part ii 45 marks answer three questions from this part all questions carry equal marks 8. (a) (i) draw a pulley - system that has a velocity ratio of 4. (ii) a body of mass 25 kg is pulled over a rough surface with a 35 n force. if the object accelerated at a rate of 1.5 m/s², calculate the frictional force acting on the object and the surface. 5 marks (b) define the following terms as applied to machines: (i) velocity ratio; (ii) efficiency. 4 marks (c) (i) a screw - jack of pitch 2 mm is to be used to lift a car of mass 8000 kg. the length of the tommy - bar of the jack is 25 cm. calculate the effort that would have been required to attain an efficiency of 85 %. (ii) explain why the efficiency of a machine is always less than 100 %. 6 marks 9. (a) (i) define the term thermal conductivity. (ii) give one difference between latent heat of fusion and latent heat of vaporization. 4 marks (b) (i) an iron rod of mass 2.5 kg at 250 °c is dropped into some quantity of water initially at 33 °c. what would be the mass of the water when the temperature is at 72 °c? (ii) a piece of ice at - 15 °c is subjected to heat until the ice changes to steam at 100 °c. sketch a heating curve to illustrate the changes in temperature during the process. 7 marks (c) (i) state two effects of heat on a substance. (ii) by how much should water of temperature - 25 °c be increased to obtain its freezing - point temperature? 4 marks 10. (a) (i) state two characteristics of resonance. (ii) mention the effects of temperature and pressure on the speed of sound. (iii) list the types of resonance as applied to wave. 7 marks (b) a reference leaning on a wall blows his whistle towards another wall 50 m away. he hears the second echo 2 seconds later. calculate the velocity of the sound of the whistle in air. speed of sound in air = 330 m/s 3 marks (c) (i) draw a diagram illustrating convergent and divergent beams of light. (ii) the critical angle for glass in air is 39°. calculate the refractive index of the glass. 5 marks

Question

Accepted Answer

### 8. (a) (i)
# Explanation:
## Step1: Design pulley system
A pulley - system with a velocity ratio of 4 can be designed by having 4 movable pulleys in series or an appropriate combination of fixed and movable pulleys. One way is to have 2 sets of 2 - pulley combinations (where each set has one fixed and one movable pulley). The effort is applied to the free - end of the rope, and the load is attached to the last movable pulley.

### 8. (a) (ii)
# Explanation:
## Step1: Apply Newton's second law
According to Newton's second law $F - f=ma$, where $F$ is the applied force, $f$ is the frictional force, $m$ is the mass and $a$ is the acceleration. Given $m = 25\ kg$, $F = 35\ N$ and $a=1.5\ m/s^{2}$.
We can re - arrange the formula for $f$: $f=F - ma$.
## Step2: Calculate the frictional force
Substitute the values into the formula: $f = 35-25	imes1.5$.
$f = 35 - 37.5=- 2.5\ N$. The negative sign indicates that the frictional force acts in the opposite direction of the motion. The magnitude of the frictional force is $2.5\ N$.
# Answer:
The frictional force is $2.5\ N$.

### 8. (b) (i)
# Brief Explanations:
The velocity ratio of a machine is the ratio of the distance moved by the effort to the distance moved by the load in the same time interval. Mathematically, $VR=\frac{d_{E}}{d_{L}}$, where $d_{E}$ is the distance moved by the effort and $d_{L}$ is the distance moved by the load.
# Answer:
The velocity ratio of a machine is the ratio of the distance moved by the effort to the distance moved by the load in the same time interval.

### 8. (b) (ii)
# Brief Explanations:
The efficiency of a machine is the ratio of the useful work output to the total work input, expressed as a percentage. Mathematically, $\eta=\frac{W_{out}}{W_{in}}	imes100\%$, where $W_{out}$ is the useful work output and $W_{in}$ is the total work input.
# Answer:
The efficiency of a machine is the ratio of the useful work output to the total work input, expressed as a percentage.

### 8. (c) (i)
# Explanation:
## Step1: Calculate the load
The load $L = mg$, where $m = 8000\ kg$ and $g = 9.8\ m/s^{2}$. So, $L=8000	imes9.8 = 78400\ N$.
The pitch of the screw $p = 2\ mm=0.002\ m$ and the length of the tommy - bar $r = 25\ cm = 0.25\ m$. The velocity ratio of a screw jack $VR=\frac{2\pi r}{p}$.
$VR=\frac{2\pi	imes0.25}{0.002}=\frac{0.5\pi}{0.002}=250\pi$.
The efficiency $\eta = 85\%=0.85$. We know that $\eta=\frac{M.A}{V.R}$, where $M.A=\frac{L}{E}$ (mechanical advantage, $L$ is the load and $E$ is the effort).
Since $\eta=\frac{\frac{L}{E}}{VR}$, we can re - arrange for $E$: $E=\frac{L}{\eta	imes VR}$.
## Step2: Calculate the effort
Substitute the values: $E=\frac{78400}{0.85	imes250\pi}$.
$E=\frac{78400}{0.85	imes250	imes3.14}\approx117.9\ N$.
# Answer:
The effort required is approximately $117.9\ N$.

### 8. (c) (ii)
# Brief Explanations:
The efficiency of a machine is always less than 100% because some of the input work is always wasted in overcoming friction and other non - ideal factors such as air resistance, deformation of the machine parts etc. These factors convert some of the input energy into heat, sound or other non - useful forms of energy, reducing the amount of useful work output.
# Answer:
Some of the input work is wasted in overcoming friction and other non - ideal factors.

### 9. (a) (i)
# Brief Explanations:
Thermal conductivity is the property of a material that determines its ability to conduct heat. It is defined as the rate of heat transfer per unit area per unit temperature gradient in the direction of heat flow. Mathematically, $k=\frac{Q/A}{\Delta T/L}$, where $k$ is the thermal conductivity, $Q$ is the heat transfer rate, $A$ is the cross - sectional area, $\Delta T$ is the temperature difference and $L$ is the length of the material.
# Answer:
Thermal conductivity is the property of a material that determines its ability to conduct heat, defined as the rate of heat transfer per unit area per unit temperature gradient in the direction of heat flow.

### 9. (a) (ii)
# Brief Explanations:
The latent heat of fusion is the amount of heat required to change a unit mass of a solid substance into its liquid state at its melting point without a change in temperature. The latent heat of vaporization is the amount of heat required to change a unit mass of a liquid substance into its gaseous state at its boiling point without a change in temperature. The main difference is that latent heat of fusion is for solid - to - liquid phase change and latent heat of vaporization is for liquid - to - gas phase change.
# Answer:
The latent heat of fusion is for solid - to - liquid phase change and latent heat of vaporization is for liquid - to - gas phase change.

### 9. (b) (i)
# Explanation:
## Step1: Use the principle of conservation of heat
The heat lost by the iron rod is equal to the heat gained by the water. The specific heat capacity of iron $c_{iron}=460\ J/(kg\cdot^{\circ}C)$ and the specific heat capacity of water $c_{water}=4200\ J/(kg\cdot^{\circ}C)$.
The heat lost by the iron rod $Q_{lost}=m_{iron}c_{iron}(T_{1}-T_{2})$, where $m_{iron}=2.5\ kg$, $T_{1}=250^{\circ}C$ and $T_{2}=72^{\circ}C$.
$Q_{lost}=2.5	imes460	imes(250 - 72)=2.5	imes460	imes178 = 2.5	imes81880 = 204700\ J$.
The heat gained by the water $Q_{gained}=m_{water}c_{water}(T_{2}-T_{3})$, where $T_{3}=33^{\circ}C$ and $T_{2}=72^{\circ}C$.
Since $Q_{lost}=Q_{gained}$, we have $m_{water}=\frac{Q_{lost}}{c_{water}(T_{2}-T_{3})}$.
## Step2: Calculate the mass of water
$m_{water}=\frac{204700}{4200	imes(72 - 33)}=\frac{204700}{4200	imes39}\approx1.25\ kg$.
# Answer:
The mass of water is approximately $1.25\ kg$.

### 9. (b) (ii)
# Brief Explanations:
The heating curve will have the following segments:
1. The temperature of ice at $- 15^{\circ}C$ rises to $0^{\circ}C$ (a sloped line as heat is added and temperature changes according to $Q = mc\Delta T$ for ice).
2. At $0^{\circ}C$, there is a horizontal line as heat is added for the phase change from ice to water (latent heat of fusion is absorbed).
3. The temperature of water rises from $0^{\circ}C$ to $100^{\circ}C$ (a sloped line as heat is added and temperature changes according to $Q = mc\Delta T$ for water).
4. At $100^{\circ}C$, there is a horizontal line as heat is added for the phase change from water to steam (latent heat of vaporization is absorbed).
# Answer:
The heating curve has segments of temperature increase for ice and water, and horizontal lines for phase changes at $0^{\circ}C$ and $100^{\circ}C$.

### 9. (c) (i)
# Brief Explanations:
Two effects of heat on a substance are: 1. Change in temperature (increase or decrease depending on heat gain or loss). 2. Change in state (solid - liquid, liquid - gas phase changes).
# Answer:
Change in temperature and change in state.

### 9. (c) (ii)
# Brief Explanations:
The freezing point of water is $0^{\circ}C$. If the initial temperature of water is $-25^{\circ}C$, the temperature increase $\Delta T=0-(-25)=25^{\circ}C$.
# Answer:
$25^{\circ}C$.

### 10. (a) (i)
# Brief Explanations:
Two characteristics of resonance are: 1. The amplitude of vibration is maximum at resonance. 2. The frequency of the external force is equal to the natural frequency of the vibrating body.
# Answer:
Maximum amplitude of vibration and the frequency of the external force equals the natural frequency of the vibrating body.

### 10. (a) (ii)
# Brief Explanations:
The speed of sound in air increases with an increase in temperature. The relationship is approximately $v = v_{0}+0.6T$, where $v$ is the speed of sound at temperature $T$ (in $^{\circ}C$) and $v_{0}$ is the speed of sound at $0^{\circ}C$. The effect of pressure on the speed of sound in air is negligible at constant temperature as long as the air can be considered an ideal gas.
# Answer:
The speed of sound in air increases with temperature and the effect of pressure is negligible at constant temperature.

### 10. (a) (iii)
# Brief Explanations:
The types of resonance as applied to waves are: 1. Mechanical resonance (e.g., in vibrating strings, pendulums). 2. Acoustic resonance (e.g., in musical instruments, air columns). 3. Electrical resonance (e.g., in LC circuits).
# Answer:
Mechanical resonance, acoustic resonance, electrical resonance.

### 10. (b)
# Explanation:
## Step1: Determine the distance traveled by sound
The sound travels to the wall and back. The distance traveled by the sound $d = 2	imes50\ m = 100\ m$ (since it goes to the wall 50 m away and then back). The time taken $t = 2\ s$.
The speed of sound $v=\frac{d}{t}$.
## Step2: Calculate the speed of sound
$v=\frac{100}{2}=50\ m/s$.
# Answer:
The velocity of the sound of the whistle in air is $50\ m/s$.

### 10. (c) (i)
# Brief Explanations:
To draw a convergent beam of light, draw rays of light that are coming together at a point. To draw a divergent beam of light, draw rays of light that are spreading out from a point.
# Answer:
Draw rays coming together for convergent and rays spreading out for divergent.

### 10. (c) (ii)
# Explanation:
## Step1: Use the formula for refractive index and critical angle
The relationship between the refractive index $n$ of a medium and the critical angle $C$ is given by $n=\frac{1}{\sin C}$.
Given $C = 39^{\circ}$.
## Step2: Calculate the refractive index
$n=\frac{1}{\sin39^{\circ}}\approx\frac{1}{0.6293}\approx1.59$.
# Answer:
The refractive index of the glass is approximately $1.59$.

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QUESTION IMAGE

Question

Explanation:

8. (a) (i)

Step1: Design pulley system

8. (a) (ii)

Step1: Apply Newton's second law

Step2: Calculate the frictional force

Answer:

8. (b) (i)