(bmw2393) williams Ch7-Hw1 haley (56990)
This print-out should have 14 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001 10.0 points
A horizontal spring with stiness 0.7 N/m has
a relaxed length of 15 cm. A mass of 20 g is
attached and you stretch the spring to a total
length of 31 cm. The mass is then released
from rest and moves with little friction. What
is the speed of the mass at the moment when
the spring returns to its relaxed length of
15 cm?
Correct answer: 0.946573 m/s.
Explanation:
From the Conservation of Energy (C.E.)
principle, Ei = Ef , where
1
E i = k ( 0 )2 ,
2
r1
0 eV
0.2 eV
0.4 eV
0.6 eV
0.8 eV
1.0 eV
1.2 eV
1.4 eV
1.6 eV
1
r
At r = r1 , what is the approximate value of
the kinetic energy K ?
Correct answer: 0.9 eV.
Explanation:
The total energy E = 0.4eV (green
horizontal line), and the potential energy
U = 1.3 eV (blue curve). Therefore,
K = E U = 0.4 (1.3) = 0.9eV.
003 (part 2 of 5) 2.0 points
At r = r1 , what is the approximate value of
the potential energy U ?
and
Correct answer: 1.3 eV.
1
2
Ef = m vf .
2
Explanation:
From the gure, we can see that U 1.3
eV.
This implies that
vf = ( 0 )
004 (part 3 of 5) 2.0 points
At r = r1 , what is the approximate value of
the quantity K + U ?
k
m
= (31 cm 15 cm)
0. 7 N /m
20 g
= 0.946573 m/s .
Remember to convert all quantities to appropriate units.
002 (part 1 of 5) 2.0 points
The gure below is a potential energy curve
for the interaction of two neutral atoms. The
two-atom system is in a vibrational state indicated by the green horizontal line.
Correct answer: 0.4 eV.
Explanation:
Based on the gure, K + U 0.4 eV.
005 (part 4 of 5) 2.0 points
What minimum energy must be supplied to
cause these two atoms to separate?
Correct answer: 0.4 eV.
Explanation:
For the two atoms to separate, K + U
0. Therefore, the minimum energy to be
supplied is 0.4 eV.
williams (bmw2393) Ch7-Hw1 haley (56990)
2
006 (part 5 of 5) 2.0 points
In some cases, when r is large, the interatomic
potential energy can be expressed approximately as
U=
a
.
r6
For large r , what is the algebraic form of the
magnitude of the force the two atoms exert
on each other in this case?
6a
r8
6a
= 6
r
6a
= 7 correct
r
6a
=8
r
6a
=7
r
6a
=6
r
1. Fr =
2. Fr
3. Fr
4. Fr
5. Fr
6. Fr
Explanation:
The force along the radial direction (direction along the axis joining the two atoms) is
given by
Fr =
dU
6a
= 7.
dr
r
Taking the origin at location A, the coordinates of the other locations are:
B< 9 m, 0 m, 0 m >; C< 0 m, 15 m, 0 m >;
D< 35 m, 0 m, 0 m >; E< 0 m, 15 m, 0 m >
Path 1 (A to E): What is the work done
by the gravitational force of the Earth on the
73 kg person during the elevator ride from A
to E?
Correct answer: 10731 J.
Explanation:
The gravitational force is
Fgrav =< 0, m g, 0 >=< 0, 715.4 N, 0 >
The work done by force this in moving from
A to E (r =< 0, 15 m, 0 >) is:
Wgrav = Fgrav r
= (715.4 N)(15 m) = 10731 J
008 (part 2 of 8) 1.0 points
Path 2 (A to B to C to E): What is the work
done by the gravitational force of the Earth
on the person as he walks from A to B?
Correct answer: 0 J.
007 (part 1 of 8) 1.0 points
There are three dierent ways to get from
location A to location E in the gure below.
Along path 1, you take an elevator directly
from location A straight up to location E.
Along path 2, you walk from A to B, climb
a rope from B to C, then walk from C to E.
Along path 3, you walk from location A to
D, then climb a ramp up to location E. The
following questions focus on the work done on
a 73 kg person by the Earth while following
each of these paths.
Explanation:
Since the displacement r =< 9 m, 0, 0 >
the scalar product with the gravitational force
< 0, 715.4 N, 0 > is zero.
009 (part 3 of 8) 1.0 points
What is the work done by the gravitational
force of the Earth on the person as he climbs
from B to C?
Correct answer: 10731 J.
Explanation:
williams (bmw2393) Ch7-Hw1 haley (56990)
r =< 0, 15 m, 0 > so
Wgrav = Fgrav r
= (715.4 N)(15 m) = 10731 J
010 (part 4 of 8) 1.0 points
What is the work done by the gravitational
force of the Earth on the person as he walks
from C to E?
3
Explanation:
r =< 0, 15 m, 0 > < 35 m, 0, 0 >
=< 35 m, 15 m, 0 >
Wgrav = Fgrav r
= (715.4 N)(15 m) = 10731 J
Correct answer: 0 J.
Explanation:
Since the displacement r =< 9 m, 0, 0 >
the scalar product with the gravitational force
< 0, 715.4 N, 0 > is zero.
011 (part 5 of 8) 1.0 points
What is the total work done by the gravitational force of the Earth on the person as the
person goes from A to E along path 2?
Correct answer: 10731 J.
Explanation:
Adding up the contributions from each segment of the path gives the total work
Wgrav = 010731 J + 0
= 10731 J
012 (part 6 of 8) 1.0 points
Path 3 (A to D to E): What is the work done
by the gravitational force of the Earth on the
person as he walks from A to D?
Correct answer: 0 J.
Explanation:
Since the displacement r =< 35 m, 0, 0 >
the scalar product with the gravitational force
< 0, 715.4 N, 0 > is zero.
013 (part 7 of 8) 2.0 points
What is the work done by the gravitational
force of the Earth on the person as he climbs
from D to E?
Correct answer: 10731 J.
014 (part 8 of 8) 2.0 points
What is the total work done by the gravitational force of the Earth on the person as the
person goes from A to E along path 3?
Correct answer: 10731 J.
Explanation:
Again, adding up individual contributions
from the dierent segments gives
Wgrav = 010731 J
= 10731 J
You calculated the work done by the gravitational force of the Earth on the person along
three dierent paths and found that they are
all the same. Does this make sense? Think
about the change in potential energy in all
three cases.