Summer Work Conceptual Questions

Question 1

Models are particularly useful in relativity and quantum mechanics, where conditions are outside those normally encountered by humans. What is a model?

Answer 1

A representation of something that is often too difficult (or impossible) to display directly. It is justified with experimental proof

Question 2

How does a model differ from a theory?

Answer 2

A model may not be completely correct. (Ex. Bohr’s model of an atom is used by many, but it isn’t completely correct.)

Question 3

If two different theories describe experimental observations equally well, can one be said to be more valid than the other (assuming both use accepted rules of logic)?

Answer 3

No

Question 4

What determines the validity of a theory?

Answer 4

the experimental evidence to back it up

Question 5

Certain criteria must be satisfied if a measurement of observation is to be believed. Will the criteria necessarily be as strict for an expected result as for an unexpected result?

Answer 5

Yes

Question 6

Can the validity of a model be limited, or must it be universally valid? How does this compare to the required validity of a theory or a law?

Answer 6

There is a range of validity for models. We use models that are not completely correct. Theories and laws, if well developed are considered valid until experimental evidence proves them invalid

Question 7

Classical physics is a good approximation to modern physics under certain circumstances. What are they?

Answer 7

In order for the laws of classical physics to apply, matter must be moving at speeds less than 1% the speed of light, the objects must be large enough to be seen with a microscope, and only weak gravitational fields can be involved.

Question 8

Under what circumstances does distance traveled equal magnitude of displacement? What is the only case in which magnitude of displacement and distance are exactly the same?

Answer 8

When the object is traveling in the positive direction on the frame of reference

Question 9

A student writes, “A bird that is diving for prey has a speed of −10m/s.” What is wrong with the student’s statement? What has the student actually described? Explain.

Answer 9

The student is incorrect because of the negative sign in their answer. Speed is a scalar quantity and therefore does not have direction, only magnitude. So the student is incorrect because they included direction in their answer.

Question 10

Scalar quantity

Answer 10

has only magnitude

Question 11

Vector quantity

Answer 11

has magnitude and direction

Question 12

Which of the following is a vector:
- A person’s height
- The altitude of Mt. Everest
- The age of the Earth
- The boiling point of water
-The cost of this book
- The Earth’s population
- The acceleration of gravity

Answer 12

the acceleration of gravity because it involves a direction (when you accelerate, you move in a certain direction)

Question 13

What do vectors and scalars have in common? How do they differ?

Answer 13

Scalars and vectors both have magnitudes and units, but only vectors have direction

Question 14

Two campers in a national park hike from their cabin to the same spot on the lake, each taking a different path, as illustrated below. The total distance traveled along Path 1 is 7.5 km, and that along Path 2 is 7.2 km. What is the final displacement of each camper?

Answer 14

5 km, 40° NE

Question 15

If an airplane pilot is told to fly 123 km in a straight line to get from San Francisco to Sacramento, explain why he could end up anywhere in a 123 km radius. What other information would he need to get to Sacramento?

Answer 15

The pilot does not know which direction he needs to fly, so he needs to be told to fly 123 km, 45° NE

Question 16

Suppose you take two steps A and B (that is, two nonzero displacements). Under what circumstances can you end up at your starting point? More generally, under what circumstances can two nonzero vectors add to give zero? Is the maximum distance you can end up from the starting point A+B the sum of the lengths of the two steps?

Answer 16

If you walk back and fourth the same distance

Question 17

Explain why it is not possible to add a scalar to a vector.

Answer 17

You cannot add something with direction to a scalar quantity.

Calculations with scalar quantities involve straight addition, and calculations with vector quantities involve trig functions.

Question 18

If you take two steps of different sizes, can you end up at your starting point? More generally, can two vectors with different magnitudes ever add to zero? Can three or more?

Answer 18

Two vectors with different magnitudes cannot add to zero. Three or more can.

Question 19

Suppose you add two vectors A and B. What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude? What relative direction between them produces the resultant with the smallest magnitude? What is the minimum magnitude?

Answer 19

The greatest magnitude is when they lie in the same direction and the sum would be a scalar sum of the two vectors. The angle between the two would be 0°

The smallest magnitude is when they are in completely opposite directions and the sum would be the difference between their magnitudes. The angle between them would technically be 180°

Question 20

Give an example of a nonzero vector that has a component of zero.

Answer 20

a horizontal or vertical vector

Question 21

Explain why a vector cannot have a component greater than its own magnitude.

Answer 21

because the hypotenuse is the largest part of the right triangle

Question 22

If the vectors A and B are perpendicular, what is the component of A along the direction of B? What is the component of B along the direction of A?

Answer 22

the component of each one relative to the other is zero