Types of Forces

(through circular motion)

Force	Describes	How to find Magnitude	How to find Direction
Weight	Force of attraction to a planet (or object)	W = mg Fg = G m1 m2 / r^2	Vertically downward towards center of planet
Normal	Force surface exerts on object when it supports that object	Free Body Diagram (F.B.D.)	Perpendicular (or normal) to surface and away from surface.
Tension	Force exerted on object via rope, string, chain,…	(F.B.D.)	Parallel to rope, string, chain and in direction of rope, string, chain…
Friction	Force exerted on object by surface	f = m FN	Parallel to surface and opposite to direction of motion or tendency…
Drag	Force exerted on object by fluid as object moves through that fluid	FD = b v^n	Opposite to direction of motion
Centripetal^*	Force exerted on object that causes circular motion	FC = m v^2 / r	Inwardly directed towards center of curvature
Net^*	Vector sum of ALL external forces acting on object	FNET = S Fi or FNET = m a	(F.B.D.) or Direction of object’s acceleration

* These are NOT separate F.B.D. forces. Centripetal force is always caused by (equal to) one (or more) of the other forces. Net force is always the vector sum of ALL the other acting forces.
Friction

1. Friction is an electromagnetic force.

2. As a force, friction has conventional force units – newtons, pounds, dynes, etc…

3. Friction is a vector quantity with magnitude and direction.

4. Friction is often caused by (due to) gravity but it is NOT gravity and is not equal to the gravitational force.

5. There must be two objects/surfaces/materials in contact (physically touching) in order for friction to occur.

6. Friction depends on the materials in contact – BOTH of the materials. Sandpaper on wood ¹ sandpaper on metal ¹ wood on metal.

Friction (continued)

7) Friction is independent of the surface area (all else being equal.)

8) Friction is independent of speed (within limits.) Faster does not necessarily mean more force of friction.

9) Friction is ALWAYS parallel to surfaces in contact.

10) Friction ALWAYS opposes motion (or the “tendency of motion”); friction is always in the opposite direction of the motion.

Note that “parallel to surface” and “in the opposite direction of motion” are really the same thing but it’s not so obvious if the object is stationary.

Friction (continued)

11) There are two (similar but different) types of friction:

* Static friction – “not moving” friction. This is the

force that holds an object in place on an incline, for

example.

* Kinetic friction – “moving” friction, also called

sliding friction. This is the frictional force between

objects moving past one another.

12) Often (usually?) kinetic friction ≤ sliding friction. It’s easier to keep a sliding box moving than to start the box moving. (This is above and beyond the inertia of the box which must be “overcome” to start the box moving.)

13) Force of friction is directly proportional to the normal force.

F_f µ F_N

* The normal force is the force a surface exerts on an

object when it supports that object.

* It’s the force between the object and the surface it’s

in contact with.

* It’s the apparent weight of an object as measured by

a scale placed between the object and the surface.

Friction (continued)

* Normal means perpendicular. The normal force is

always perpendicular to the surface.

* The normal force is always directed away from the

surface.

Note from these three (common, though not inclusive) examples that F_N must be determined from analysis of the free body diagram.

14) F_f = m F_N

where m is a constant of proportionality called the coefficient of friction.

Friction (continued)

15) Coefficient of friction is a number between 0 and (approximately) 1.0 that says something about the slipperiness of the two materials in contact.

Low m means low friction, materials are slippery.

High m means high friction, materials are not slippery.

Coefficient of friction is a scalar value; it has no direction.

m = F_f / F_N

Since m is a ratio of two forces, the units cancel. m has NO units.

16) The magnitude of the static frictional force ranges from zero up to a maximum determined by the coefficient of static friction.

F_sf ≤ F_sf^max = m_s F_N

(Just how does that inclined plane know how much friction to apply in order to keep a book in place over a variety of angles?!)

Equilibrium

An object is in equilibrium if it is not accelerating.

- Translational equilibrium = “straightline” equilibrium

- All forces must be balanced.

S F_x = 0 S F_y = 0

- Rotational equilibrium is later in the course.

- It is imperative that you can correctly draw the free

body diagram(s), identifying all acting forces.

- It is equally important that you can resolve all forces

into their x and y components. (Vectors!)

Nonequilibrium

An object is not in equilibrium if it is accelerating.

- There must be some unbalanced force(s).

S F_x = ma_x S F_y = ma_y

- It is imperative that you can correctly draw the free

body diagram(s), identifying all acting forces.

- It is equally important that you can resolve all forces

into their x and y components. (Vectors!)

Solving Newton’s 2^nd Law Problems

Special cases/hints/places students commonly screw up:

- For objects on inclines, be careful with resolution of the

weight vector into its “normal” and downhill components.

- Weight (in these problems) is the hypotenuse – the

longest side – of the vector diagram.

- Weight is ALWAYS vertically directed!!

- Tension in a string/rope/cable is constant throughout the string/rope/cable.

- Our pulleys are massless and frictionless (so far!). They do not add any forces to the problem.

- A string/rope/cable passing over a pulley does NOT change the tension – it merely redirects it!

- NORMAL FORCE DOES NOT NECESSARILY EQUAL THE WEIGHT. Look at all forces acting normal to the surface (F.B.D.) to determine normal force.