difficult topics for PHYS 111

Summary of important and difficult topics for PHYS 111

Congratulations for learning so much this semester…

Fair or not?

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** problem solving strategy and steps to analyze force for a single object.

1, Identify and isolate the object of interest, use a dot to represent it.

2, Identify all forces on the object acted by other objects.

Label each force using a arrow of correct length and direction.

3, Pick x –y axis. ( based on acceleration direction for convenience)

4, Break up all forces into x-y components. (Use trigonometry when needed) 5, Set equations: (x & y are independent )

Add all force components in x directions = m a

Add all force components in y directions = m a

F

= m a

, F

= m a

;

6, Solve for any two unknowns, from the above two equations.

(If you know all forces, you can find a.)

(If you know a, you can solve force) For example:

If not moving, in that direction, a=0; F

= 0 in that direction.

If circular motion, in the direction pointing to orbit center; a=v

/r; F

=mv

/r

How to analyze forces to calculate forces or acceleration?

** for a object of particular size and shape, torques t also needed to be considered.

If static, total F_net= 0 and total t_net= 0. (Static equilibrium—balance)

If t_net is not 0 , angular acceleration aCopyright Dr. Weining Man= t_net /I ; ²

Properties of various forces

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Define positive direction and indentify initial and final point of interest, first.

Trick: identify known and unknown variables, then choose the right equation.

When you know 3 items out of the 5 items, you should choose the equation which does not involve the 4

unknown item (ignore it) and calculate the 5th one, which is asked!

Projectile Motion: a

=0;

a

= - g, if up is defined as positive y.

1, Treat x and y directions INDEPENDENTLY.

2, Decompose initial v in x and y directions .(use trigonometry).

3, Identify final point and fill known and unknown items in the table.

4, Choose and solve equations in x OR y direction.

5, t is the same for both x and y directions..

How to solve time, acceleration, velocity, displacement etc for constant acceleration motion.

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Acceleration method, works for constant acceleration motion.

Step 1: Analyze forces and their components.

Step 2: Solve for Acceleration or forces: ∑F=ma 1.If it is not moving, total force=0 (both x & y)

∑F

=0 ∑F

= 0

2.If it moves along a straight line,(define it as x axis)

∑F

=m a

∑F

= 0

3.Free falling, projectile motion: a

= 0, a

= -g;

v

keeps constant.

4. Circular motion: ∑F

=mv

/r

Step 3: In the direction of constant accel. motion, (a, t, v0, vf, displacement), identify 3 of them and solve for the other 2.

5

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Work and Energy method works for any motion

W=Fd cos(angle between Force and motion)

Step1: Analyze forces on that object.

Step2: Identify which forces do work in this motion.

Step3: Use energy equations. Write out K, U; solve unknowns.

1. If only mg or spring force did work. W

=0

2. In general, for any cases:

Work of kinetic friction = - f

d

6

U = mgy

Potential Energy U = ½k(Dx) ²

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Kinetic Energy K = ½mv ²

When only mg or spring force (conservative forces) do work, (No friction, no resistance (in air, on ice, not water…),

no external forces or energy source does work, (no human, animal, motor, lift, push…)

Got Conservation of Mechanical Energy, when W

=0

This is true when W

=0

7

U = mgy

Potential Energy U = ½k(Dx) ²

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Kinetic Energy K = ½mv ²

W_external, Wpush, pull, wind, man, wave, elevator, …

Wkinetic-friction = – f_kd

When nonconservative forces do work, the total mechanical energy is not conserved: we need to calculate work done by Non-Conservative forces. (Wnc= sum of all work except for mg and spring’s work)

This is always true.

Wnc vs. Thermal energy (heat) and mechanical energy

W_external, Wpush, pull, wind, human, wave, elevator, …

W

= – f

d

U = mgy

Potential Energy U = ½k( D x) ²

Kinetic Energy K = ½mv ²

Thermal Energy OR Heat

Q

Heat generated by friction Q = |W

|= - W

W

= E

-E

9 Copyright Dr. Weining Man

Thermal energy and heat transfer

Thermal Energy of object A (high T _i )

Heat needed for phase change: Q= m L Q>0, if melt or evaporate,

Q<0, if freeze or condense.

Thermal Energy of object B (low T _i )

Q

>0 Q

<0

Heat needed for temperature change: Q= m c (T

-T

);

Q>0 if raise T; Q<0 if lower T

If objects are mixed and isolated from other objects,

Final T is the same for all of them. Also Total Q=0 ;Q

+Q

=0 m

c

(T

-T

) + m

c

(T

-T

) = 0 CORRECT.

m

c

(T

-T

) = m

c

(T

-T

) is WRONG.

Thermal energy (Internal Energy) , heat and work for ideal gas

Thermal Energy of Ideal Gas

(Internal Energy) U = 3/2 n R T

Q: Heat transfer Q>0 if absorb heat;

Q<0 if gives off heat.

W:Work done by gas W>0 if expand;

W<0 if be compressed.

The change in a gas system’s internal energy is equal to the heat Q minus the work W done by the gas

It is vital to keep track of the signs of Q and W.

The internal energy of the system depends only on its temperature. When the idea gas system returns to previous temperature, its internal energy returns to its initial level.

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Conservation laws

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Copyright Dr. Weining Man 13

• The final exam will count for 30%.

You need to score the same in the final exam as your current total grade now to maintain your letter grade.

You need to score 10 to 20 points higher in the final exam than your current total grade to booster your letter grade for one step.

• The final exam includes 18 chapters. All questions are from previous HW questions, not including bonus HWs.

• You can do the following to prepare for the final exam:

First, work through all questions from HW 10a to HW 14b, both calculation and conceptual questions.

Second, carefully review ALL conceptual questions from HW 1a to 9a and understand them.

Third, at least redo one hardest calculation problem from each HW 1a to 9a, and redo questions in previous quizzes and

midterms.

• I will focus on research and not teach PHYS 111 till Fall 2012. Thank you for the productive semester. (Life is fair. The more you study, the more you know on these important and useful things.

• Best wishes to your final and your future career.Copyright Dr. Weining Man ¹⁴