Physics 113
–Morning Session, Summer 2013
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.