9.1 A driver gear on the shaft of an electrical motor has 30 teeth and meshes with a gear on a countershaft which has 80 teeth - NSC Mechanical Technology Welding and Metalwork - Question 9 - 2016 - Paper 1

The speed ratio can be calculated using the formula:

$\text{Speed ratio} = \frac{\text{Driver teeth}}{\text{Driven teeth}}$

For the final driven gear:

$\text{Speed ratio} = \frac{80}{30} = 2.67 ext{ or } 4.2 : 1$

Using the relationship between the diameters and rotational speeds:

$N_1 \times D_1 = N_2 \times D_2$

Where:

• $D_1$ = Diameter of driven pulley = 600mm
• $D_2$ = Diameter of driving pulley = 800mm

Rearranging:

$N_2 = \frac{N_1 \times D_1}{D_2} = \frac{7.2 \times 600}{800} = 5.4 \text{ r/s}$

Power can be calculated using the formula:

$P = (T_1 - T_2) \times F$

Where:

• $T_1 = 300N$
• $T_2 = 2.5$

Thus:

$P = (300 - 120) \times 5.4 = 2442.90 ext{ W or } 2.44 kW$

The volume of a given mass of gas can be changed by altering its pressure, its temperature, or both. Increasing the temperature will increase the volume, while increasing the pressure will decrease the volume.

Boyle's law states that the volume of a given mass of gas is inversely proportional to the pressure exerted on it, provided the temperature remains constant. Mathematically, this can be expressed as:

$PV = k$

where $P$ is the pressure, $V$ is the volume, and $k$ is a constant.

To find the fluid pressure:

$P_A = \frac{F}{A}$

Where:

• Load, $F = 320N$
• Area, $A = \frac{\pi (D^2)}{4}$
• Piston Area calculation gives:

$A_A = \frac{80 \times D^2 / 4}{1.26 \times 10^{-3}}$

Thus fluid pressure is:

$P_A = \frac{F_A}{A_A} = 63661.98 ext{ Pa or } 63.66 ext{ kPa}$

Using the pressure equation:

$P_B = P_A$

Given that:

• Force on piston B = 320N

Using the same area relation:

$A_B = \frac{F_B}{P_B}$

And substituting accordingly leads to:

$D_B = 80 mm$