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PCS 211: Mechanics
MIDTERM #2
Fall 2023
1
Toronto Metropolitan University – Department of Physics
PCS 211 – Physics: Mechanics
Midterm Test 2 – November 17, 2023
Check the name of your professor:
Read the following attentively:
•
This test consists of 1 long answer problem and 14 multiple-choice questions.
•
Each multiple choice question is out of 2 points. In order to score 2 points, you should both
select a correct answer and reasonably justify your selection in the space provided with
maximum clarity and detail. If you only select a correct answer without meaningful
justification, you can only score 1 point.
•
Select the option that is closest to the correct answer.
Circle it in this booklet
and
fill in the
appropriate bubble on the bubble sheet. The bubbles must be filled using a pencil.
•
This is a closed book test; pens, pencils, erasers, calculators (Sharp EL-546 and the Casio
FX-991 only) and your Toronto Metropolitan University ID are the only allowed items on
your desk.
•
Show all your work in this booklet.
We will check your work for all questions, and if your
choice is not justified by the work done on this booklet, credit will not be given.
•
All electronic devices INCLUDING WATCHES must be turned off and placed out of
reach.
•
Coats, jackets and bags must be placed out of reach (under the seats).
•
Your TMU photo ID must be on your desk at all times.
•
Perform ALL your calculations to an accuracy of 5 significant figures and provide your
final answer to an accuracy of 3 significant figures.
Sign here to signify you read the instructions
Please Print Clearly:
Student:
Last Name
First Name
Student Number: _
_
Section:
Dr. Da Silva
Dr. Falou
Dr. Rebello
Dr. Singh
Dr. Toronov
Dr. Yuan
PCS 211: Mechanics
MIDTERM #2
Fall 2023
2
PART 1: This is a full answer problem. Ensure that you write out your full solution, with all
steps, clearly and completely [6 marks].
The figure below shows three blocks initially at rest
on a frictionless table. The blocks have masses,
࠵?
!
= 1.00࠵?࠵?
,
࠵?
"
= 2.00࠵?࠵?
,
࠵?
#
= 3.00 ࠵?࠵?
. You
exert a horizontal force
࠵?
⃗
= 18.0 ࠵? ࠵?
on the block on
the left.
1)
Find the acceleration of the blocks [2 marks]. Write the solution in the space below.
(Make sure your equations are understandable, or this part will be marked as zero)
Newton’s Second Law - dynamic:
࠵?
⃗
$%&
= ࠵?
’(
)⃗
!"!
’&
= ࠵?࠵?
⃗
+,+
System: All three masses (
࠵?
!
= 1࠵?࠵?
,
࠵?
"
= 2࠵?࠵?
,
࠵?
#
= 3 ࠵?࠵?
)
Surroundings:
Earth, Surface
Ignore verAcal (y) direcAon, because weight of each block balanced by normal reacAon.
Focus on x direcAon
࠵?
⃗
$%&
= (࠵?
!
+ ࠵?
"
+ ࠵?
#
)࠵?
⃗
à
࠵?
⃗
= (࠵?
!
+ ࠵?
"
+ ࠵?
#
)࠵?
⃗
à
࠵?
5555⃗ =
࠵?
)⃗
(࠵?
࠵?
0࠵?
࠵?
0࠵?
࠵?
)
= 3.00 i m/s
2
2)
Draw the free body diagram for the middle block in the space below [2 marks]. (Make
sure your diagram is understandable, clearly label each force with subscripts like F
A on B
or this part will be marked as zero)
3)
Find the force that the block on the right exerts on the middle block [2 marks]. (Make
sure your equations in the space below are understandable, or this part will be marked as
zero)
Next use Newton’s third law because force of
࠵?
#
on
࠵?
"
is equal and opposite to force of
࠵?
"
o
࠵?
#
:
࠵?
⃗
# 3$ "
= −࠵?
⃗
" 3$ #
We do this b/c it is easier to solve for forces on
࠵?
#
than on
࠵?
"
, since there is only one
force acAng on
࠵?
#
System: Masse (
࠵?
#
= 3 ࠵?࠵?
)
n
m
2
g
F
3 on 2
F
1 on 2
PCS 211: Mechanics
MIDTERM #2
Fall 2023
3
Surroundings:
Earth, Surface, Mass (
࠵?
"
= 2࠵?࠵?
)
Ignore verAcal (y) direcAon, because weight of each block balanced by normal reacAon.
Focus on x direcAon, and note that acceleraAon is the same for ALL blocks, because they
move together
࠵?
⃗
$%& 3$ #
= ࠵?
#
࠵?
à
࠵?
⃗
" 3$ #
= ࠵?
#
࠵?
à
࠵?
⃗
" 3$ #
= ࠵?
#
4
⃗
(5
&
05
’
05
(
)
Finally:
࠵?
⃗
# 3$ "
= −࠵?
⃗
" 3$ #
= −
5
(
4
⃗
(5
&
05
’
05
(
)
= −
(#)(!6࠵?)
8
= −9.00 ࠵? ࠵?
PCS 211: Mechanics
MIDTERM #2
Fall 2023
4
PART 2: Multiple choice questions. Enter your response on your bubble sheet starting at
question #1.
1. A particle is moving with a kinetic energy of 1 kJ and a momentum of 55.0 kg m/s at a given
point in time
t
. What is the speed of this particle at this point in time?
a) 17.6 m/s
b) 28.9 m/s
c) 36.4 m/s
d) 59.8 m/s
c) 61.2 m/s
࠵? =
1
2
࠵?࠵?
"
࠵? = ࠵?࠵? →
࠵? =
࠵?
࠵?
࠵? =
2࠵?
࠵?
=
2(1000)
55
= 36.4 ࠵?/࠵?
2. A 22.0 g lead bullet is shot at “bullet proof” glass. At the point of impact, the bullet has a
velocity of -1250
i
m/s. The impact with the wall lasted 0.600 micro-seconds and resulted in the
bullet travelling at a velocity of 625
i
m/s after the collision. What is the average force exerted on
the bullet during this collision?
a) 6.88 x 10
7
B̂
N
b) 7.98 x 10
7
B̂
N
c) 5.99 x 10
6
B̂
N
d) (7.21
B̂
+ 8.92
D̂
) x 10
6
N
e) (7.25
B̂
+ 8.45
D̂
) x 10
7
N
࠵? = ࠵?
࠵?
− ࠵?
࠵?
= ࠵?(࠵?
࠵?
− ࠵?
࠵?
) = 0.022 kg J625 ࠵?
m
s
− M−1250 ࠵?
m
s
NO = 41.25 ࠵? kg m/s
MP ࠵?N
;(<
=
࠵?
Δ࠵?
=
41.25 ࠵? kg m/s
0.600 × 10
=8
s
= 6.88 × 10
>
࠵? N
PCS 211: Mechanics
MIDTERM #2
Fall 2023
5
3. How much work must an external force do to change the length of a spring (with spring
constant 50.0 N/m and an unstretched length of 5.00 dm) from 7.00 dm to 6.00 dm?
(a)
0.750 J
(b)
3.25 J
(c)
0.500 J
(d)
-0.750 J
(e)
-3.25 J
W =
kx
f
2
/2-
kx
i
2
/2 = 50/2*[(0.6-0.5)
2
-(0.7-0.5)
2
] = -0.750 J
4. A constant force of magnitude
F
= 16.0 N directed at an angle
࠵?
= 22.0° below the horizontal
(as shown in the figure below) pushes a
m
= 2.40 kg crate a distance
d
= 2.00 m along the
frictionless floor. Determine the work done by this force on the crate.
a.
0.00 J
b.
29.7 J
c.
60.1 J
d.
−29.7
J
e.
−60.1
J
The applied force does work given by
W
=
F
Δ
r
cos(
࠵?
) = (16.0 N)(2.00 m)cos(22.0°) = 29.7 J.
5. A 36.5 kg box initially at rest is pushed 5.80 m along a rough, horizontal
floor with a constant applied horizontal force of 145 N. If the coefficient of
friction between box and floor is 0.300, find the change in kinetic energy
of the box.
a)
37.1 J
b) 62.0 J
c) 78.0 J
d) 89.4 J
e) 219 J
࠵? = ࠵?∆࠵? cos ࠵? = (145)(5.80) = 841 ࠵?
∆࠵?
?$&
= ࠵?
@
∆࠵? = ࠵?࠵?࠵?
@
Δ࠵? = 622.398 ࠵?
∆࠵? = ࠵?
A
− ࠵?
?
= P ࠵?
3&B%C
− ∆࠵?
?$&
= 219 ࠵?
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- Please do this carefully.arrow_forwardHead or tails Context To play heads or tails, you toss a 25 cent coin in the air straight up. To make sure you don't hit the ceiling, you want to predict the maximum height the room will reach, taking into account uncertainty as well. Constraints The initial height of your hand is fixed, and accompanied by uncertainty;The gravitational acceleration used will be ?=(9.81±0.01)m/s^2;The movement is perfectly vertical. Modelization Start by modeling the situation by writing an equation that calculates the maximum height reached by the coin (ymax) based only on the initial speed of the throw as well as the height of your hand when you throw the coin. Then test your model with the following values: Height of your hand = (1.01±0.02)m; Speed of the coin when it leaves your hand = (2.17±0.04)m/s;arrow_forwardPhysics Laboratory Final Exam * (FINAL EXAM 105/125 - I Section 1 ' Experiment " Measurement of Density I3D Q1. If you are given 5 samples of a particular substance; their measured densities are: 17.53 g/cm3, 16.98 g/cm3, 17.09 g/cm3, 17.32 g/cm3 & 16.78 g/cm3. Then the value of the standard deviation & the standard error respectively are )2 نقطة( 17.14,0.13arrow_forward
- PHYSICS ASSIGNEMENT DUE DATE: 12 MAY 2021 1. Find the dimensional formula of the following quantity: The universal constant of gravitation G. Use the formula below which contains this quantity. F= Gm2m1 r2 2. The distance covered by a particle in time t is given by x = a + bt + ct 2 + dt3; find the dimensions of a, b, c and d. 3. A man is in a 100meters sprint. He accelerates at 4 ms-2 for the first 20meters and runs at a constant velocity thereafter until the last 10meters when he starts to decelerate at 0.1 ms-2. a. How fast is he travelling after 1.5s? b. How far does he travel in this time? c. How fast is he travelling at 20 m? d. How long does he take to cover the next 10m? e. How far can he travel in 1s? f. How long does he take to cover the middle section of the distance (20-90 meters)? g. What is his velocity as he crosses the finishing line? h. What was his time for the race? TECNO SPARKarrow_forwardargest lear X ! Unacademy - India's largest + macademy.com/educator/doubts/solve?topic3DVKKVN a help with this question neutron beam of initial kinetic energy Eo is divided into two beams at point O by some echanism. Thereafter the beams proceed on the path OAC and OBC without a phase change i the corners A and B to interfere with each other at point C. Here OACB is a square of side I, Ited at an angle 0 above the horizontal. Mass of the neutron is m, Planck's constant is h and cceleration of free fall is g. the possible expression(s) for angle 0 at which a Maxima is detected at C is/are B Horizontal 2hl/2mE, 2hl /2mE, -h 2m2gl 2h? (A) sin (B) sin m°gl m'gl 6hl/2mE, 2m gl 2hl /2mE, -h 2m gl - 9h? (D) tan (C) sin 29°C Partly cloudy Type here to search Home F9 10 FB F7 F5 F3 F2 FI 23 2$ 6 7 2 3 47 A LOarrow_forwardHomework-2 (page 5 of 5) - Google Chrome mod/quiz/attempt.php?attempt=1866798&cmid%3D3903&page%3D4 E Physics II (CRN: 50010) (9 THE FOLLOWING QUESTIONS ARE BASED ON THE INFORMATION GIVEN BELOW. An electron at point A as shown in the figure has a speed vo = 2.9 x 10° m/s. The distance between points A and B is given as l = 6 cm. (Mass and charge of the electron are me = 9.109 x 1031 kg and qe = 1.602 x 10 19 C, respectively.) A) Find the magnitude of the magnetic field, in units of microtesla, that will cause the electron to follow the semicircular path from A to B. Answer: B) Find the time, in units of nanoseconds, required for the electron to move from A to B. Answer: ge Finish attempt .. Windows'u Et Mindowsu etfinlearrow_forward
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ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning