Forces & the Laws of Motion

Chapter 4

4.1 Changes in Motion

• Objectives:

• Explain how force affects the motion of an object

• Distinguish between contact forces and field forces

• Interpret and construct free-body diagrams

Force

• What is a force?• A push or pull that can change the motion of an

object• What is the SI unit for force?• The newton (N)• One newton is the force required to accelerate a

1-kg mass at 1 m/s2

• 1N = 1 kg·m/s2 1N = 0.225 lbf• 1lbf = 4.448 N

Forces act through contact or at a distance

• Contact forces:• Forces that affect an object through

physical contact with another object• Example: a baseball bat hitting a baseball• Field forces:• Forces that affect an object without

physical contact• Examples: gravitational, magnetic, and

electrostatic forces

Field Theory

• Explains how forces can affect an object without physical contact

• Explanation of field forces…• An object affects the space surrounding it

so that a force is exerted on other objects in that space.

• The “field” is the region of space in which the force is exerted

• Example: magnetic field

Electrostatic Forces

• Example of a field force• Stream of ethanol is

attracted to an electrically charged probe

Force Diagrams

• Force is a vector

• Force diagrams:– Diagram the objects involved in a situation

and the forces acting on the objects

• Free-body diagrams:– Diagram the forces acting on a single object– i.e. diagram the object “free” from influence of

other objects and their forces

Representing Forces

• Force is a vector• Free-body diagrams illustrate forces acting on

an object isolated from its surroundings

Free-body Diagrams

• Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation

• Represent object as a box with forces originating from center of box

Example of a Free-Body Diagram

Common Forces in Force Diagrams

• Applied force Fappapp

• Weight Fg (mg)

• Normal force FN ┴ to surface • Friction Ff

• Air resistance Fair

• Tension Ftens

• Spring force Fspring

Force Equilibrium

• Force equilibrium

• All forces “cancel”

• No net force acting on an object

• Can an object in force equilibrium be in motion?

0F

4.2 Newton’s First Law:Law of Inertia

• Galileo noted that things tend to slide further on smoother surfaces

• Concluded that an object would slide forever on a perfectly smooth surface in the absence of any applied force

• This led to Newton’s First Law of Motion

Newton’s First Law of Motion:Inertia

• An object at rest remains at rest, and an object in motion continues in motion in a straight line, with a constant velocity, unless acted upon by a net external force

• Inertia: the tendency of an object to maintain its state of motion

• When net force on an object is zero, acceleration is zero (∆v/∆t = 0)

Newton’s First Law of Motion

• An object at rest remains at rest, and an object in motion continues in motion with a constant velocity unless acted upon by a net external force

• A net force is required to change the state of motion of an object

• Net external force– Resultant force produced from combination of

all forces acting on an object

Net External Force

• Typical external forces:gravity (weight = mg) = 22N

normal force ┴ to surface = 18N

push/pull =0

friction = 11N

• A book is left on a drafting table with an incline of 35˚

• Identify forces acting on the book & calculate Fnet

(sum of x & y components)

Forces Acting on Inclined Planes

1. FN, normal force, surface acting on object

2. Fg, weight = mg

3. Fgx, component of g, ║ to surface

4. Fgy, component of g ┴ surface

5. Ff, friction

Calculating Net External Force

• Identify variables & select equation

• Draw free-body diagram and apply coordinate system

• Calculate x & y components of all vectors

• Calculate x & y components of the resultant Fnet (Fx, Fy)

• Calculate net external force (Fnet)

Inertia

• Inertia is tendency of an object to maintain its state of motion unless acted upon by a net force

• Mass is a measurement of inertia

• ↑ mass → ↑ inertia• As the same speed, a

rolling car is more difficult to stop than a rolling basketball

Equilibrium

• The state of a body in which there is no change in motion

• Net force acting on a body is zero

4.3 Newtons 2nd & 3rd LawsLearning objectives

1. Describe acceleration of an object in terms of its mass and the net external force acting on it

2. Predict direction & magnitude of acceleration caused by a known net external force

3. Identify action-reaction force pairs4. Explain why action-reaction pairs do not

result in equilibrium

Newtons 2nd Law

• The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the mass of the object

• a = ΣFnet /m , where Σ means “sum of”

• ΣFnet = ma

Conceptual Question

A grain truck filled with soy beans accelerates along the highway at 0.50 m/s2. If the driving force on the truck remains the same, what happens to the acceleration of the truck if soybeans leak from it at a constant rate?Answer: The loss of soy beans is a decrease in mass. Since a = ΣFnet /m , acceleration increases.

Newton’s 3rd Law

• "For every action, there is an equal and opposite reaction." equal magnitude and opposite direction

• In every interaction, there is a pair of forces acting on the two interacting objects.

• Action-reaction force pairs: equal in magnitude, but opposite in direction.

Action-Reaction Force Pairs

• Since force pairs are equal in magnitude, but opposite in direction, why do they not result in equilibrium?

• Because they act on different objects.• If equal but opposite forces acted on the same object,

there would be equilibrium, i.e. no net force.

4.4 Everyday Forces

• WeightForce of gravity acting on a mass

Fg = mg W = mg Fw = mg

• Normal Force

contact force exerted by one object on another in a direction ┴ surface of contact

• Friction

contact force that opposes motion….

opposes applied force

Weight & Normal Force

• Fg = mg• Always ┴ surface of

earth• Directed toward

center of earth• FN = Fgcos (θ)• Always ┴ surface of

contact• Always opposes Fg

Identify Forces Acting on Inclined Planes

1. FN, normal force, surface acting on object

2. Fg, weight = mg

3. Fgx, component of g, ║ to surface

4. Fgy, component of g ┴ surface

5. Ff, friction

Force of Friction

• Ff opposes applied force• Static friction Ffs ….

force exerted by environment on motionless body to resist applied force

• Kinetic friction Ffk ….force exerted by environment on moving

object to resist applied force• Ffs > Ffk

• Depends on surfaces in contact….Types and smoothness

• Proportional to FN

Static vs. Kinetic Friction

Relationship of Ff and Fn

• Ff is proportional to FN

• Proportionality constant is the coefficient of friction, μ

• μ = Ff / FN

• Depends on types of surfaces in contact

• Depends on static or kinetic friction

μs = Fs / FN μk = Fk / FN

Problem 4C

• A crate of mass 24 kg is set in motion on a horizontal surface with a horizontal force of 75 N. Find the coefficient of static friction, μs

• μs = Fs / FN

• = Fs / mg

• = 75 N / (24 kg x 9.81 m/s2)

• = 0.32

Coefficients of Friction(Approximate)

Materials μs μk Materials μs μk

Steel on steel 0.74 0.57 Waxed wood on wet snow

0.14 0.10

Aluminum on steel 0.61 0.47 Waxed wood on dry snow

---- 0.04

Rubber on dry concrete

1.00 0.80 Metal on metal (lubricated)

0.15 0.06

Rubber on wet concrete

---- 0.50 Ice on ice 0.10 0.03

Wood on wood 0.40 0.20 Teflon on Teflon 0.04 0.04

Glass on glass 0.90 0.40 Synovial joints in humans

0.01 0.003

Role of Surface in Friction

• Static friction increases with increasing force until overcome

• Kinetic friction is less than the maximum static friction

Frictional & Applied Force

Fk

Fa

Fg

Fn

Fk

Fa

Fg

Fn

Fax

Fay