part ii 45 marks answer three questions from this part. all questions carry equal marks. 8. (a) (i) draw a…

8. (a) (i)

To draw a pulley - system with a velocity ratio of 4, we can use a combination of fixed and movable pulleys. One possible arrangement is a system with 2 movable pulleys. In a pulley - system, the velocity ratio (VR) is equal to the number of ropes supporting the load. For a system with 2 movable pulleys, the number of ropes supporting the load is 4.

8. (a) (ii)

Explanation:

Step1: Use 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 of the body and $a$ is the acceleration. Given $m = 25\ kg$, $F = 35\ N$, $a=1.5\ m/s^{2}$ We need to find $f$.

Step2: Rearrange the formula for $f$

$f=F - ma$ Substitute the given values: $f = 35-25\times1.5$ $f = 35 - 37.5=- 2.5\ N$. 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.

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 ($\eta$) of a machine is the ratio of the useful work output to the total work input, expressed as a percentage. Mathematically, $\eta=\frac{W_{output}}{W_{input}}\times100%$

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 $L=8000\times9.8 = 78400\ N$ The pitch of the screw jack $p = 2\ mm=0.002\ m$ and the length of the tommy - bar $r = 25\ cm = 0.25\ m$ The velocity ratio of a screw jack $VR=\frac{2\pi r}{p}$ $VR=\frac{2\pi\times0.25}{0.002}=\frac{0.5\pi}{0.002}=250\pi$

Step2: Use the efficiency formula

We know that $\eta=\frac{M.A.}{V.R.}\times100%$, where $M.A.=\frac{L}{E}$ (mechanical advantage, $L$ is load and $E$ is effort) Given $\eta = 85%=0.85$ $0.85=\frac{\frac{L}{E}}{VR}$ $E=\frac{L}{0.85\times VR}$ Substitute $L = 78400\ N$ and $VR = 250\pi$ $E=\frac{78400}{0.85\times250\pi}=\frac{78400}{0.85\times250\times3.14}\approx117.9\ N$

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 work is always done against friction and other resistive forces within the machine. This non - useful work reduces the ratio of useful work output to total work input.

Answer:

Some work is always done against friction and other resistive forces within the machine.

9. (a) (i)

Brief Explanations:

Thermal conductivity is the property of a material that determines the rate at which heat is conducted through it under steady - state conditions. It is defined as the amount of heat energy ($Q$) transferred per unit time ($t$), per unit cross - sectional area ($A$), per unit temperature gradient ($\frac{\Delta T}{\Delta x}$). Mathematically, $k=\frac{Q/A}{(\Delta T/\Delta x)}$

Answer:

The property of a material that determines the rate at which heat is conducted through it under steady - state conditions.

9. (a) (ii)

Brief Explanations:

The latent heat of fusion is the heat energy required to change a solid into a liquid at its melting point without a change in temperature. The latent heat of vaporization is the heat energy required to change a liquid into a gas at its boiling point without a change in temperature. The main difference is that latent heat of fusion is for the solid - to - liquid phase change and latent heat of vaporization is for the liquid - to - gas phase change.

Answer:

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 $Q_{lost}=m_{iron}c_{iron}(T_{1}-T_{2})$ The heat gained by the water $Q_{gained}=m_{water}c_{water}(T_{2}-T_{3})$ Given $m_{iron}=2.5\ kg$, $T_{1}=250^{\circ}C$, $T_{2}=72^{\circ}C$, $T_{3}=33^{\circ}C$ $m_{iron}c_{iron}(T_{1}-T_{2})=m_{water}c_{water}(T_{2}-T_{3})$ $m_{water}=\frac{m_{iron}c_{iron}(T_{1}-T_{2})}{c_{water}(T_{2}-T_{3})}$ $m_{water}=\frac{2.5\times460\times(250 - 72)}{4200\times(72 - 33)}$ $m_{water}=\frac{2.5\times460\times178}{4200\times39}$ $m_{water}=\frac{2.5\times460\times178}{4200\times39}\approx1.94\ kg$

Answer:

The mass of water is approximately $1.94\ kg$

9. (b) (ii)

Brief Explanations:

The heating curve will have five distinct parts:

1. Heating the ice from $- 15^{\circ}C$ to $0^{\circ}C$ (temperature increases linearly).
2. Melting of ice at $0^{\circ}C$ (temperature remains constant while heat is absorbed for phase change).
3. Heating the water from $0^{\circ}C$ to $100^{\circ}C$ (temperature increases linearly).
4. Vaporization of water at $100^{\circ}C$ (temperature remains constant while heat is absorbed for phase change).
5. Heating the steam above $100^{\circ}C$ (temperature increases linearly).

Answer:

The heating curve has five parts as described above.

9. (c) (i)

Brief Explanations:

Two effects of heat on a substance are: 1. Change in temperature (increase or decrease). 2. Change in state (solid - 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 required is $\Delta T=0-(-25)=25^{\circ}C$

Answer:

The temperature should be increased by $25^{\circ}C$

10. (a) (i)

Brief Explanations:

Two characteristics of resonance are: 1. Large amplitude vibrations occur when the frequency of the applied force is equal to the natural frequency of the system. 2. Energy transfer to the system is maximum at resonance.

Answer:

Large amplitude vibrations and maximum energy transfer at the natural frequency.

10. (a) (ii)

Brief Explanations:

The speed of sound in a gas increases with an increase in temperature. Mathematically, $v\propto\sqrt{T}$ (for an ideal gas, $v$ is speed of sound and $T$ is absolute temperature). The effect of pressure on the speed of sound in a gas is negligible for a given mass of gas at constant temperature.

Answer:

Speed of sound increases with temperature and pressure has negligible effect at constant temperature.

10. (a) (iii)

Brief Explanations:

Types of resonance as applied to waves include: 1. Mechanical resonance (e.g., in vibrating strings or pendulums). 2. Acoustic resonance (e.g., in musical instruments). 3. Electrical resonance (e.g., in LC - circuits).

Answer:

Mechanical resonance, acoustic resonance, electrical resonance

10. (b)

Explanation:

Step1: Determine the distance traveled by the sound

The sound travels to the wall and back. The distance traveled $d = 2\times50\ m=100\ m$ The time taken $t = 2\ s$

Step2: Use the speed formula

The speed of sound $v=\frac{d}{t}$ $v=\frac{100}{2}=50\ m/s$

Answer:

The velocity of the sound of the whistle in air is $50\ m/s$

10. (c) (i)

A convergent beam of light is a beam of light rays that meet at a point (converge). A divergent beam of light is a beam of light rays that spread out from a point (diverge). You can draw a diagram with arrows representing light rays. For a convergent beam, the arrows come together at a point, and for a divergent beam, the arrows spread out from a point.

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 $C = 39^{\circ}$ $n=\frac{1}{\sin39^{\circ}}$ $n=\frac{1}{0.6293}\approx1.59$

Answer:

The refractive index of the glass is approximately $1.59$