NANYANG TECHNOLOGICAL UNIVERSITY
A
A
PH1012 QUIZ 1 SEMESTER 1, 2018-2019
22nd September 2018, 1:15 pm to 2:45 pm
Short Q
/26
Name:
Q1
/10
Matric Number:
Q2
/14
Q3
/10
Total
/60
Tutorial Group:
Constants and Formula List
Gravitational Acceleration
Mass of Earth
Gravitational constant
g
Me
G
9.8 m/s²
5.97×1024kg
Avogadro’s number
Universal gas constant
Absolute zero
Pressure conversion
NA
R
0K
1 bar
6.02×1023 molecules/mol
8.314 J/mol K
– 273.15°C
105 N/m2 (or Pa)
1 atm
1.01 × 105 𝑃𝑎
6.67 1011 N  m2 kg 2
Basics and Thermal Physics
∆𝐿 = 𝛼𝐿𝑖 ∆𝑇
𝑇=
∆𝑉 = 𝛽𝑉𝑖 ∆𝑇,
,
𝑃(𝑇) − 𝑃(0)
× 100,
𝑃(100) − 𝑃(0)
𝑃𝑉 = 𝑛𝑅𝑇,
𝑇 = 273.16 𝐾 𝑙𝑖𝑚
Linear Motion
𝑣⃑𝑎𝑣𝑔 =
Δ𝑟⃑ 𝑟⃑𝑓 − 𝑟⃑𝑖
=
,
Δ𝑡 𝑡𝑓 − 𝑡𝑖
𝑎⃑𝑎𝑣𝑔 =
Δ𝑣⃑ 𝑣⃑𝑓 − 𝑣⃑𝑖
=
,
Δ𝑡
𝑡𝑓 − 𝑡𝑖
𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡,
𝑣⃑𝑖𝑛𝑡 ≡ lim
Δ𝑟⃑
Δ𝑡→0 Δ𝑡
=
𝑑𝑟⃑
,
𝑑𝑡
𝑑𝑥
,
𝑑𝑡
Δ𝑣⃑ 𝑑𝑣⃑ 𝑑2 𝑟⃑
=
=
,
Δ𝑡→0 Δ𝑡
𝑑𝑡 𝑑𝑡 2
1
𝑥𝑓 = 𝑥𝑖 + (𝑣𝑖 + 𝑣𝑓 )𝑡,
2
𝑑𝑝⃑
= 𝑚𝑎⃑,
𝑑𝑡
𝑣=
,
𝑎⃑𝑖𝑛𝑡 ≡ lim
𝑔
𝑦 = (tan 𝜃𝑖 )𝑥 − ( 2
) 𝑥 2,
2𝑣𝑖 cos2 𝜃𝑖
Σ 𝐹⃑ =
𝑃
𝑃𝑡𝑟 →0 𝑃𝑡𝑟
𝑝⃑ = 𝑚𝑣⃑,
ℎ=
𝑄 = 𝑚𝑐∆𝑇, 𝑄 = 𝑚𝑙
𝑎=
𝑑𝑣
𝑑𝑡
𝑣𝑓2 = 𝑣𝑖2 + 2𝑎(𝑥𝑓 − 𝑥𝑖 ),
𝑣𝑖2 sin2 𝜃𝑖
,
2𝑔
𝑓𝑘 = 𝜇𝑘 𝑁,
𝑅=
1
𝑥𝑓 = 𝑥𝑖 + 𝑣𝑖 𝑡 + 𝑎𝑡 2
2
𝑣𝑖2 sin 2𝜃𝑖
𝑔
𝑓𝑠 ≤ 𝜇𝑠 𝑁
|𝐹𝑠𝑝 | = 𝑘𝑥
𝑣=
𝑏
𝑚𝑔
(1 − 𝑒 −𝑚𝑡 )
𝑏
𝐹 = 𝐺𝑀1 𝑀2 /𝑟 2
Rotational Motion
𝑣2
⃑⃑|
𝑑|𝑣
= 𝑟𝜔2 , 𝑎𝑡 =
,
𝑑𝑡
1
𝜃𝑓 = 𝜃𝑖 + (𝜔𝑖 + 𝜔𝑓 )𝑡,
2
𝑎𝑐 =
𝑟
𝑠 = 𝑟𝜃, 𝜔 =
𝑑𝜃
𝑑𝑡
𝑣
𝑑𝜔
𝑟
𝑑𝑡
= , 𝛼=
𝜔𝑓2 = 𝜔𝑖2 + 2𝛼(𝜃𝑓 − 𝜃𝑖 ),
=
𝑎
; 𝜔𝑓 = 𝜔𝑖 + 𝛼𝑡,
1
𝜃𝑓 = 𝜃𝑖 + 𝜔𝑖 𝑡 + 𝛼𝑡 2
2
𝑟
Mathematics
1
−𝑏±√𝑏2 −4𝑎𝑐
tan 𝐴 = sin 𝐴⁄cos 𝐴 ; sin2 𝐴 + cos2 𝐴 = 1; sec 2 𝐴 = 2 = tan2 𝐴 + 1; 𝑥1,2 =
where 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0;
cos 𝐴
2𝑎
𝑑
(𝑎𝑥 𝑛 )
𝑑𝑥
= 𝑎𝑛𝑥 𝑛−1 ; ∫ 𝑥 𝑛 𝑑𝑥 =
𝑥 𝑛+1
𝑛+1
+ 𝐶 (𝑛 ≠ 1); ∫
A-1
𝑑𝑥
𝑥
= ln 𝑥
Instructions:
a) Answer all questions.
b) Working for all questions must be shown clearly in the space provided.
Short Questions (26 points)
1. [2 points] Can an object have increasing speed while its acceleration is decreasing? Support
your answer with an example.
A.
B.
C.
D.
E.
Yes, and an example would be an object falling in the absence of air resistance.
Yes, and an example would be an object released from rest in the presence of air resistance.
Yes, and an example would be an object rising in the absence of air resistance.
No, this is impossible because of the way in which acceleration is defined.
No, because if acceleration is decreasing the object will be slowing down.
ANS: __________________
2. [2 points] A graph of position as a function of time is shown
in the figure. During which time interval could the object be
possibly moving with non-zero constant acceleration?
A. 2.1 s to 3.9 s
B. 0.1 s to 1.9 s
C. 6.1 s to 7.9 s
D. 4.1 s to 5.9 s
E. There is no interval that is consistent with constant nonzero acceleration.
ANS: __________________
3. [4 points] The position of an object at time 𝑡 is given by
𝑚
𝑚
𝑟⃗(𝑡) = [2.0 𝑚 + (5.00 𝑠3 ) 𝑡 3 ] 𝑖̂ + [3.0 𝑚 − (2.00 𝑠2 ) 𝑡 2 ] 𝑗̂.
What is the magnitude of the acceleration of the object at time 𝑡 = 2.00 𝑠?
4 m/s^2
ANS: __________________
A-2
4. [4 points] The submarine below displaces 1,130 tons of seawater when it is floating on surface
and displaces 1,200 tons of seawater when it is just totally submerged. If the 20% of the ballast
tank is filled when the submarine is just totally submerged, use the information given and
estimate the downward acceleration 𝑎 of submarine when the ballast tanks are 100% filled
(1 ton = 1000 kg, density of seawater is 1020 kg m-3). You can ignore any resistive / viscous
forces due to the motion of the submarine in water.
Empty ballast tanks
Floating on surface
(displaces 1,130 tons
of seawater)
𝑎
Ballast tanks
20% filled with
sea water
Ballast tanks
100% filled
with sea water
Just totally submerged
(displaces 1,200 tons
of seawater) and in
equilibrium
Totally submerged and
accelerating down
ANS: __________________
5. [4 points] What is the velocity of a satellite circling Mars 100 𝑘𝑚 above the planet's surface?
The mass of Mars is 6.42 × 1023 𝑘𝑔, its radius is 3.40 × 106 𝑚.
ANS: __________________
A-3
6. [4 points] An ideal gas in a container of volume 100 𝑐𝑚3 at 20∘ 𝐶 has a pressure of 100 𝑁/𝑚2 .
Determine the number of gas molecules in the container.
ANS: __________________
7. [6 points] A standard mercury thermometer consists of a hollow glass cylinder, the stem,
attached to a bulb filled with mercury. As the temperature of the thermometer changes, the
mercury expands (or contracts) and the height of the mercury column in the stem changes.
Marks are made on the stem to denote the height of the mercury column at different
temperatures such as the freezing point (0∘ 𝐶) and the boiling point (100∘ 𝐶) of water. Other
temperature markings are interpolated between these two points.
Due to concerns about the toxic properties of mercury, many thermometers are made with
other liquids. Consider draining the mercury from the above thermometer and replacing it with
another, such as alcohol. Alcohol has a coefficient of volume expansion 5.6 times greater than
that of mercury. The amount of alcohol is adjusted such that when placed in ice water, the
thermometer accurately records 0∘ 𝐶. No other changes are made to the thermometer.
i. When the alcohol thermometer is placed in 20∘ 𝐶 water, what temperature will the thermometer
record?
A. less than 20∘ 𝐶
B. 20∘ 𝐶
C. greater than 20∘ 𝐶
C
ANS: __________________
ii. When the alcohol thermometer is placed in −10∘ 𝐶 substance, what temperature will the
thermometer record?
A. less than −10∘ 𝐶
B. −10∘ 𝐶
C. greater than −10∘ 𝐶
A
ANS: __________________
iii. If you want to design a thermometer with the same spacing between temperature markings as
a mercury thermometer, how many times must the diameter of the inner hollow cylinder of the
stem of the alcohol thermometer compare to that of the mercury thermometer? Assume that
the bulb has a much larger volume than the stem.
√5.6 𝑤𝑖𝑑𝑒𝑟
ANS: __________________
11
A-4
Structured Questions (34 points)
Q1. [10 points] Samson works as a porter in a hotel and he helps hotel
guests bring their luggage to their room after they checked in or to
the hotel lobby after they check out. One day, he met a very fussy
hotel guest who insisted that his two bags must be hand carried and
not touch the floor. The two bags have a mass of 15 kg each. He
entered lift and the acceleration of the lift changes with time as
shown in the vertical acceleration versus time graph.
(The
convention is upwards is positive.) The lift starts to move from rest
at 𝑡 = 1.0 𝑠.
i. Using the graph below to determine if he is going down or up or if you
need additional information to determine that. Please circle.
Going up / Going down / More information needed.
ii. Determine the minimum and maximum force
experienced by each of Samson’s arm while
he is holding on to the luggage in the lift.
ANS: __________________
iii. Using the graph, determine the vertical displacement of Samson when he is in the lift.
ANS: __________________
A-5
Q2. [14 points] You are on the roof of the Physics building, 𝐻 = 50 𝑚 above ground. Your
Physics professor who is ℎ = 1.70 𝑚 tall is walking briskly alongside the building at a
constant speed of 𝑣 = 2.00 𝑚/𝑠. You dropped an egg from the top of the building such
that it will land on the professor’s head when he reaches the base of the 50 m building.
At the moment you released the egg, you hear toy-gun shot fired from the roof top of
another 20 m building 35.8 m away. Suddenly, you remember the “Monkey and the
Gun” video demonstration from the Physics lecture and understood the intent of the
shot – it is to intercept the egg that you dropped.
You also own one of these toy-guns and you know that the plastic bullets are fired at a
velocity of 𝑣 = 50 𝑚/𝑠. Judging from the location of the other classmate who fired the
shot, the angle 𝜃 = 40∘ . For all your calculations, ignore the effects of air resistance
and the time taken for sound to travel.
i.
Determine how much time is taken by the plastic bullet takes to reach the 50 m
building.
t = 0.933 s
ANS: __________________
ii.
Determine how high above the ground the plastic bullet will be when it reaches the
50 m building.
ANS: __________________
A-6
iii.
Show that the egg will be at the same height at the same time as the plastic bullet
when the plastic bullet reaches the 50 m building and thus be hit by it.
iv.
If the velocity of the bullet 𝑣 is larger and 𝜃 remains as 40∘ , the egg will be hit at
____________ above the ground compared to when 𝑣 = 50 𝑚/𝑠.
A. a greater height
B. same height
C. lower height
ANS: __________________
Explain your answer.
_____________________________________________________________________
_____________________________________________________________________
v.
You have another egg at hand and you threw it vertically down with an initial velocity 𝑣𝑖
at 0.6 𝑠 after the first egg was hit by the plastic bullet. The unaware professor
continues to walk at the same speed towards the 50 m building. If this second egg hits
the professor’s head, determine 𝑣𝑖 .
ANS: __________________
A-7
Q3. [10 points]
a.
A 1-kg block and a 2-kg block made of the same material are released from rest from
the top of a rough 30∘ inclined plane. The coefficient of kinetic friction 𝜇𝐾 is the same
for both blocks. The velocities of the 1-kg block and the 2-kg block at the base of the
incline plane are 𝑣1 and 𝑣2 respectively. Determine the ratio 𝑣1 /𝑣2 .
ANS: __________________
b.
As shown in the figure, two blocks made of the same
material have masses 𝑚𝐴 = 3.2 𝑘𝑔 and 𝑚𝐵 = 2.4 𝑘𝑔 .
They are connected via a massless string over a
smooth pulley and are sliding downwards together with
the string taut at all times. The coefficient of kinetic
friction between the blocks and inclines is 𝜇𝑘 = 0.35
and the angles of the inclines are shown in the figure.
i.
Using the diagram below, indicate the forces acting on
block A (with labelled arrows).
ii.
Determine the acceleration of the two blocks and the tension in the string.
ANS: ____________
____________
------- The End --------A-8