted by the ball onto the foot
  • These forces will always be equal in magnitude and opposite in direction
• Does not explain what the effects of forces will be. However, Newton’s 2nd law explains the effects of a force onto a body.