Linear Kinetics Objectives

• Identify Newton’s laws of motion and gravitation and describe practical illustrations of the laws

• Explain what factors affect friction and discuss the role of friction in daily activities and sports

• Define impulse and momentum and explain the relationship between them

• Explain what factors govern the outcome of a collision between two bodies

• Discuss the interrelationship among mechanical work, power, and energy

• Solve quantitative problems related to kinetic concepts

Linear Kinetics Outline - The Relationship between force and motion

• Read Chapter 12 in text• Classification of forces• Types of forces encountered by humans• Force and motion relationships – three ways to look at it:

– Instantaneous effect – Newton’s law of acceleration (F=ma)– Force applied through time (Impulse-momentum)(Ft = mv)

• Conservation of Momentum

– Force applied through distance (work-energy) (Fd = 1/2mv2)• Conservation of Energy

• Self-study problems– Sample problems: #2 p 392; #3 p 396, #4 p 397, #5 p 402, #6 p 405, #7 p 408– Introductory problems, p 411: 1,3,5,7,8,10

• Homework problems (Due Monday, November 14)– Additional problems, p 412: 6,8,9

Effect of forces on the system (can be total human body, or a part of the body)

• Action vs reaction

• Internal vs external

• Motive vs resistive

• Force resolution – horizontal and vertical components

• Simultaneous application of forces – determining the net force through vector summation

External forces commonly encountered by humans

• Gravitational force (weight = mg)

• Ground Reaction Force (GRF)(Figure 12-4, p 386)– Vertical– Horizontal (frictional)

• Frictional force (coefficient of friction) (pp 389-395)

• Elastic force (coefficient of restitution) (pp 399-402)

• Free body diagram - force graph (p 63)

Force Plates – Measurement of ground

reaction forces

Coefficient of friction, resistance to sliding:

Cfr = Frf /Nof

Sample Prob# 2, p 392

Coefficient of Restitution (COR)• COR is a measure of the liveliness of an object

• When 2 objects collide:

• When one object is stationary,

this reduces to:

• An alternative way to measure COR

is to drop a ball and measure the ht

bounced compared to ht dropped:

Coefficient of Restitution (COR)• COR of balls dropped or thrown at a rigid wooden

surface is shown here.

• COR increases

directly with

temperature and

inversely with

impact velocity.

Coefficient of Restitution (liveliness or bounciness)

Free body diagrams:

Instantaneous Effect of Force on an Object

• Remember the concept of net force?• Need to combine, or add forces, to

determine net force • Newton’s third law of motion (F = ma)• Inverse dynamics – estimating net forces

from the acceleration of an object• Illustrations from Kreighbaum: Figures F.4,

F.5, and F.6 (pp 283-284)

Force Applied Through a Time: Impulse-Momentum Relationship (pp 295-399)

• Force applied through a time • Impulse - the area under the force-time curve• Momentum - total amount of movement (mass x velocity)• An impulse applied to an object will cause a change in its

momentum (Ft = mv)• Conservation of momentum (collisions, or impacts)

– in a closed system, momentum will not change

– what is a closed system?

Impulse: areaunder force-time curve

Net impulse (Ft) produces a change in momentum (mV)

Sample problem #4, p 397

Vertical impulse While Running: Area underForce-timecurve

Anterioposterior(frictional) component of GRF: impulseIs area under Force-time curvePositive andNegative impulseAre equal ifHorizontal compOf velocity isconstant

Conservation of momentum: when net impulse is zero (i.e. the system is closed), momentum does not change

Sample prob#3, p 396

Force Applied Through a Distance: Work, Power, Energy (pp 403-409)

• Work - force X distance (Newton-meters, or Joules)– On a bicycle: Work = F (2r X N)– On a treadmill: Work = Weightd X per cent grade– Running up stairs: Work = Weightd

• Power - work rate, or combination of strength and speed (Newton-meters/second, or watts)– On a treadmill: P = Weightd X per cent grade/ time– On a bicycle: P = F (2r X N) / time– Running up stairs: P = Weightd /time (See next slide)

• Energy - capacity to do work– kinetic, the energy by virtue of movement (KE = 1/2 mv2 ) – gravitational potential, energy of position (PE = weight x height)– elastic potential, or strain, energy of condition (PE = Fd)

Power running up stairs: Work rate = (weight X vertical dist) ÷ time

Sample prob#6, p 405

Work while running on treadmill:

Note that %grade = tan θ X 100,and tan θ and sin θ are very similar below 20% grade

From McArdle and Katch. Exercise Physiology

Calculating Power on a Treadmill

• Problem: What is workload (power) of a 100 kg man running on a treadmill at 10% grade at 4 m/s?

• Solution:– Power = force x velocity– Force is simply body weight, or 100 x 9.8 = 980 N– Velocity is vertical velocity, or rate of climbing

• Rate of climbing = treadmill speed x percent grade = 4 m/s x .1 = .4 m/s

– Workload, workrate, or power = 980N X .4 m/s = 392 Watts• Note: 4 m/s = 9 mph, or a 6 min, 40 sec mile

• Calculate your workload if you are running on a treadmill set at 5% grade and 5 m/s.– Answer for 200 lb wt (91 kg) is: 223 Watts

Conservation of Energy• In some situations, total amount of mechanical energy

(potential + kinetic) does not change– Stored elastic energy converted to kinetic energy

• diving board• bow (archery)• bending of pole in pole vault• landing on an elastic object (trampoline)

– Gravitational potential energy converted to kinetic energy• Falling objects

• Videodisk on pole vault

Energy conservation – Case I : elastic potential (strain) and kinetic

Potential energy (FD) + Kinetic energy (1/2mv2) remains constant

Energy conservation – Case II : gravitational potential and kinetic

Potential energy(Wh) + kineticenergy (1/2mv2) remains constant

Conservation of energy: gravitational potential and kinetic

Sample problem #7, p 408

Falling objects and work-energy relationship

• Problem:– If a 2 kg object is dropped from a height of 1.5 meters, what will

be its velocity and kinetic energy when it hits the ground?

• Solution:– Kinetic energy at impact (mgh) equals the potential energy at drop height (½ mv2)

• Potential energy at drop(mgh)= 29.43 Nm

• Kinetic energy at impact = 29.43 Nm; v = 5.42 m/s

5

Three ways to minimize impact force of 2 colliding objects

• Force-time, or impulse-momentum relationship (Ft = mv)– Increase time through which force is applied

• Force-distance, or work-energy relationship (FD = ½ mv2)– Increase distance through which force is applied

• Force-area, or pressure concept (P = F/a)– Increase area over which force is applied

Linear Kinetics Formulae