Physics 116a02: Extra Hints for Assignment 4
Department of Physics and Astronomy, Vanderbilt University
Things to Think About for Assignment 4
- Object accelerating on a ramp
- For parts B and C: When the object is at the bottom of the curve, or at the top of the curve,
think of the object as being momentarily in circular motion. Then think where is the
center of that circle each time.
- Conceptual problem about projectile motion
- For part B: Remember that t0 = 0.
- Position, velocity and acceleration
- For part C: All the kinematic variables which are mentioned are vectors,
and remember how vectors are defined.
- Introduction to projectile motion
- For part A: In two dimensional motion, the components of a vector will
have an algebraic sign.
- For part C: The red dots on the left vertical of the applet result, and the
cyan colored dots on the bottom horizontal, represent the equal time interval
projections of the projectile's motion (green dots) on the vertical and the
horizontal axes. You can reset and re-run the applet if you like.
- For part D: You have to run a second applet, and the answer is obtained
using g = 10 meters/second-squared instead of 9.8
meters/second-squared.
- After you complete part E, you can run another applet which allows you to
change the horizontal speed of one or both of the falling balls. You can do
this as often as you like, and there are no extra questions to answer. You
have to reset each time before changing the horizontal speeds again. It's a
good learning experience.
- Accelerating along a racetrack
- For part A: This section of the track is actually curved, like all the
other track sections except for section F. Remember that all the cars are
traveling at constant speed. (Would your answers change if the speeds were not
constant, as would likely be the case for a real race track?)
- For part E: Imagine what size circle would be tangent to the path
of the car at each of the points. (Also there are two letters in the answer to
part E, and the letters need a comma between them.)
- Arrow hits apple
- For part A: You are now to use g = 9.8 meters/second-squared.
- For part B: This is not the equivalent of the "shoot-the-monkey"
demonstration done in class on Thursday.
- Circular launch
- The several hints will walk you through the solution of this problem, which may
not be obvious to you immediately. When the ball exits the top of the chute
it is momentarily traveling horizontally, and then it begins its free-fall
acceleration. Also, you don't have to worry about anything that
happens while the ball is traveling inside the chute. All that matters is the
speed which the ball has when it exits the chute. (Extra thought question: Is
the horizontal speed of the ball the same when it enters the chute as when it
exits the chute? If not then why not? This involves concepts not covered in
the first few chapters, but doesn't affect your answer to the MasteringPhysics
question.)
- Projectile motion conceptual
- Direction of velocity at various times in flight for a projectile motion
conceptual question
- For parts C and D: You need to be looking at the second (Intro 2) figure.
- Projectile motion ranking task
- For Part A: Notice that the balls do not all have the same initial speeds.
- Extra thought questions for part B: If the rankings for part B is the same as for part A, think
about why this must be so. On the other hand, if the part B and part A
rankings are different, what accounts for that difference?
- Delivering a package by air
- For part A: The wording is changed from dropped in the problem
statement on the left, to ejected in this question. This is a poor
choice of wording since ejected could mean with some initial downward
velocity component. In fact, you should assume that the package is dropped,
meaning no initial vertical speed, but it does have an initial horizontal speed
component.
- Throwing stones
- Exercise 3.12
- The problem statement refers to a 510 N swimmer. The 510 N,
where N is the abbreviation for Newtons, refers to the weight of the
swimmer. Weight is a physical quantity which we will introduce in Chapter 4,
and weight w = mg where m is the mass of an object. So this
swimmer has a mass of 510/9.8 = 52 kg, which is equivalent to about
114 pounds (expert that pounds is a unit of force). You don't need to use the
weight, nor the mass, in order to solve this problem.
- Exercise 3.20
- The y axis is being defined as usual with positive in the upward
direction.
- For part F: It is unusual to ask for an answer to 4 significant digits
when only 3 significant digits are in the problem statement.
- For part H: Before submitting your answer you should think whether your
result is consistent with how high off the ground a normal height shot-putter
will typically release the object (i.e., a few cm, or several meters
would be unusual.)
- Exercise 3.29
- For Part A: This radial acceleration is associated with the speed that an object has
by virtue of being fixed on the Earth's rotating surface.
- For Part C: The fact that if the Earth were spinning too fast then any
object could no longer be kept on its surface by gravity alone is something you will appreciate
more after you complete Chapters 4 and 5. For this problem you just have to
figure out what is needed to make arad > g.
- Exercise 3.42
- For part A: The problem statement (left side) does not mention the speed
of the boat in the water. The part A question does give that speed, in a
parenthetical sentence. This boat speed is essential to solving the problem.
- For parts B and C: A good diagram of velocity vector addition and the motion
is also essential.
- Problem 3.89
- For part A: The initial angle of the ball above the horizontal is theta
+ phi. The resulting answer is a pretty lengthy expression in the four parameters.
- For part B: The maximum range along the incline is the x/cos(theta)
function which is the answer to part A. How do you find the maximum of a
function with respect to a particular variable? (Answer can be given in either
radians or degrees since theta could have been given in either radians or degrees.)
- Exercise 3.2
- Exercise 3.6
- Although the problem describes motion in the x and y
directions, both of these coordinates are in a flat, horizontal plane ("open field"). The acceleration
due to gravity is not relevant in this problem. If it were necessary to
introduce gravity, then we would also introduce a z coordinate for the
third dimension of position.
- For Part C: Even though I used the 2 significant digit answers to part A
and part B, the program still gave feedback about a round-off error, although
the answer was accepted. If I used the actual 3 significant digit answers,
then I got the answer that the program said was correct. These kinds of
round-off issues are not important if no points are deducted. (The same thing
happened with part D, but may not happen to you since this is a randomized
input number problem.)
- Test your understanding of the velocity vector
- Test your understanding of the acceleration vector
- Test your understanding of projectile motion
- Test your understanding of circular motion
This page was last updated on January 23, 2008