1. Forces in One Dimension
Chapter 4
Forces in One Dimension

2. I. Force and Motion
A force is a push or pull exerted on an object
A force exerted on an object causes that object’s velocity to change; that is, a force causes an acceleration

3. A. Contact Forces and Field Forces
An object of interest when considering how force affects motion, is called the system
Everything around the system that exerts forces on it is called the external world

4. Contact forces exist when an object from the external world touches a system and thereby exerts a force on it
Field forces exist when a force is exerted on the system without contact (i.e. gravity, magnetism)
The cause of a force is called the agent

5. B. Force and Acceleration
Acceleration is graphed on the vertical axis while force is graphed on the horizontal axis
It has been observed that the slope of a line on the acceleration-force graph decreases as mass increases in direct proportion (i.e. mass increases x4, acceleration decreases by ¼)

6. The value of the slope therefor is 1/m
y=mx+b
y = acceleration, a (m/s2)
m = slope, 1/m (kg)
x = force, F
a = 1/m·F or a = F/m
F = m·a or F = 1kg·m/s2 = 1 Newton
Force is represented by Newtons

7. C. Combining Forces
More than one force can act on an object at any given time
When forces move in equal, but opposite directions, they cancel each other out

8. When forces move unequally to one another in opposite directions, the difference between the two forces is called the net force

9. D. Newton’s Second Law
a = Fnet/mass
The acceleration of an object is directly proportional to the net force exerted on it
The acceleration of an object is inversely proportional to the mass of the object

10. E. Newton’s First Law
An object that is at rest will remain at rest
An object that is moving will continue to move in a straight line with constant speed if the net force acting on the object is zero
- In the ideal case of zero resistance, horizontal motion would never stop

11. 1. Inertia - The tendency of an object to resist change

12. 2. Equilibrium - An object is at equilibrium when the net force acting on it is zero - An object has zero net force when it is stationary, or is moving at constant velocity - A net force acting on an object disrupts its state of equilibrium, or changes its velocity

13. II. Using Newton’s Laws
The only force acting on an object in free-fall is its weight force, Fg (when air resistance is neglected)
The acceleration of an object in free-fall is the acceleration due to gravity, g, 9.80 m/s
Acceleration
= 9.80 m/s

14. Remember a = F/m, where in this case, acceleration = g and F = Fg
g = Fg/ m Fg = mg
The magnitude of the force of an object in free-fall is directly proportional to its mass

15. A. Scales
When standing on a bathroom scale, the scale exerts an upward force on you, equal to Fg pushing down on you
The reading on the scale is determined by the amount of force the springs inside it exerts on you

16. Remember F=m·a or F=1kg·m/s2
1kg·m/s2 = 1 Newton
Therefore the proper unit used to express weight is the newton

17. B. Apparent Weight
Fg is also directly proportional to g
If you stood on a scale in an upward moving elevator, g would be pushing down on you, but the scale would be pushing up on you at a greater magnitude so the scale would read greater than your actual weight.

18. The force exerted by the scale is called the apparent weight
If you were standing on a scale while in free-fall, the scale would not be pushing up on you and it would read zero
Weightlessness does not mean an object’s weight is zero; rather it means that there is no contact force pushing up on the object

19. C. Drag Force and Terminal Velocity
A drag force is a force exerted by a fluid on an object moving through the fluid
Drag force is dependent on the motion of the object, the properties of the object, and the properties of the fluid

20. Drag force increases as the velocity of an object increases
Eventually the drag force equals the force of gravity acting on the object in the opposite direction
When the forces equal one another, the net force is zero and the velocity of the object is constant
This constant velocity is called the terminal velocity

22. Large surface areas are affected by drag force more than small surface areas
Light objects are also affected by drag force more than heavier objects

23. III. Interaction Forces
A. Identifying Interaction Forces
Forces always come in pairs
An interaction pair is two forces that are in opposite directions and have equal magnitude

24. B. Newton’s Third Law
States that all forces come in pairs and that the two forces in a pair act on different objects and are equal in strength and opposite in direction
FAonB = -FBonA

25. C. Forces of Ropes and Strings
Tension is the force exerted by a string or rope
When a rope is suspending an abject, there is an interaction pair between the top of the rope and the bottom of the rope
The tension everywhere in the rope is equal to the weight of the object being suspended

26. D. The Normal Force
The perpendicular contact force exerted by a surface on another object
The normal force is not always equal to an objects weight