Forces & Motion

Overview(ref. p120 Holt)

Mechanics Progression

To this point the focus has been

• kinematics – the characteristics of motion Now, the focus will become

• dynamics – the causes of motion

Forces

Cause change in state of motion

Units

• Newtons (N)• Ex. 25 N @ 45 degrees to horizontal

• (Pounds in English system)

4 Different Forces

Applied Force (Fa)

• Force of push or pull Force due to gravity (Fg or W)

• Gravitational force or weight of a body • Weight = mass * acceleration = mg

Normal (or Reactive) Force (Fn)

• Force applied by a surface perpendicular to the plane of the surface

Frictional Force (Ff)

• Force opposing the direction of the applied force on a body resting on a rough surface, and resulting from the interaction of the body and the surface.

Free Body Diagrams (FBD)

Diagrams showing all forces acting on

an object.

Fa

Fg or W

Ff

Fn

Net Force

Definition• The resultant force acting on a body after all the

interacting forces are accounted for vectorally,

State of Equilibrium (Balanced forces)• All the forces acting on a body cancel out,

resulting in a net force of ZERO!

IF • the net force on an object is non-zero

THEN • a change in the state of motion occurs

FORCE is a VECTOR!

Net Force Examples

Net Forces of Flight

If Lift > Gravity, then the plane …..

If Thrust < Drag, then the plane …..

Newton’s Laws - First

First Law

• “A body will continue in its state of rest or steady motion in a straight line, unless acted upon by an external force.”• Known as the “law of inertia”• Inertia implies “resistance to

change”

• The larger the mass, the greater the inertia.

• Locomotive vs Honda

Newton’s Laws - Second

Second Law

• The applied force required to change the state of an object is proportional to the mass of the object, and

• The applied force is also proportional to the resulting acceleration of the object, or

• Forcenet = mass * acceleration, known simply as• Fnet= ma• Net force acting on a body of mass m causes an acceleration

of a.• If the net force is ZERO, there is NO acceleration!

Weight vs Mass

• w = mass * gravitational acceleration• w = mg

Newton’s Laws - Third

Third Law

• “To every action there is an equal and opposite reaction”

• Known as action/reaction force pairs

Forces in Action

Practice

What is the weight of a 60 kg (mass)

person on Earth?

Solve: m= 60 kg, g = 9.8 m/s2, Find W?

• Weight (Fg↓) = m * g = 60 * 9.8 = 588 N

On the moon where g = 1.6 m/s2?

• Weight (Fg↓) = m * g = 60 * 1.6 = 96 N

http://www.google.com/imgres?imgurl=http://www.clipproject.info/Cliparts_Free/Menschen_Free/Clipart-Cartoon-Design-10.gif&imgrefurl=http://vip2vip.co.tv/img/cartoon-people-clip-art&usg=__-Z4ChJCTIJoOeBOpAzuoScpCnxg=&h=350&w=350&sz=21&hl=en&start=79&zoom=1&um=1&itbs=1&tbnid=6MIFW-0lKf0oQM:&tbnh=120&tbnw=120&prev=/images%3Fq%3Dcartoon%2Bperson%26start%3D60%26um%3D1%26hl%3Den%26safe%3Dactive%26sa%3DN%26rls%3Dcom.microsoft:en-us%26ndsp%3D20%26tbs%3Disch:1&ei=401ZTbK8KYG78gae5MyvBw

Practice

If a 6 kg object undergoes an acceleration of 2 m/s2

• What was the magnitude of the force on the object causing this acceleration?

• If the same force is applied to a 4 kg object, what is the acceleration?

Solve: m= 6, a = 2, Find Fnet?• Fnet = m * a = 6 * 2 = 12 N

Solve Fnet = 12, m = 4, Find a?• Fnet = m * a > 12 = 4 * a > a = 3 m/s2

Practice

What is the resulting acceleration from

2 opposing forces of 200 N and 600 N

acting on a 50 kg object?

Solve m = 50, Fnet = 600-200 = 100, a=?

• Fnet = m * a• 600-200 = 50 * a• a = 400/50 = 8 m/s2

Practice

A body is slowed from 30 m/s to rest

over a distance of 120 meters.

• What is the acceleration on the body?• If the body has a mass of 50 kg, what is the

net force acting on the body?

Solve: vo = 30, vf = 0, d = 120, a?

• (ii) vf2 = vo2 – 2ad > a = -3.75 m/s2

Solve: m = 50, a = -3.75, Fnet = ?

• Fnet = m * a = 50 * (-3.75) = -187.5 N

Practice

Two tug-of-war teams, A and B, are competing. If team A has a mass of 980 kg and pulls with a force of 5000 N, and team B has a mass of 1090 kg and pulls with a force of 6000 N, • Find the magnitude of the net force on the system• Find the acceleration of the system?

Solve: mA = 980, mB = 1090, FA = 5000, FB = 6000 for Fnet• Fnet = |FB-FA| = |6000-5000| = 1000N

Solve Fnet = ma for a• Fnet = m* a (m is the total mass of the system)• 1000N = (980+1090) * a• a = 0.48 m/s2

Practice

A 3.7 x 103 kg elevator is being lifted by a cable that exerts a 4.00 x 104 N force upwards.• What is the acceleration of the elevator?

Solve: m = 3700 kg, F↑=4x104 N, a=?• Fnet = m * a • F↓-F↑ = m*a > weight↓-force↑= m * a• (3700 * 9.8 – 4x104) = 3700 * a• -3740 = 3700 * a • a = -1.01 m/s2

http://quantumprogress.files.wordpress.com/2010/11/screen-shot-2010-11-23-at-11-09-03-pm.png

What about an Inclined Plane?

Component of

gravitational force that

causes motion down

the plane

Practice – inclined plane

A 10 kg box is released on a frictionless

30˚ inclined plane.

• What is the force causing the motion?• What is the magnitude of the normal force?

Solve: m = 10kg, θ = 30˚, F||=?

• F|| = mg*sinθ = 10*9.8*sin(30) = 49 N Solve: m = 10kg, θ = 30˚, FN = ?

• FN = mg*cosθ = 10*9.8*cos(30) = 84.87 N

What about friction?

Friction

Friction Notes.ppt