Physics 113 –Morning
Session, Summer 2012
Participation Points #1
To be turned in at the end
each discussion session
First do “quick answer” then
try “detailed answer” when available
Student’s Name:_______________________ Team #______________
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1-1.
Changing
units. In many highways in
In
many
1.2.
Dimensional
analysis. The spring elastic
potential energy is given by U=½ k xα , where k is a constant
with dimensions M/T2, and x is the elongation with obviously
dimension of length, which is written as L. Determine α using dimensional
analysis.
Quick
answer:
Detailed
answer: The dimension of energy (e.g. from a kinetic energy
½ mv2) is 
, while the dimension of U is 
, by comparison α=
1.3.
Estimation. Estimate the number of people holding hands needed
to form a line from NY to LA. Fill in the blank.
Quick
answer:
Detailed
answer:
One way to estimate the NY-LA distance is based on
how long a flight would take with an average airplane speed
2.1.
Acceleration. An egg falls from a second story, taking 1.1s and
reaching a speed of 11m/s just before hitting the ground. On contact with the
ground, the egg stops completely in 0.11s. Calculate the average acceleration
when falling and deceleration when stopping. Note the signs of these
accelerations.
Quick
answer:
Detailed
answer: 
2.2.
Using
the equation of motion. A horse accelerates from
rest at 4 m/s2 over a distance of 50 m to outrun a predator. What is
its final speed?
Quick
answer:
Detailed
answer: the equations of motion are
v=at, and x=½ at2, the final speed v is needed, with the
acceleration a and distance x given. Expression: Since t is not given neither asked for, it can be
eliminated from the two equations to obtain:
x=½ v2/a, or
v=_________________
Number: Substituting
in the data v=________________=______________m/s
2.3.
Constant
acceleration of gravity. A
model rocket leaves the ground, heading straight up at 49m/s. What is it
maximum altitude?
Quick
answer:
Detailed
answer: Since a= - g; the equations
of motion are (1) v=vi –gt; and (2) x=vit - ½ gt2. The maximum altitude x is needed and the
known quantities are the gravity constant g and the ___________________
(quantity name and symbol),
Expression: t is unknown but can be eliminated from the equation (2)
by noting that at the maximum altitude, v=____m/s, then from equation (1)
t=__________(expression), which is now used in equation (2) to leave x in term
of the known quantities, that are again
_____ and ______, i.e. x=___________________________________(expression).
Number: x=½ vi2/g = ½ __________/9.81=
______m
Comment: This equation and that in the previous
question come from a same more general equation, consult the textbook.
3.1
Vectors. Two vectors A and B have the
same magnitudes L and are at right angles, draw the vector 3A-B and
write its magnitude of in term of L,
3.2
Unit
vectors. Write the expression for the unit
vector sum of i, j, k ; give its
magnitude the spherical angles φ
(of the vector’s projection onto the XY plane, w.r.t the X-axis) and θ (of
the vector w.r.t. the Z-axis)
3.3 Relative motion. You wish to row straight
across a 65m wide river. If you can row at a steady 4m/s relative to the water
and the river flows at 3m/s, in what direction should you head, and how long
will you take to cross it?
Quick
answer:
Detailed
answer: Let’s assume the river
flows to your right
(1) If you just head straight across the river
where will you end up? (a) Straight across the river (b) To the right of that
point (c) to the left of that point.
(2) Since you should head to the _______, draw the
river velocity vector (this velocity is with respect to the ground); then your
velocity vector (this velocity is with respect to the river, since you row ‘on
top’ of it) such that your actual velocity vector (this is with respect to the
ground) points straight across the river.
From Pithagoras Theorem, the your actual velocity
has a magnitude of _______________________________________(m/s). And so it will
take __________________ (s) to straight cross the river.