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 as follows:

$\text{Speed ratio} = \frac{\text{Input}}{\text{Output}}$
Where:

• Input = 80 (driven teeth)
• Output = 30 (driver teeth)

Substituting the values gives:

$\text{Speed ratio} = \frac{80}{30} = 2.67 : 1$
This indicates that for every 2.67 rotations of the driver gear, the driven gear makes 1 rotation.

The rotational frequency of the driven pulley can be derived using the gearbox ratio:

$N_1 \times D_1 = N_2 \times D_2$
Where:

• $N_1$ = Rotational frequency of washing machine pulley
• $D_1$ = Diameter of washing machine pulley = 600 mm
• $N_2$ = Rotational frequency of driven pulley = 7.2 r.s-1
• $D_2$ = Diameter of driven pulley = 800 mm

Rearranging the equation yields:

$N_1 = \frac{N_2 \times D_2}{D_1} = \frac{7.2 \times 800}{600} = 9.6 r.s-1$

To find the power transmitted, we can use the formula:

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

• $T_1$ = Force in tight side of the belt = 300 N
• $T_2$ = Tension in the slack side of the belt = 120 N
• $F$ = Factor of rotation = 7.2

From the tension values, calculating gives:

$P = (300 - 120) \times 7.2 = 1296 Watt$
This shows the power that can be transmitted by the pulley system.

The volume of a certain mass of gas can be changed through its pressure and temperature. Adjusting these two variables allows for expansion or compression, changing the volume of the 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. This means as the pressure increases, the volume decreases, and vice versa.

The fluid pressure can be calculated using the area and the force applied:

$P = \frac{F}{A}$
Where:

• $F$ = Applied load = 320 N
• $A$ = Area of piston A = $\pi (0.04 m)^2 / 4$
  Calculating gives:

$P = \frac{320}{A_A}$
Thus, the pressure in the hydraulic system is determined based on the area of piston A.

To find the diameter of piston B, we start with:

$P_B = P_A$
From the equilibrium of forces:

• We know $F_B = F_A$. Then use: $A = \frac{F}{P}$
  From the values of forces and pressure calculated, determine: $D_B = \sqrt{\frac{4A_B}{\pi}}$ This will yield the diameter of the piston B.