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 Automotive - Question 9 - 2016 - Paper 1

The speed ratio of the gear train can be calculated using:

$\text{Speed ratio} = \frac{\text{Input (Driver teeth)}}{\text{Output (Driven teeth)}}$

Substituting the values:

$\text{Speed ratio} = \frac{30}{63} = 4.2 : 1$

Using the diameter of the pulleys and their rotational speeds, we can calculate:

$N_1 \times D_1 = N_2 \times D_2$

Where:

• $N_1$ = rotational frequency of the driven pulley
• $N_2$ = rotational frequency of the driving pulley = 7.2 r.s-1
• $D_1$ = diameter of the driven pulley = 800 mm
• $D_2$ = diameter of the driving pulley = 600 mm

Solving for $N_1$ gives:

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

Power can be transmitted using the formula:

$P = (T_1 - T_2) \cdot \frac{F}{n}$

Substituting into the equation we get:

For the tension values $T_1 = 300$ N and $T_2 = 2.5 \cdot 300 = 120$ N:

$P = (300 - 120) \cdot 7.2 = 2400 \text{ Watt}$

The volume of a certain mass of gas can be changed by varying:

1. Its pressure
2. Its temperature Both pressure and temperature affect the volume of gas while keeping the mass constant.

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.

To calculate the fluid pressure, we use:

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

Where:

• $F = 80 N$
• $A_A = 0.04\text{ m}^2$

Calculating gives:

$P_A = \frac{80}{0.04} = 2000 \text{ Pa}$

Using the relationship between the pressures in both pistons, we can set:

$P_B = P_A$

Calculating for $A_B = \frac{F_B}{P_B}$:

determining the diameter:

$D_B = \sqrt{A_B / \pi}$ We obtain: $D_B = 80 mm$