PHHYA10S-Test-1-SOL-2023-grading
pdf
keyboard_arrow_up
School
University of Toronto, Scarborough *
*We aren’t endorsed by this school
Course
10
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
10
Uploaded by CommodoreIce7997
PHYA10F – TEST#1
Sample Solution
1
Instructor: Prof. Salam Tawfiq
Oct. 14, 2023
Time:
90 Minutes
Note: Write your official name as it appeared in ACRON and write your practical
group number and/or name of your TA. Falling to do so, 2 points will be deducted.
You may use a non-programmable calculator and one aid sheet.
The aid sheet must
be hand-written on a normal (8.5 by 11) page, one side is acceptable with a maximum
of 20 equations
. It should contain formulae only no definitions, graphs, explanation or
problems and will be collected at the end of the test. No other aids are allowed. This
includes neighboring students. Cell phones and other electronic devices will be
confiscated if they make noise or if you are using them.
Answer all the questions.
There are 10 multiple-choice (MC) questions and 3 short
answer questions & problems.
The multiple-choice questions are worth 3 mark each. The
short answer questions and problems are worth 10 marks each. The test is out of a total of
60 marks.
Do not remove the staple. There are a couple of blank sheets at the end for rough work;
you may carefully remove them if you wish.
You have a total of
90 Minutes
to write this test. You are advised not to
spend more
than 4 minutes
on each question on part-A of the test and
not more than 14 minutes
on
each question of part-B.
Do not open this booklet before the Test begins.
Part-A (MC)
/30
Part-B
Q1
/10
Q2
/10
Q3
/10
Total
Out of 60
GOOD LUCK
PHYA10F – TEST#1
Sample Solution
2
Fill in the table below with your best choice
for part A
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
C
C
E
B
A
A
C
C
Q9
Q10
A
B
Provide your solution for part-B in the space provided.
PHYA10F – TEST#1
Sample Solution
3
Part-B: Problem Solving
Q1:
(10 points total)
A.
i.
What is the rocket's maximum altitude?
The maximum altitude is
In the acceleration phase:
In the coasting phase,
The maximum altitude is 54.8 km
ii.
How long is the rocket in the air before hitting the ground?
Then
is found by considering the time needed to fall 54,800 m:
iii.
Draw a clear velocity-time graph for the rocket from liftoff until it hits the
ground. On the graph, identify the time when the rocket runs out of fuel, max
altitude & hitting the ground.
a
=
−
g
.
y
2
.
y
1
=
y
0
+
v
0
(
t
1
−
t
0
)
+
1
2
a
(
t
1
−
t
0
)
2
=
1
2
at
1
2
=
1
2
(30 m/s
2
)(30 s)
2
=
13,500 m
v
1
=
v
0
+
a
(
t
1
−
t
0
)
=
at
1
=
(30 m/s
2
)(30 s)
=
900 m/s
v
2
2
=
0
=
v
1
2
−
2
g
(
y
2
−
y
1
)
⇒
y
2
=
y
1
+
v
1
2
2
g
=
13,500 m
+
(900 m/s)
2
2(9.8 m/s
2
)
=
54,800 m
=
54.8 km
(
≈
33 miles).
v
2
=
0 m/s
=
v
1
−
g
(
t
2
−
t
1
)
⇒
t
2
=
t
1
+
v
1
g
=
122 s
t
3
y
3
=
0 m
=
y
2
+
v
2
(
t
3
−
t
2
)
−
1
2
g
(
t
3
−
t
2
)
2
=
y
2
−
1
2
g
(
t
3
−
t
2
)
2
⇒
t
3
=
t
2
+
2
y
2
g
=
228 s
2 points
2 points
2 points
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
PHYA10F – TEST#1
Sample Solution
4
B.
The displacement (or angular position) is the area under the angular velocity graph (see
Figure to right), but we need calculus to do this for a nonlinear graph.
2 points
2 points
PHYA10F – TEST#1
Sample Solution
5
Q2:
(10 points total)
A.
i.
Draw a free body diagram for
࠵?
!
,
࠵?
"
& the knot.
The free body diagram for the two blocks and the knot are shown below.
ii.
What is the ratio of the masses
࠵?
!
/࠵?
"
?
The free body diagram for the two blocks and the knot are shown above
We need to look at the forces acting on the knot (the junction of the three cables). These
are shown in Fig.(a) above. The vertical cord must have a tension equal to the weight of block A
(which we’ll call WA, see Fig (c)) because at its other end this cord is pulling up on A to support
it. Let the tensions in the other cords be T
1
for the horizontal rope and T
2
for the rope that pulls at
30
!
above the horizontal. The knot is in equilibrium so the forces acting on it add up to zero. In
particular, the vertical components of the forces add to zero, giving:
knot
2 points
1 point
1 point
PHYA10F – TEST#1
Sample Solution
6
So, the masses ratio is
#
!
#
"
= ࠵?
$
࠵?࠵?࠵?࠵?
2 points
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
PHYA10F – TEST#1
Sample Solution
7
B.
i.
What is the magnitude and direction of the acceleration of the mass?
ii.
Determine the tension in the cable.
See FBD of mass at right.
iii.
What is the value of
࠵?
on the planet?
1 point
1 point
2 points
PHYA10F – TEST#1
Sample Solution
8
Q3:
(10 points total)
.
Part-I
For this part, assume the blocks are moving together.
a)
Draw the free-body diagram (FBD) for each one of the blocks.
b)
What is the minimum force
࠵?
%
to get the blocks moving (assuming they are static
at
࠵? = 0
)?
c)
Find the maximum force
࠵?
&
to pull the large block with, such that the little block
doesn’t slide.
From the FBD of the two blocks, we have
2 points
2 points
1 point
PHYA10F – TEST#1
Sample Solution
9
d)
Find the acceleration
࠵?
&
of the blocks in this case.
Part-II
For this part of the problem, assume the force
࠵? = ࠵?
’
> ࠵?
&
is large enough that the
little block starts sliding. Both coefficients of friction are now
࠵?
(
so be careful about the
labeling and magnitudes of your friction forces. You may want to redraw your free-body
diagrams.
e)
Which way will the little block move with respect to the large block? Which way
will the little block moves with respect to the desk. Briefly explain.
f)
Find the acceleration
࠵?
)
of the top (small) block.
g)
Find the acceleration
࠵?
*
of the bottom (large) block. Assume that the magnitude
of
࠵?
’
is given.
1 point
1 point
1 point
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
PHYA10F – TEST#1
Sample Solution
10
h)
(Bonus)
The blocks are at rest when we start applying the force
࠵?
’
at time
࠵? = 0
.
Find the time
࠵?
when the little block falls off from the large block. Neglect the
size of the small block and express your answer in terms of
࠵?
,
࠵?
)
, and
࠵?
*
,
2 points
2 points