Physics 116a02: Extra Hints for Assignment 9
Department of Physics and Astronomy, Vanderbilt University
This hints page completed on February 21.
Things to Think About for Assignment 9
- Conservation of Momentum in Inelastic Collisions
- For part A: The "this collision" means a completely inelastic collision of
two masses, which were presumably moving before the collision.
- For part B: A somewhat tricky question in my opinion. In one dimensional collisions,
many physicists would give answer C, assuming that they will attach an algebraic
sign to each speed. However, this program takes the view that the speeds are
always positive, so you should given your answer with that assumption in mind.
Finally, the question doesn't specify whether the collision is in one or two
dimensions, and that should give you another clue as to what answer is correct
for this program.
- For part C: Remember part B.
- For part D: Only one answer is possibly correct, even though the question
is qualified as "Of what can one be certain?".
These problems are assuming that no external forces are acting.
- For part E: Review the comments which I added on the homeworks web page
after Assignment 5, in light of the correct answer to part D.
- Impulse on a baseball
- For part A: No extra hint needed. As an aside for baseball realism, one can consider
the batter to have a weight of 200 pounds, assuming steroids are no longer an
option. This corresponds to a mass of about 91 kg, and a weight of 891 N.
So a 12,000 N force on a ball is more than 13 times the batter's own weight.
- For part C: Look at the Intro 2 figure. Note that the two figures have
the force acting over the same time interval too.
- For part E: No extra hint needed. For comparison to major league or even
SEC baseball, a good fastball pitcher should throw a baseball at least as
fast as 85 miles/hour. An excellent fastball pitcher (such as Randy Johnson in prior
years) would have speeds above 95 miles/hour. The speed of 32 m/s in this
example works out to 72 miles/hour. A great major league hitter, like Mickey
Mantle 55 years ago, could hit a 95 mile/hour fastball with a speed of
130 miles/hour going out. Assuming that the ball was pitched to Mantle on a horizontal
line, and then he hit the ball such that it left the bat at
45 degrees above the horizontal, what
force would have been required taking again that the bat was on the ball for 0.0007
seconds? (Good multiple choice question!)
- Momentum and Internal Forces
- For part A: No extra hint needed. Note that even though there are no
arrows above the quantities, the momentum and the velocity variables are
vectors.
- For part B: You might be tempted to just write 0 for the derivative,
since the problem statement specified a closed system, meaning
that there are no external forces and hence the system momentum is
conserved (constant). However, the program wants an answer in terms
of the variables which are listed.
- For part D: Interpret "due to" as "caused by", and you are not being
asked how is acceleration defined in kinematics.
- A Bullet is Fired into a Wooden Block
For part A: The "collision" includes the time from when the bullet entered
to block of wood until the time that the bullet has stopped inside the block.
All collisions take place over some small interval of time in fact.
- Energy in an Inelastic Collision
- Kinetic Energy and Momentum Conceptual Question
- No extra hints needed. This is a good, straightforward conceptual
question which tests how well you can relate the various kinematic
quantities using the assumption of a constant force acting on different
sized masses.
- Momentum and Kinetic Energy
- A one-dimensional inelastic collision
- For part A: Give your numerical answer to 3 significant digits.
- Center of Mass and External Forces
- For part B: The coordinate x2 in the figure is more
postive than the coordinate x1. So the distance
x2 - x1 is a positive number in all the answer options.
- For part F: Compare your answer to the correct answer to part D.
- For part I: Change to the new figure for this part.
- For part J: Change to the new figure for this part.
- For part K: Think about what it means when the problem statement
says that F1x and F2x are components.
- For part L: Change to the new figure for this part. You might
be tempted to give the simplest answer to this problem, and you
would be correct to do so this time. Also, assume that no external forces
are acting, even though the problem does not explicitly state that.
- Exercise 8.48: Center of mass for the Sun-Jupiter combination
- For part A: You have to look up the solar system data which is on
page A-8 in the appendix section of the text. Don't confuse
the Radius column (smaller distances) with the Orbital radius
column. This is a simpler version of the water molecule
problem which we did in class on Thursday.
- For part B: You might check what would be the answer for say
Uranus or Neptune, to see if these two planets would give the
same answer as for Jupiter.
- Exercise 8.50: Center of mass for two moving cars
- For part A: Compute the center-of-mass position for the instant of
time shown in the figure.
- For part B: Instead of saying "for the above data" (answer to part A),
the data are in figure describing the problem.
- Exercise 8.58: Rocket ejecting gas at high speed
- You should be able to figure this out without needing
to read section 8.6 in the textbook, but using the impluse
equations instead. You can read section 8.6 on your own,
but it will not be covered in the test. The important
equation in section 8.6 is Equation 8.39, which is known
as the Rocket Equation. This equation in turn leads
the Equation 8.40 which calculates the speed which
a rocket achieves in free space, given some initial
speed v0, an exhaust speed of the burned fuel vex,
and a constant rate of fuel burn which takes the rocket's
mass (including fuel) from an initial large value m0
to a much smaller value m. Most of a rocket's initial
mass is composed of fuel to be burned. The subject of
rocket propulsion is covered in the advanced mechanics
course, Physics 227a.
- Exercise 8.100: Woman walking in a canoe
- We talked about this kind of problem in class on Thursday,
the two men on a smooth ice surface pulling each other together on a rope,
with no external forces acting. You can ignore gravity in this
problem.
- Exercise 8.2: Test your understanding of conservation of momentum
- There is also another not-possible occurence, which has
the third piece going at negative y-velocity, no matter what
the value of the x-velocity.
- Exercise 8.3: Test your understanding of collisions
- As usual in collisions, assume that there are only internal forces
acting during the collision.
- Exercise 8.22: Fission (splitting) of a nucleus
Back to Main Menu
This page was last updated on February 21, 2008