Honors Physics-Chapter 3 CONCEPTUAL QUESTIONS

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

A nonzero vector with a component of 0 would either be straight up/down (x component is zero) or straight left/right (y component is zero).

Which of the following is a vector: a person's height, the altitude on 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?

Acceleration- the only one that has a direction

Two campers in a national park hike from their cabin to the same spot on a 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 8.2 km. What is the final displacement of each camper?

Displacement is the distance from where they started to where they ended. 5 km at 40o NE

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?

Greatest magnitude is when they lie in the same direction and the sum would be the scalar sum of the two vectors. Technically, the angle between the two would be 0o . Smallest magnitude is when they are in complete opposite directions and the sum would be the difference between their magnitudes. The angle between them would technically be 180o . In general, the possible resultants are somewhere between the sum of the two vectors and the difference between them. A 5 m vector and a 2 m vector can never give you an 8 m vector or a 1 m vector, but can give you anything from 3 - 7 m.

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 ?

If they are perpendicular, then the component of each one relative to the other is 0. (don't worry about this so much, we are going to orient our vectors in relation to the x axis).

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 on the circle shown in Figure 3.53. What other information would he need to get to Sacramento?

In order to get to Sacramento, he needs to know which direction to fly. If he flies SW, he will end up somewhere in the ocean. He needs to fly 123 km at 45o NE.

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?

No, the steps need to be of the same size. You can if you add a third step.

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

Scalars and vectors both have magnitude (size) and a unit. Only vectors have a direction also.

Give a specific example of a vector, stating its magnitude, units, and direction.

The Earth is pulling down on me with a force of 600 N.

A basketball player dribbling down the court usually keeps his eyes fixed on the players around him. He is moving fast. Why doesn't he need to keep his eyes on the ball?

The ball will move with him because he is giving it the same horizontal velocity as he has.

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

The components would be the parts that turn a slanted arrow into a right triangle. The hypotenuse of a right triangle is the longest side.

The hat of a jogger running at constant velocity falls off the back of his head. Draw a sketch showing the path of the hat in the jogger's frame of reference. Draw its path as viewed by a stationary observer.

The hat would land at the joggers feet. An observer would observe the hat falling forward (in the same direction as the jogger was traveling) in projectile motion.

For a fixed initial speed, the range of a projectile is determined by the angle at which it is fired. For all but the maximum, there are two angles that give the same range. Considering factors that might affect the ability of an archer to hit a target, such as wind, explain why the smaller angle (closer to the horizontal) is preferable. When would it be necessary for the archer to use the larger angle? Why does the punter in a football game use the higher trajectory?

The two angles that give the same range are complementary angles. An archer would want to use the smaller of the two angles (closer to the ground) because it is in the air for the shortest amount of time, so would be affected less by wind and air resistance. An archer might want to use the larger angle if s/he needed to shoot over something like a wall. The punter in a football game uses the larger angle because that keeps the ball in the air for a long time, allowing his team to get down to where the ball will land so they can tackle the guy that catches the ball more easily.

During a lecture demonstration, a professor places two coins on the edge of a table. She then flicks one of the coins horizontally off the table, simultaneously nudging the other over the edge. Describe the subsequent motion of the two coins, in particular discussing whether they hit the floor at the same time.

The two coins will fall at the same rate. The nudged one will fall straight down, whereas the flung one will fall in a half parabola. Both coins though will land at the same time, because when they land is determined by their initial vertical velocity, and both coins had an initial vertical velocity of 0 m/s.

A clod of dirt falls from the bed of a moving truck. It strikes the ground directly below the end of the truck. What is the direction of its velocity relative to the truck just before it hits? Is this the same as the direction of its velocity relative to ground just before it hits? Explain your answers.

Velocity relative to the truck (compared to the truck) would be zero. It has the same velocity as the truck. It's velocity relative to the ground is that it continues to move forward.

What frame or frames of reference do you instinctively use when driving a car? When flying in a commercial jet airplane?

When driving a car, we instinctively compare our motion (frame of reference) to the road. When flying, the ground is often out of sight (unless landing/taking off), so the plane itself or the clouds become the frame of reference. If I were walking on the plane, I would use the plane as a frame of reference; if I were judging my speed, I would probably compare my motion to the clouds below me.

If someone is riding in the back of a pickup truck and throws a softball straight backward, is it possible for the ball to fall straight down as viewed by a person standing at the side of the road? Under what condition would this occur? How would the motion of the ball appear to the person who threw it?

Yes, there is a video demo of that. You would have to throw it backwards at the exact same speed the truck was going. https://www.youtube.com/watch?v=BLuI118nhzc From the point of view of the person who threw it, it would look like it was shot out and follow parabolic motion.

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?

You can end up back at your starting point if you step one way, then step back the same distance.

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

You cannot add a scalar to a vector because you don't have a direction for the scalar. Scalar addition uses straight addition, vector addition uses trig functions.

Answer the following questions for projectile motion on level ground assuming negligible air resistance (the initial angle being neither 0º nor 90º): (a) Is the acceleration ever zero? (b) Is the acceleration ever in the same direction as a component of velocity? (c) Is the acceleration ever opposite in direction to a component of velocity?

a) the acceleration is never zero... gravity is what is accelerating it, and no one turned the earth off. b) yes the acceleration is in the same direction as the vertical component of the velocity after the halfway point when the projectile is on its way back down. c) Yes, the acceleration is opposite the vertical component of the velocity during the first half when the projectile is still on its way up.

Answer the following questions for projectile motion on level ground assuming negligible air resistance (the initial angle being neither 0º nor 90º): (a) Is the velocity ever zero? (b) When is the velocity a minimum? A maximum? (c) Can the velocity ever be the same as the initial velocity at a time other than at t = 0 ? (d) Can the speed ever be the same as the initial speed at a time other than at t = 0 ?

a) the velocity is never zero... it is still moving horizontally even when it stops moving vertically. b) The velocity is at a minimum at the top of the flight where the vertical velocity becomes zero. It is at a maximum at the beginning and the end where the vertical velocity is at its max. The vertical velocity at the beginning is equal but opposite to the vertical velocity at the end. c) no because they are opposite directions so they have opposite signs... not the same d) yes, see b