second _law of motion__accelertion__.ppt

Acceleration

1. Distance
The length an object actually travels.
How far you go.
Scalar
Displacement
The change in position of an object.
Length between start and finish
Vector

2. Average Velocity
average velocity =
change in position
change in time
=
displacement
time interval
f i
avg
f i
x xx
v
t t t

 
 

3. Velocity vs. Speed
•Velocity describes motion with both a
direction and a numerical value
(i.e. magnitude). (vector)
•Speed has no direction, only magnitude.
•Average speed is equal to the total
distance traveled divided by the time
interval. (scalar)
distance traveled
average speed =
time of travel

4. Sign Conventions for Velocity

5. Interpreting Velocity Graphically
The instantaneous
velocity at a given time
can be determined by
measuring the slope of
the line that is tangent
to that point on the
position-versus-time
graph.
The instantaneous velocity is the
velocity of an object at some instant or
at a specific point in the object’s path.

6. Acceleration
Units for acceleration are 1 m/s/s or m/s
2

This means that every second
you increase your velocity by one m/s.
change in velocity
average acceleration =
time required for change

7. Changes in Velocity
•Acceleration is the rate at which velocity
changes over time.
f i
avg
f i
v vv
a
t t t

 
 
•An object accelerates if its speed, direction,
or both change.
•Acceleration has direction and magnitude.
Thus, acceleration is a vector quantity.

8. Acceleration

9. Changes in Velocity
•Consider a train moving to the right, so that the
displacement and the velocity are positive.
•The slope of the velocity-time graph is the
average acceleration.
–When the velocity in the positive direction is
increasing, the acceleration is positive, as
at A.
–When the velocity is constant, there is no
acceleration, as at B.
–When the velocity in the positive direction is
decreasing, the acceleration is negative,
as at C.

10. Graphical Representations of Acceleration

11. Practice
•A car accelerates east from rest to a final
velocity of 20 m/s east in a time interval
of 5.0 s. What is the average
acceleration of the car?

12. Practice
•A car traveling initially at +3.0 m/s
accelerates to 24 m/s during an interval of
20 s. What is the acceleration during this
time?

13. There Are Other Uses for the
Formula
v
f
= v
i
+ at
Final Velocity = Initial Velocity + Acceleration x Time

14. Practice
•A car traveling initially at +3.0 m/s
accelerates at the rate of +1.20 m/s
2
for an
interval of 20 s. What is the velocity at the
end of the acceleration?

15. Velocity and Acceleration

17. Objectives
•Relate the motion of a freely falling body to
motion with constant acceleration.
•Calculate displacement, velocity, and time at
various points in the motion of a freely falling
object.
•Compare the motions of different objects in
free fall.

18. Free Fall

19. Free Fall
•Free fall is the motion of a body when only the
force due to gravity is acting on the body.
•The acceleration on an object in free fall is
called the acceleration due to gravity, or free-
fall acceleration.
•Free-fall acceleration is denoted with the
symbols a
g
(generally) or g (on Earth’s surface).

20. Free-Fall Acceleration

21. Free-Fall Acceleration
•Free-fall acceleration is the same for all
objects, regardless of mass.
•we use the value g = 9.8 m/s
2
.
•Free-fall acceleration on Earth’s surface is
–9.8 m/s
2
at all points in the object’s
motion.

22. Free-Fall Acceleration
•Consider a ball thrown up into the air.
–Moving upward: velocity is decreasing,
acceleration is –9.8 m/s
2
–Top of path: velocity is zero, acceleration is –
9.8 m/s
2
–Moving downward: velocity is increasing,
acceleration is –9.8 m/s
2

23. Velocity and Acceleration of
an Object in Free Fall

24. Newton’s First Law
•An object at rest remains at rest, and an
object in motion continues in motion with
constant velocity (that is, constant speed in a
straight line) unless the object experiences a
net external force.
•In other words, when the net total external
force on an object is zero, the object’s
acceleration is zero. (i.e. the change in the
object’s velocity is zero)

25. 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.
F = ma
net force = mass  acceleration
F represents the vector sum of all external forces acting
on the object, or the net force.

26. Newton’s Second Law

27. Newton’s Third Law
•If two objects interact, the magnitude of the force
exerted on object 1 by object 2 is equal to the
magnitude of the force simultaneously exerted on
object 2 by object 1, and these two forces are
opposite in direction.
•In other words, for every action, there is an
equal and opposite reaction.
•Because the forces coexist, either force can be
called the action or the reaction.

28. Action and Reaction Forces
•Action-reaction pairs do not imply that the net
force on either object is zero.
•The action-reaction forces are equal and opposite,
but either object may still have a net force on it.
Consider driving a nail into wood with a hammer. The force that the nail exerts
on the hammer is equal and opposite to the force that the hammer exerts on
the nail.
But there is a net force acting on the nail, which drives the nail into the wood.

29. Newton’s Third Law

30. Weight
•The gravitational force (F
g) exerted on an
object by Earth is a vector quantity, directed
toward the center of Earth.
•The magnitude of this force (F
g) is a scalar
quantity called weight.
•Weight changes with the location of an
object in the universe.

31. Weight, continued
•Calculating weight at any location:
F
g
= ma
g

a
g
= free-fall acceleration at that location
•Calculating weight on Earth's surface:
a
g = g = 9.81 m/s
2
F
g = mg = m(9.81 m/s
2
)

32. Gravity as a Force
•The gravitational force (F
g
) exerted on an
object by Earth is a vector quantity, directed
toward the center of Earth.
•Force is in Newtons
•Masses are in kg
•Distance is in meters

33. Gravity as a Force
•The gravitational force constant is G
•G = 6.67 x 10
-11
N-m
2
/kg
2
•The masses are simply the mass of the two
gravitational bodies (i.e. your mass and the
earth’s)
•When using G and M
E
, then it simplifies to g