Download Problem Set 04

Physics 213
Fall (12) 2016
Fundamentals of Physics: Problem Set #4
Momentum and Energy Conservation: Review
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1
dV (x)
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Vspring (r) = k s (r – r0 ) 2 ; Fx = −
; dKCM = Fext • drCM ; W = F • dr
2
dx
Due: Wednesday Sept. 21 in class
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Note: Exam I is next Friday (9/23). This exam will cover material through chapter C10 (excluding
C7). The exam will consist of a number of "two-minute" like problems and a few real calculation
problems. The exam is closed book, closed notes but you may bring in one-half of an 8.5x11" sheet
of paper with handwritten notes and equations (but not worked-out problem examples). Your crib
sheet will be collected with the exam. This problem set should serve as a partial review and practice.
We will have our problem session on Tuesday evening (6:30-9:30 PM in G123) and I will hold an
exam review session on Thursday evening at 8:00 (in G123).
Reading assignment: for Monday,
C10 (Work)
for Wednesday, C11 (Rotational Energy)
Problem assignment:
C9-B.1 (Force from a potential energy graph)
C9-B.11 (Spring compression)
C9-M.9 (Glider launch with a spring)
C10-B.1 & B.2 (Dot product calculations)
C10-B.6 (Driving up a hill) [Answer: (a) –34,900 J]
C10-M.9 (Can you coast over the hill?)
Bonus: C10-M.8 (The new canyon swinging craze) [Answer: ~74 mi/hr]
A1. A hockey puck (mass = 200 g) sliding due north with speed 1.0 m/s is struck by a bb-pellet
(mass = 1.0 g) travelling due east at 30.0 m/s. The pellet imbeds itself into the puck on impact.
a) Draw figures showing the "before" and "after" states for this collision. Define symbols for all
relevant quantities in these figures.
b) Write symbolic expressions, using column vector notation, which gives the total momentum
before and the total momentum immediately after the collision.
c) Determine the velocity (magnitude and direction) of the puck (with imbedded bb) after the
collision.
(OVER)
A2. Stars are stabilized by a balance between an inward gravitational force and outward pressure due
to the intense heat generated by nuclear fusion reactions taking place in the star core. As stars age they
consume their fuel and the fusion reactions slow down. This can lead to a gravitational collapse of the
star. In extreme cases the unbalanced gravitational force is so large that even the atoms in the star
collapse with electrons and protons combining to form neutrons leading to an extremely dense object
known as a "neutron star" (for example, a neutron star with the mass of our sun has a radius of only
~12 km). Currently our sun has a radius 700,000 km and a rotation period of 30 days. If our sun
underwent the above type of collapse what would the rotation period of the resulting neutron star be?
Treat the sun as a solid sphere with I = (2/5) MR2.
[Check: many neutron stars are observed to have rotation periods on the order of a millisecond].
vo h ks A3. The above figure shows a 10,000 kg flatbed train car initially moving at 6.0 m/s, which rolls down
a 2.0 m hill and collides with 20,000 kg boxcar initially at rest. The two cars couple in the collision
and roll into a large spring (with spring constant 4.0×106 N/m). The spring sends the coupled cars
back left towards the hill. Given this information please determine the following (being sure to draw
initial and final-state pictures in each case):
a) The speed of the first car just before the collision. (Use energy conservation.)
b) The speed of the coupled cars just after the collision. (Use momentum conservation.)
c) Assuming the collision with the spring is elastic (i.e., no energy is converted to "hidden" forms),
how high back up the hill the cars go. [Hint: you do NOT need to calculate the spring compression
to answer this part.]