Forces and the Laws of Motion

Fresistance Fforward

Fground-on-car

Fgravity

Force

• A force is a push or a pull on an object

• An object’s motion will change with time if the forces acting on it are unbalanced– Change in motion change in velocity– Change in velocity acceleration

• If the forces are balanced the object’s motion will not change– No change in motion velocity is constant– Velocity is constant acceleration is zero

Force (cont.)

• There are two kinds of force:– Contact forces– Field forces

• Contact forces happen when objects touch

• Field forces act at a distance– Gravity– Electrostatic forces– Magnetic forces

Force (cont.)• Force is a vector

• To find out if the forces on an object are balance or unbalanced, we must add them as vectors

• A free-body diagram shows all the forces on an object

Fresistance Fforward

Fground-on-car

Fgravity

Newton’s First Law

• An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless the object experiences a net external force– “At rest” means zero velocity– “Net force” means the forces are unbalanced

and do not add up to zero– “External force” means the force comes from

outside the object itself

Newton’s First Law (cont.)

• The tendency of an object with mass to resist a change in motion is called inertia

• Newton’s first law is called the law of inertia: it says that without a net force an object’s motion will remain unchanged

• Mass gives objects the property of inertia• The greater the mass, the greater the

inertia

Equilibrium

• If all of the forces acting on an object add to zero, the object is in equilibrium– The forces acting on the object are balanced– Net force equals zero

• Equilibrium means zero acceleration– The object is at rest, or– The object is moving with constant velocity

Newton’s Second Law• The acceleration of an object is directly

proportional to the net force acting on the object and inversely proportional to the object’s mass: a = F/m

F = ma

net force = mass acceleration

Newton’s 2nd (cont.)

F is the vector sum of all external forces acting on the object

• Net force (F) and acceleration (a) are in the same direction

• When a is zero, F is zero, and vice versaa = 0 F = 0

• The net force (F) is sometimes called Fnet

Unit of Force: The Newton

• Because F = ma, force has units of mass (kg) times acceleration (m/s2)

• Define the newton, N, as1 N = 1 (kgm)/s2

• One newton is about 0.225 pounds of force

• One pound of force is about 4.45 N

Example of Newton’s 2nd:

• Two boys are pulling on a 5.2-kg wagon in opposite directions. B1 is pulling to the right with a force of 38 N, and B2 is pulling to the left with a force of 17 N. What is the wagons acceleration?F = F1 – F2 = 38 N – 17 N = 21 N (to the right)

m = 5.2 kg

a = F/m = (21 N)/(5.2 kg) = 4.0 m/s2 (to the right)

Component Version of 2nd Law • The equation F = ma is not very useful as is!• We often use this equation in component form to

solve problems:

Fx = max

Fy = may

where Fx = sum of forces in x-dir.

= x-comp of F

Fy = sum of forces in y-dir.

= y-comp of F

ax = x-comp of accel.

ay = y-comp of accel.

Example

Newton’s Third Law• The magnitude of the force exerted on Object 1

by Object 2 is equal to the magnitude of the force exerted on Object 2 by Object 1, and these two forces are opposite in direction

• The two forces act on different objects:– One force acts on Object 1– The other acts on Object 2

• Field forces also exist in pairs– Example: Earth/Moon System

– Force on Earth is same size as force on Moon

FF

Everyday Forces

• The three most common forces:– Weight, Fg

– Normal Force, FN

– Friction Force, Ff

FN

Ff

Fg

Weight

• Weight is the force of Earth’s gravity on an object– Symbol: Fg

– Direction: toward the center of the Earth

– Magnitude: Fg = mg

where g = 9.80 m/s2 on the surface of Earth

• Weight is a “field force” (no contact required)

Normal Force• Normal Force is the contact force

of a surface on an object– Symbol: FN

– Direction: perpendicular to the surface

– Magnitude: Is determined by analyzing the y-direction

FN

Fg

Ff

Friction Force

• Friction force is caused by surfaces sliding over each other– Symbol: Ff

– Direction: Opposite the motion of the object– Magnitude: If object is sliding,

Ff = FN

where = coefficient of kinetic friction

• Air resistance is a form of friction (it always opposes the motion)

ExampleA box of books is being dragged across the ground ( = 0.81) by a rope (FA = 170 N, 33 from horizontal). If m = 15 kg, calculate ax.

Fx = FAcos Ff = max

ax = (FAcos Ff)

We would be done except we don’t know Ff

How do we get Ff?

m = 15 kg

ax = ?FA = 170 N

= 33

= 0.81

FA

Fg

FN

Ff

1m

Fy = FAsin + FN Fg = may = 0

FN = Fg FAsin

= mg FAsin = (15 kg)(9.8 m/s2) (170 N)sin(33) = 54.4 N

Ff = FN

= (0.81)(54.4 N)= 44.1 N

ax = [(170 N)cos(33) 44.1 N]

= 6.6 m/s2

1(15 kg)