# SOLUTIONS - PHY430 - Test 3

```UiTM – Faculty of Applied Science
Test 3 – Set B - PHY430 – AS2232/CS2273 – 21.6.12
SOLUTIONS
Answer all the questions (g = 9.80 m/s2)
1.
a)
State and explain Continuity Equation.
Continuity Equation: A1v1 = A2v2 = constant
The product of the area and the fluid speed at all points along a pipe is constant
for an incompressible fluid.
Volume : symbol capital V
speed: symbol small v
๐๐
The product Av is called the volume flow rate ( ) which has the dimension of
๐๐ก
volume per unit time.
b)
Water flowing through a garden hose of diameter 0.030 m fills a 0.025-m3 bucket
in 90 s. Determine
i) the rate at which the water fills the bucket
๐๐
๐๐ก
=
0.025
90
๐3
= 2.8 &times; 10−4
๐
ii) the speed of the water leaving the end of the hose
๐ด1 ๐ฃ1 =
๐ฃ1 =
๐๐
๐๐ก
2.8 &times; 10−4
0.030 2
๐(
)
2
= 0.40
๐
๐
iii) the speed of the water leaving the end of the hose if the cross-sectional area
of the end of the hose is reduced to one-third its original cross-sectional area.
๐ด2 ๐ฃ2 =
๐ฃ2 =
๐๐
๐๐ก
2.8 &times; 10−4
1
0.030 2
( )๐(
)
3
2
= 1.2
๐
๐
2.
A sinusoidal travelling wave on a string is represented by y = 0.15 sin (0.80x + 50t)
where y and x are in meters and t is in seconds. For this wave determine
Compare
y = 0.15 sin (0.80x + 50t)
y = A sin (kx + ๏ทt)
k = 0.80 m๏ญ1 and ๏ท = 50 rad/s
a) the wavelength
๐=
2๐
2๐
2๐
โน๐=
=
= 7.9 ๐
๐
๐
0.80
b) frequency
๐ = 2๐๐ โน ๐ =
๏ท 50
=
= 8.0 ๐  −1
2๏ฐ 2๏ฐ
c) velocity of the wave (magnitude and direction)
๐ฃ = ๐๐ = (7.9)(8.0) = 63
๐
๐ก๐ ๐กโ๐ ๐๐๐๐ก
๐
d) maximum and minimum speed of the particles of the string.
๐ฃ๐๐๐๐ก๐๐๐๐ =
๐๐ฆ
= 0.15 ๐๐๐ (0.80๐ฅ + 50๐ก)(50)
๐๐ก
= 7.5 ๐๐๐ (0.80๐ฅ + 50๐ก)
๐ฃ๐๐๐๐ก๐๐๐๐ ๐๐๐๐๐๐ข๐ = 0 ๐คโ๐๐ ๐๐๐ (0.80๐ฅ + 50๐ก) = 0
๐
๐ฃ๐๐๐๐ก๐๐๐๐ ๐๐๐ฅ๐๐๐ข๐ = 7.5
๐คโ๐๐ ๐๐๐ (0.80๐ฅ + 50๐ก) = 1
๐
3.
a)
State the meaning of
i)
specific heat capacity
Heat needed to increase the temperature of a 1 kg substance by 1 K.
๐ฝ
The unit is ๐๐โ๐พ.
ii)
latent heat of vaporization.
Heat needed to change a 1 kg substance from liquid to gas without any
temperature change.
The unit is
๐ฝ
.
๐๐
b) Calculate the amount of thermal energy needed to change a 0.720-kg ice at ๏ญ10๏ฐC
to water at 15๏ฐC.
Q needed =
Q to increase the temperature of ice from ๏ญ10๏ฐC to 0๏ฐC
+ Q to melt all the ice at 0๏ฐC
+ Q to increase the temperature of water from 0๏ฐC to 15๏ฐC
=
mi ci ๏๏ฑi + mi Lf + mw cw ๏๏ฑw
=
(0.720)(2100)(0 ๏ญ ๏ญ10) + (0.720)( 3.33 ๏ด 105) +
(0.720)(4200)(15 ๏ญ 0)
=
3.00 ๏ด 105 J
Specific heat of ice = 2100 J/kg.K
Specific heat of water = 4200 J/kg.K
Latent heat of fusion of water = 3.33 ๏ด 105 J/kg
```