1. Newton’s Laws of Motion
1. An object won’t change its motion unless a force acts on it: Inertia
2. Force is needed to change the state of motion: F = ma
3. When you push on something, it pushes back on you.

2. Qualitatively describe the system
A block (m2) slides on a frictionless table pulled by a string attached to a mass (m1) hanging over the side. What is the acceleration of the system? a2 m2
What is the relationship between the magnitudes of the acceleration of the two blocks?
A) a1 = a2 B) a1 < a2 C) a1 > a2 a1 m1 2

3. What is the net force on the system?
A block (m2) slides on a frictionless table pulled by a string attached to a mass (m1) hanging over the side. What is the acceleration of the system? a2
a = F/m m2
M1 = 2 kg
M2 = 3 kg a1 m1 3

4. What is the acceleration of the system now?
M1 = 2 kg
M2 = 3 kg

5. Train Example A locomotive pulls 10 freight cars Each car is 30,000 kg
The locomotive is 50,000 kg
The acceleration of the train is 0.05 m/s2
What is the force the locomotive provides?
What is the force of each coupler between cars?

6. Qualitatively Describe the System 1st
You are traveling on an elevator up the Sears tower. As you near the top floor and are slowing down, your acceleration
A) is upward
B) is downward
C) is zero V a mg N

7. Qualitatively Describe the System 1st
You are traveling on an elevator up the Sears tower, and you are standing on a bathroom scale that measures N.
As you near the top floor and are slowing down, the Normal force is.
A) More than your usual weight
B) Less than your usual weight
C) Your usual weight a mg N

8. Friction Force: Obeys Newton’s Laws Always opposes relative motion
Contact force
This force will depend on the
material surfaces sliding
and the normal force between
the surfaces.
Two kinds
Kinetic: sliding taking place
Static: no sliding  rolling

9. Static and Kinetic Frictional Forces
Static friction opposes the impending relative motion between
two objects.
Kinetic friction opposes the relative sliding motion motions that
actually does occur.
is called the coefficient of kinetic friction.

10. Normal Force
Normal force is the force perpendicular to the surface that prevents the objects from passing through each other.
Direction: Perpendicular to surface and out
Magnitude: As much or little required keep objects separate.

11. Static and Kinetic Frictional Forces
When the two surfaces are
not sliding across one another
the friction is called
static friction.

12. Static and Kinetic Frictional Forces
The magnitude of the static frictional force can have any value
from zero up to a maximum value.
is called the coefficient of static friction.

13. Note that the magnitude of the frictional force does
not depend on the contact area of the surfaces.

14. Friction Summary Static friction Kinetic friction f ≤ sn
Magnitude can vary up to limit (sn)
Kinetic friction
f = kn

15. Example
2 kg box slides across a table. Coefficient of friction is 0.32
What is the frictional force?

16. Concept Check
A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives.
If the truck moves with constant accelerating to the left as shown, which of the following diagrams best describes the static frictional force acting on the box: S a A B C

17. What do you think? m2 m2
Case 1
(No Friction)
Case 2
(With Friction) m1 m1
In which case is the acceleration of the blocks biggest? A) Case 1 B) Case 2 C) Same 17

18. What is the force on the front box?
10 kg
5 kg

19. Circular Motion and Gravity

20. Body moving in a circle

21. Body moving in a circle Velocity changes direction
What direction is the change?

22. Circular motion

23. Body moving in a circle

24. Body moving in a circle
Velocity changes toward the center of the circle (curve)
Centripetal acceleration
Velocity is always changing for circular motion
There is always an acceleration

25. Centripetal Acceleration
Acceleration = Dv/Dt = (vf – vi)/(tf - ti)
No change in |v|
Change in direction
Velocity tangent to circle
Acceleration toward center of circle
a is constantly changing

26. Centripetal Acceleration
a = v2/r
Newton’s Second Law
F = ma
Centripetal force
F = mv2/r

27. Centripetal Force
Equations tell the size of the acceleration or the force
What produces the force?

28. Centripetal Force: F = mv2/r
The force can come from
Friction
Rope
gravity

29. Centripetal Acceleration
A car drives around a 20 m radius circle at a speed 10 m/s.
What is the acceleration of the car?
What is the force on the car?