Chapter 4

The Laws of Motion

Chapter 4 Homework

Chapter 4 Homework
Hch4CQ2 (481281)  
2. SerCP7 4.CQ.002. (465249)  
3. SerCP7 4.CQ.006. (411964)  
4. SerCP7 4.CQ.007. (411976)  
5. SerCP7 4.CQ.008. (411952)  
6. SerCP7 4.CQ.009. (411942)  
7. SerCP7 4.CQ.012. (411945)  
8. SerCP7 4.CQ.013. (411944)  
9. SerCP7 4.CQ.014. (411933)  
10. SerCP7 4.CQ.016. (411961)  
11. SerCP7 4.CQ.017. (411918)  
12. SerCP7 4.CQ.018. (411982)  

Problems:

           

1. SerCP7 4.P.001. (552434)  
2. SerCP7 4.P.002. (411951)  
3. SerCP7 4.P.005. (411985)  
4. SerCP7 4.P.006. (411975)  
5. SerCP7 4.P.007. (411987)  
6. SerCP7 4.P.008. (411917)  
7. SerCP7 4.P.011. (411963)  
8. SerCP7 4.P.012. (411910)  
9. SerCP7 4.P.015.soln. (535280)  
10. SerCP7 4.P.018.soln. (411948)  
11. SerCP7 4.P.020. (411988)  
12. SerCP7 4.P.023. (411916)  
13. SerCP7 4.P.024.soln. (411913)  
14. SerCP7 4.P.026.AF. (413726)  
15. SerCP7 4.P.027.AF. (457221)  
16. SerCP7 4.P.028.AF. (457229)  
17. SerCP7 4.P.029. (411923)  
18. SerCP7 4.P.030.AF. (413738)  
19. SerCP7 4.P.032. (411960)  
20. SerCP7 4.P.034. (411955)  
21. SerCP7 4.P.035.AF. (413737)  
22. SerCP7 4.P.036.AF. (413746)  
23. SerCP7 4.P.037. (411908)  
24. SerCP7 4.P.038. (411947)  
25. SerCP7 4.P.039. (411915)  
26. SerCP7 4.P.042. (411965)  
27. SerCP7 4.P.044. (411914)  
28. SerCP7 4.P.045.AF. (413752)  
29. SerCP7 4.P.050.AF. (413742)  
30. SerCP7 4.P.055. (411989)  
31. SerCP7 4.P.058.AF. (413747)  
32. SerCP7 4.P.062. (411940)  
33. SerCP7 4.P.065. (411967)  
34. SerCP7 4.P.067.soln. (411909)  
35. SerCP7 4.P.073. (411921)  
36. Walker2 5.P.037. (236017)  
37. Walker2 5.P.066. (236034)  
38. Walker2 5.P.059. (236030)  
39. Walker2 5.P.051. (236026)  
40. Ch 4 myq1 (381883)  
41. Walker2 5.P.023. (236008)  
42. Walker2 5.P.033. (236014)

 

Classical Mechanics

Describes the relationship between the motion of objects in our everyday world and the forces acting on them

Conditions when Classical Mechanics does not apply

very tiny objects (< atomic sizes)

objects moving near the speed of light

Forces

Usually think of a force as a push or pull

Vector quantity

May be contact or field force (magnetic/electrical/gravity)

Contact and Field Forces

Fundamental Forces

Types

Strong nuclear force

Electromagnetic force

Weak nuclear force

Gravity

Characteristics

All field forces

Listed in order of decreasing strength

Only gravity and electromagnetic in mechanics

 

 

Newton’s First Law (law of inertia)

If no forces act on an object, it continues in its original state of motion; that is, unless something exerts an external force on it, an object at rest remains at rest and an object moving with some velocity continues with that same velocity.

 

 

Newton’s First Law, cont.

External force

any force that results from the interaction between the object and its environment

Alternative statement of Newton’s First Law

When there are no external forces acting on an object, the acceleration of the object is zero.

Inertia

Is the tendency of an object to continue in its original motion

 

Mass

A measure of the resistance of an object to changes in its motion due to a force

Scalar quantity

SI units are kg

Newton’s Second Law

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

F and a are both vectors

 

 

Can also be applied three-dimensionally

 

Units of Force

SI unit of force is a Newton (N)

US Customary unit of force is a pound (lb)

1 N = 0.225 lb

Gravitational Force

Mutual force of attraction between any two objects

Expressed by Newton’s Law of Universal Gravitation:

 

 

Weight

The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object

w = m g is a special case of Newton’s Second Law

g can also be found from the Law of Universal Gravitation

More about weight

Weight is not an inherent property of an object

mass is an inherent property

Weight depends upon location

Newton’s Third Law

If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force F21 exerted by object 2 on object 1.

Equivalent to saying a single isolated force cannot exist

Newton’s Third Law cont.

F12 may be called the action force and F21 the reaction force

Actually, either force can be the action or the reaction force

The action and reaction forces act on different objects

Some Action-Reaction Pairs

n and n’

n is the normal force, the force the table exerts on the TV

n is always perpendicular to the surface

n’ is the reaction – the TV on the table

n = - n’

More Action-Reaction pairs

Fg and Fg’

Fg is the force the Earth exerts on the object

Fg’ is the force the object exerts on the earth

Fg = -Fg’

 

Forces Acting on an Object

Newton’s 2nd Law uses the forces acting on an object

n and Fg are acting on the object

n’ and Fg’ are acting on other objects

 

Applying Newton’s Laws

Assumptions

Objects behave as particles

can ignore rotational motion (for now)

Masses of strings or ropes are negligible

Interested only in the forces acting on the object

can neglect reaction forces

Free Body Diagram

Must identify all the forces acting on the object of interest

Choose an appropriate coordinate system

If the free body diagram is incorrect, the solution will likely be incorrect

     

 

 

 

Equilibrium

An object either at rest or moving with a constant velocity is said to be in equilibrium

The net force acting on the object is zero

 

 

Equilibrium cont.

Easier to work with the equation in terms of its components:

Solving Equilibrium Problems

Make a sketch of the situation described in the problem

Draw a free body diagram for the isolated object under consideration and label all the forces acting on it

Resolve the forces into x- and y-components, using a convenient coordinate system

Apply equations, keeping track of signs

Solve the resulting equations

 

Equilibrium Example – Free Body Diagrams

Newton’s Second Law Problems

Similar to equilibrium except

Use components

 

ax or ay may be zero

 

Solving Newton’s Second Law
Problems

Inclined Planes

Choose the coordinate system with x along the incline and y perpendicular to the incline

Replace the force of gravity with its components

  

 

  • Elevator type problems
    •

     

     

    Forces of Friction

    When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion

    This is due to the interactions between the object and its environment

    This is resistance is called the force of friction

     

     

     

    More About Friction

    Friction is proportional to the normal force

    The force of static friction is generally greater than the force of kinetic friction

    The coefficient of friction (µ) depends on the surfaces in contact (rough / smooth)

    The direction of the frictional force is opposite the direction of motion

    The coefficients of friction are nearly independent of the area of contact

     

     

     

    Static Friction, ƒs

    Static friction acts to keep the object from moving

    If F increases, so does ƒs

    If F decreases, so does ƒs

    ƒs £ µ n

     

    Kinetic Friction

    The force of kinetic friction acts when the object is in motion

    ƒk = µ n

     

    Hint:

    Use this derived equation when given the coefficient of friction and acceleration of an object on a flat plane or its component on an incline

     

     

    Connected Objects

    Apply Newton’s Laws separately to each object

    The acceleration of both objects will be the same

    The tension is the same in each diagram

    Solve the simultaneous equations

     

     

    More About Connected Objects

    Treating the system as one object allows an alternative method or a check

    Use only external forces

    Not the tension – it’s internal

    The mass is the mass of the system (all objects connected)

    Doesn’t tell you anything about any internal forces

                       

     

    Terminal Speed

    Another type of friction is air resistance

    Air resistance is proportional to the speed of the object

    When the upward force of air resistance equals the downward force of gravity, the net force on the object is zero

    The constant speed of the object is the terminal speed