Applied Natural Sciences

Exam tips and tricks Leo Pel

e‐mail:3nab0@tue.nl

http://tiny.cc/3NAB0

Solving problems in physics

A problem-solving strategy offers techniques for setting up and solving problems efficiently and accurately.

No recipe or plug-and-chug works all the time, but here are some guidelines: 1. Read the problem carefully.

2. Draw a sketch of the system.

3. Visualize the physical process involved.

4. Devise a strategy for solving the problem.

5. Identify the appropriate equations.

6. Solve the equations symbolically. Then fill in the numbers and calculate the answer.

7. Check your answer. 1. Dimensions? Check dimensions, units.

2. Reasonable? Make a rough estimate of the relevant quantities to one significant figure, preferably some power of 10, combine the quantities to make the estimate.

8. Explore the limits and special cases. Are they reasonable?

Solving problems in physics

1. Read carefully

• Look for clues\keywords that help solve the problem:

• Check units of the given values. Immediately rewrite them to standard SI units (kg, m, s, ...).

• Take care with unit prefixes. At least know the most common ones (femto – peta).

•Small

•Light(weight)

•Assume

•May be neglected

•Frictionless

•(In)elastic

•Perfect

•Ideal

•Steady state

•Constant

• .... (not to be used)

2. Draw a sketch

• Make your sketch large enough so you can add variable names, angles, help lines and so on

• Use a protractor triangle (Dutch: “geo driehoek”)

• Rather use 30/60 degree angles as opposed to 40/50 degrees. This makes it easier to see corresponding angles

A thermal window with an area of 6.00 m2 is constructed of two layers of glass, each 4.00 mm thick, and separated from each other by an air space of 5.00 mm. If the inside surface is at 20.0°C and the outside is at ‐30.0°C, what is the rate of energy transfer by conduction through the window?

The heat conduction coefficient of air is 0.0234 W/mK and the heat conduction coefficient of glass is 0.800 W/mK. Heat transfer by convection and radiation maybe neglected.

3, 4, 5. Physics, solving strategy, equations

An open cylindrical tank of acid rests at the edge of a table 1.0 m above the floor of the chemistry lab. If this tank springs a small hole in the side at its base, how far from the foot of the table will the acid hit the floor if the acid in the tank is 75 cm deep?

6. Solve symbolically

A cowboy fires a silver bullet with a muzzle speed of 200 m/s into the pine wall of a saloon. Assume that all the internal energy generated by the impact remains with the bullet. What is the temperature change ∆T of the bullet? The specific heat of silver is 234 J/Kg*K.

𝐾 =12𝑚𝑣2 Kinetic energy

𝑄 = 𝑚𝑚∆𝑇 Energy for heating

𝐾 = 𝑄

→ 12𝑚𝑣2= 𝑚𝑚∆𝑇

→ 12𝑣2= 𝑚∆𝑇

→ ∆𝑇= 12𝑣2

𝑐 Temperature change independent of mass of bullet! We

don’t need mass of bullet to calculate the result.

Check units: (m2/s2)/{J/(kg.K)}=(m2/s2)/{(N.m)/(kg.K)}

= (m2/s2)/[{(kg.m/s2).m}/(kg.K) ]=K

Math basics you should know

• Know how to solve sets of linear equations with 2 or 3 variables:

Equation 1: a x + b y + c z = d

Equation 2: e x + f y + g z = h

Equation 3: I x + j y + k z = m

Find unknown x, y and z given constants a, ..., m?

• Solve quadratic equations:

x = x0 + vot + 0.5 a t2

Find unknown t given constants x0 , vo, a?

• Areas and volumes of common objects

• ...

Vectors: some required goniometric knowledge

Corresponding angles Goniometric functions sin, cos, tan and their inverse functions. Radians and degrees

360𝑜 = 2𝜋 𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑥𝑜 =𝑥

3602𝜋 𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑦 𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =𝑦

2𝜋360𝑜

Vector notations

Vector 𝐴: mostly used in sketches and general high level equations. Variable having a direction and magnitude

• Magnitude 𝐴 = 𝐴 used in problem descriptions and calculation (results).

• Direction Ɵ (for 2 dimensional problems): used in problem descriptions and calculation (results).

Note that Ɵ is given based on a certain axis that may or may not correspond to the positive x-axis in your problem!

Component vectors 𝐴𝑥, 𝐴𝑦: components of a vector in the axis directions. Not that frequently used, but their magnitudes called components are.

Components 𝐴𝑥 = 𝐴𝑥 , 𝐴𝑦 = 𝐴𝑦 : used frequently in calculations (especially in vector additions/subtractions).

Unit vectors �̂�, 𝒋̂ vector having magnitude 1 in x resp. y direction

so 𝐴𝑥 = 𝐴𝑥�̂� 𝑟𝑟𝑟 𝐴𝑦 = 𝐴𝑦𝒋̂ 𝑟𝑟𝑟 𝐴 = 𝐴𝑥�̂� + 𝐴𝑦𝒋̂

When at exam

• Look through exam, assess difficulty per question. Difficult questions contribute the same amount of points as easy ones but cost more time and effort....

• Teachers want to see insight in the physics behind the problem at hand.

• Write down your solving strategy starting from the basic equations (often conservation laws)

• Do not write random equations from the summary or nonsense equations (e.g. 2018 igloo area: 𝐴 = 4

3𝜋𝑅3)

• If you cannot solve exactly, at least indicate how to do it. Assume a variable, then solve symbolically.

• Exam 2018 igloo: assume area is A or 𝑚𝜋𝑅2 and continue symbolically.

• Check dimensions or units, not only for final results, also intermediate in (longer) calculations.

• Rather write line extra instead of making larger steps

Planning: work on exam questions

Today:

• General advice, some basics (this presentation)

• Ch. 25, 26, 17 maybe 2, 3

Next week:

• Newton’s laws Ch. 4 through Ch. 11: be prepared!

Third week:

• Remainder.

• Last minute questions/remarks

END