Wee 6 Impulse, Momentum And Average Force

Question 1

Newton’s Laws of Motion

Answer 1

1st Law – Law of Inertia
A body which is at rest or in a state of uniform motion will remain at rest or in motion at the
same speed in a straight line unless acted upon by a resultant force

2nd Law – Law of Acceleration
A body accelerates in the direction of the net force acting upon it with the magnitude
proportional to the force:

F=ma. (N) = kg m / s2

3rd Law – Law of Reaction
To every action there is an equal and opposite reaction

Question 2

Example: Centre of mass trajectories in walking and running

Answer 2

Walking
For each stride the trajectory of the centre of mass is approximately an arc of constant radius. The elevation increases from initial contact to mid-stance, and decreases from mid-stance to toe-off. At mid- stance the elevation is at maximum and vertical ground reaction force is at minimum.

Running

In the aerial phase the trajectory is parabolic. In the contact phase the elevation decreases from initial contact to mid-stance, and increases from mid -stance to toe-off. At mid-stance the elevation is at minimum and vertical ground reaction force at maximum.

Question 3

Ground reaction force: push-off in jumping disciplines

Answer 3

Vertical force:
Positive, much higher than in running (>10 mg), but of
short duration
Phase I: impact in which the initial downward movement is quickly reversed
Phases II and III: lift-off, in which the vertical
component of velocity is increased

Horizontal force:
Mostly negative. The run-up horizontal speed (10 m/s) is
decreased by 1-3 m/s
Phases I-II: braking in which the horizontal component is decreased
Phase III: push-off in which the horizontal
component of speed is slightly increased

Need to physical be bale to tolerate vertical GRF otherwise you buckle and lose it

Longer contact with floor = more time to produce floor
Need to minimise breaking impulse so not wasting effort from run up
Need a ratio for long jump

Question 4

Inertia

Answer 4

A Stationary object - exhibits a certain reluctance to move.

^ mass of an object ^ effort needed to move it.

The reluctance of an object to move is called its inertia and
the mass of the object is a measure of its inertia.

Unit =kg

Question 5

Momentum

Answer 5

A Moving object - exhibits a reluctance to change the way it is moving. In this case, the inertia of the object depends not only on its mass, but also on its linear velocity.

The product of this is referred to as the (linear)
momentum of the object

Momentum = mv (kg m/s)

Question 6

Law of Conservation of Momentum

Answer 6

“In the absence of external forces, the total momentum of a system remains constant”

Total momentum before impact = Total momentum after impact

If an object collides with the earth it may stop or rebound, depending on the elasticity of the collision.
If the object comes to a stop or deforms an external force MUST act to decelerate the object
Therefore when landing from a jump or a stride a force must be applied to change our momentum

Changes in momentum depend not only on the magnitude of the acting external forces but also on
the length of time over which each force acts.

Question 7

Impulse

Answer 7

Impulse of force is the effect of that force in a period of time. Impulse is the integral of force over that period of time with the unit of (Ns)

                I = Ft

Since F = ma
F = m (v2 – v1)
/ t
Ft = m x v2 - m x v1

So Impulse = change in momentum

Force x time = impulse

Hard landing = less contact with floor, less likely to slow down and maintain higher velocity snd have the same impulse
= more injury risk

The amount of impulse generated manipulates how much momentum is generated

Question 8

Average Force

Answer 8

Using Impulse to decrease momentum – e.g. Landing, Catching

Using Impulse to increase momentum – e.g. Throwing, Jumping

Often there is a trade off between maximising force and maximising time of application

Impulse and momentum can be used to determine the average force that can accelerate a body

We can calculate the average force for a time period of interest as the impulse divided by that time period (Dt =t2-t1)

F average = I/ change t

Question 9

Impulse-momentum theorem
.

Answer 9

It follows directly from Newton’s second law that change in momentum of an object over a certain period of time is equal to the net impulse of all forces acting on that object over that period of time. If at time t1 the velocity is v1, at time t2 the velocity is v2, and I is the net impulse acting over the period change t=t2-t1, then:

Mv2- mv1= I

This also means that the average net force acting over the period t2-t1 can be calculated as:

F average = mv2-mv1 / change t

Question 10

Average ground reaction force

Answer 10

When ground reaction force and gravity are the only forces acting on the body, the components of the average ground reaction force over a time period change in t=t2-t1can be calculated from the impulse-momentum theorem using the following formulae:
FGRX= MV2X- MV1X / CHANGE IN T

FGRY= MV2Y- MV1Y / CHANGE IN T

FGRZ= MV2Z - MV1Z / CHANGE IN T + mg

Question 11

Key points

Answer 11

Momentum is the product of mass and velocity, and is conserved in the absence of external forces

Impulse of a force (Ft) is equal to the change in momentum

Average net force can be calculated from the change in momentum