1. Forces and the Laws of Motion
Fresistance
Fforward
Fground-on-car
Fgravity

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. net force = mass  acceleration
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

9. 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 versa
a = 0  F = 0
The net force (F) is sometimes called Fnet

10. Unit of Force: The Newton
Because F = ma, force has units of mass (kg) times acceleration (m/s2)
Define the newton, N, as
1 N = 1 (kgm)/s2
One newton is about pounds of force
One pound of force is about 4.45 N

11. 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)

12. 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.

13. Example

14. 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 F

15. Everyday Forces Ff The three most common forces: Weight, Fg
Normal Force, FN
Friction Force, Ff Ff FN

16. 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)

17. 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

18. 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)

19. Example
A 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 1 m

20. 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)