UNIVERSITEIT VAN PRETORIA
UNIVERSITY OF PRETORIA
YUNIBESITHI YA PRETORIA
Test information:
Marks
Duration of paper:
90
120 minutes
Total
Lecturer
This test consists of pages including this cover sheet
K Oerder
IMPORTANT
1.
The examination regulations of the university of Pretoria apply
2.
All questions are to be answered on this question paper.
3.
Please show all your working
4.
Formulas and Useful Constants are given on the last page
Name: _____________________________________ Student No: _________________
Registered Degree/Field of study: ________________________________
Group: ___________________________________
Total Q1
/90 /14
Q2
/9
Q3
/12
Q4 Q5
/11 /12
Q6
/12
Q7
/7
Q8
/10

Question 1 [14]
1) If 𝑎⃗ ∙ 𝑏⃗⃗ = 𝑎⃗ ∙ 𝑐⃗ then must 𝑏⃗⃗ = 𝑐⃗ ? Explain or give an example?
No. Consider 𝑎⃗ = 1𝑖̂ + 1𝑗̂ and 𝑏⃗⃗ = 1𝑖̂ + 0𝑗̂ and 𝑐⃗ = 0𝑖̂ + 1𝑗̂ then 𝑎⃗ ∙ 𝑏⃗⃗ = 𝑎⃗ ∙ 𝑐⃗ = 1 but 𝑏⃗⃗ ≠ 𝑐⃗
2) Consider the following four vectors:
(3)
𝐴⃗ = 2.00𝑚𝑖̂ + 3.00𝑚𝑗̂ 𝐵
𝐶⃗ = −4.00𝑚𝑖̂ − 6.00𝑚𝑗̂ 𝐷 a.
What is the sum of these four vectors in unit vector notation? (5)
𝐵
𝐵
= 4.22𝑖̂ − 1.48𝑗̂ b.
What is the magnitude of the sum of these four vectors?
𝑅 = √𝑥 2 + 𝑦 2 = √4.22
2 + (−1.48) 2 = 4.48
c.
What is the direction of the sum of these four vectors? 𝜃 = tan
−1
( 𝑦 𝑥
) = tan
−1
(−
1.49
4.22
) = −19°
R is 19° clockwise to +x axis
(3)
(3)

Question 2 [9]
A recycling centre collects metal pipes, which it separates according to the metal of which the pipe is manufactured, and then melts to form ingots which can be sold. The recycling centre has a furnace which provides heat at a constant rate. The centre collects pipes made of either aluminium, copper or lead. All the pipes have equal mass. The pipes, initially at room temperature are to be melted.
1) If two pipes, one of aluminium and one of copper, are placed in the furnace at the same time, which will reach 500 °C first? (3)
Copper.Since the specific heat of aluminium is higher than that of copper and both pipes have the same mass then aluminium will require more energy to reach 500°C and thus will need more time to reach this temperature. Hence since energy is supplied at the same constant rate for both metals then Aluminium will take the longer time to reach this temperature.
2) Draw and label, on the same set of axes, the temperature vs heat added graph, for a pipe of each metal, in order to completely melt the pipe (6)
1200
Copper
1000
800
Tin
600
Aluminium
Temperature
(°C))
400
200
0
Q (J)

Question 3 [12]
1) If you heat a uniform metal plate with a hole cut out of it, will the hole get smaller, bigger or remain the same size? Explain (3)
Bigger. Hole will act in same way as if metal piece was still present and the metal piece will expand when heated. If it did not then the original piece would not fit back into the hole that it is created by its removal
2) To raise the temperature of an object a heat transfer must occur to it. But if heat is transferred to an object does its temperature necessarily have to change? Explain
No. Phase changes occur at constant temperature even though heat transfer occurs
(3)
3) A newspaper article on recent weather events describes the temperature of an object as
“the amount of heat that the object contains”. Is this description correct? Explain (3)
No. Temperature is a measure of the average internal kinetic energy of an object and is a property of the object alone. Heat is an energy transfer due to two bodies being at different temperatures. It requires two bodies to make sense and is therefore not a measurable property of a body.
4) Why does putting a glass jar with a metal lid in hot water make it easier to open? Explain (3)
Glass jar and lid both expand due to a temperature increase but the metal lid has a higher coefficient of linear expansion hence will expand more that the lid for the same temperature increase. This means that the lid will not fit as snugly to the glass jar and be easier to open

Question 4 [11]
An insulated thermos flask (isolated container) contains 130 cm 3
of hot coffee at 80.0 ℃ . You put in a 12.0 g ice cube at its melting point. Treat the coffee as though it were pure water and neglect energy exchanges with the environment.
Draw a temperature vs time graph for the above mixture (4)
By how many degrees has your coffee cooled once the ice has melted and equilibrium has been reached? Show all workings (7)
𝑄 𝑖𝑐𝑒
= −𝑄 𝑐𝑜𝑓𝑓𝑒𝑒
𝐿𝑚 𝑖
+ 𝑚 𝑖 𝑐∆𝑇 𝑖
= −𝑚 𝑐 𝑐∆𝑇 𝑐𝑜𝑓𝑓𝑒𝑒
𝐿𝑚 𝑖
+ 𝑚 𝑖 𝑐(𝑇
𝐹
− 273.15) = −𝑚 𝑐 𝑐(𝑇
𝐹
− 353.15)
𝑇
𝐹
= 𝑚 𝑐 𝑐(353.15𝐾) + 𝑚 𝑖 𝑐(273.15𝐾) − 𝐿𝑚 𝑖
(𝑚 𝑖
+ 𝑚 𝑐
)𝑐
= 339.67𝐾 = 66.5°𝐶
∆𝑇 𝑐𝑜𝑓𝑓𝑒𝑒
= 80.0 − 66.5 = 13.5°𝐶

Question 5 [12]
Three different metals of identical mass are placed one at a time in a special freezer that can extract energy from a material at a certain constant rate. During the cooling process, each material begins in the liquid state and ends in the solid state. The temperature versus time graphs for each metal is shown below
1
2
3
0 2 4 6
Time
8 10 12 14 a) Rank the three metals according to freezing point temperature. Explain (3)
1,2,3. Phase change is denoted by horizontal lines of constant temperature. The higher this line is the higher the freezing point b) Rank the three metals according to specific heat in liquid phase. Explain (3)
3,1,2 or 3=1,2. Since heat transfer is at a constant rate then
𝑄 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 =
∆𝑡
= 𝑚𝑐
Δ𝑇
Δ𝑡
Thus the larger the gradient (
Δ𝑇
Δ𝑡
) of the liquid phase (left hand side of the graph) then the greater the specific heat.

c) Rank the three metals according to specific heat in solid phase. Explain
1,2,3.
Similar reasoning to (b) but referring to right portion of graph after phase change
(3) d) Rank the three metals according to heat of fusion. Explain
2,1,3.
(3)
Since heat transfer is at a constant rate then
𝑄 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 =
∆𝑡
= 𝑚𝐿
∆𝑡
Then the longer it takes to change phase (Δt) then the larger heat of fusion must be (m is constant)

Question 6 [12]
You drop an egg from rest from the top of ENG I. The egg is viewed by three startled workers on its path to the ground past three consecutive windows one above the other as shown below
1
2
3 a) Rank the magnitude of the acceleration of the egg as it passes each window. Explain your answer (3)
All tied.
The egg is a projectile which has a constant acceleration of 9.8 m/s 2 downwards b) Rank the average speed of the egg as it by each window. Explain your answer
3,2,1
Acceleration is downwards hence magnitude of velocity increases as it passes each window
(3)

c) Rank the time the egg takes to pass each window. Explain you answer
1,2,3
(3)
The time it takes an egg to pass each window will decrease as it increases the average speed past each window since the windows are all the same size d) Rank the change in speed of the egg, ∆𝑣 , as it passes from the top of the window to the bottom of the window. Explain your answer (3)
1,2,3
∆𝑣 = 𝑎∆𝑡 thus since a is constant the longer the egg takes to pass a window the greater the change in velocity

Question 7 [7]
A ball is shot vertically upwards from the surface of another planet. A plot of height as a function of time for the ball is shown below
30
25
20
15
10
5
0
0 1 2 3 4 5 t (s)
What is the magnitude of the free-fall acceleration on the planet? Show all your working
∆𝑦 = 𝑣
0 𝑡 +
1
2 𝑎𝑡 2
−25 = 0 +
1
2 𝑎(2.5)
2
50 𝑎 = −
2.5
2
= −8 𝑚. 𝑠
−2
What is the initial velocity of the ball? Show all your working 𝑣 = 𝑣
0
+ 𝑎𝑡 𝑣
0
= 𝑣 − 𝑎𝑡 = 0 − (−8)(2.5) = 20 𝑚. 𝑠
−1
(4)
(3)

Question 8 [13]
The table below gives the sign of the initial velocity and acceleration of a particle that only moves back and forth in the x-direction in three different cases. The particle has a positive initial position in each case.
Case Initial velocity Initial acceleration
A - +
B
C
+
+
-
+
Describe the motion that the particle would experience in each case, including whether the particle will ever be at position x=0 m and whether the particle stops momentarily. Explain your answers.
A)
A starts off moving to the negative direction and due to positive acceleration slows down to a stop momentarily then will move in positive direction with increasing speed. It will move past x=0 m pending on the magnitude of v and a
B)
B starts moving to the positive direction and due to negative acceleration slows down to a stop momentarily then will move in the negative direction speeding up as it does so and crossing the x=0 m position.
C)
C moves in the positive direction and speeding up as it does so due to positive acceleration. It never stops and never passes origin

Specific Heats (J kg -1 K -1 ):
Aluminium
Ice
Lead
900
2220
128
Other thermodynamic information:
Water
Copper
4187
386
Substance
Aluminium
Water
Copper
Lead
Melting Boiling
Melting Point (K) Heat of Fusion (J/kg) Boiling Point (K) Heat of Vaporization (J/kg)
933
273
399000
333000
2723
373
10530000
2256000
1356
601
207000
23200
2868
2017
4730000
858000
∆𝑙 = 𝑙𝛼∆𝑇 ∆𝑉 = 𝑉𝛽∆𝑇
2 𝑦
𝑄 = 𝐿𝑚
0
0
1
2
2
𝑄 = 𝑚𝑐∆𝑇
0
0
2
0
0
1
2
0