Transpose the Young's Modulus formula E = FL / (A * delta L) to make Extension (delta L) the subject. 2. Calculate the total extension of the 20m cable in mm when lifting 5000 N, assuming the modulus

The transposed formula is $\boxed{\Delta L = \frac{FL}{EA}}$.

2. Using the transposed formula, calculate the total extension of the 20m cable in mm when lifting a maximum load of 5000 N, assuming the modulus of elasticity for the steel is 210 GPa.

• Length of cable, $L = 20 \text{ m}$
• Maximum load (Force), $F = 5000 \text{ N}$
• Modulus of elasticity, $E = 210 \text{ GPa} = 210 \times 10^9 \text{ Pa}$
• Cross-sectional area of cable, $A = 50 \text{ mm}^2 = 50 \times (10^{-3} \text{ m})^2 = 50 \times 10^{-6} \text{ m}^2$

The total extension of the cable is approximately $\boxed{9.52 \text{ mm}}$.

3. The system operates on a 48 V DC supply with a total circuit resistance of 2.4 $\Omega$. Calculate the current flowing during the motor's operation.

• Voltage, $V = 48 \text{ V}$
• Resistance, $R = 2.4 \Omega$

The current flowing during the motor's operation is $\boxed{20 \text{ A}}$.

4. If the lift is used for a total of 2 hours during a busy work shift, calculate the total electrical energy consumed in kilowatt-hours (kWh).

• Motor input power, $P = 3.5 \text{ kW}$ (from the case scenario)
• Time of operation, $t = 2 \text{ hours}$

The total electrical energy consumed is $\boxed{7.0 \text{ kWh}}$.

5. Draw a professional circuit schematic including the 48 V source, a control switch, a safety fuse, and the hoist motor.

A circuit schematic would typically be drawn with standard symbols. Here is a description of the components and their arrangement:

• A DC voltage source (represented by two parallel lines, one longer positive and one shorter negative) labeled 48 V.
• A fuse (represented by a rectangle with a line passing through it) connected in series with the source.
• A switch (represented by a break in the line with a hinged arm) connected in series after the fuse.
• A motor (represented by a circle with an 'M' inside) connected in series after the switch.
• All components are connected in a single series loop, with wires connecting them back to the voltage source.

      +----[ Fuse ]----[ Switch ]----( M )----
      |                                     |
     --- 48V                                ---
     ---                                    |
      |                                     |
      +-------------------------------------+

This represents a series circuit where the fuse, switch, and motor are connected sequentially to the 48 V DC power source.

Task 2

1. A train runs along a level track with a velocity of 5m/s. The driver presses the accelerator, causing the train to increase speed by 2m/s2. The motion of the train is defined by the equation, $S = ut + \frac{1}{2}at^2$ meters. Calculate the time the train takes to travel a distance of 6m.

• Initial velocity, $u = 5 \text{ m/s}$
• Acceleration, $a = 2 \text{ m/s}^2$
• Distance, $S = 6 \text{ m}$

We can factor the quadratic equation.

This gives two possible solutions for $t$:

Time cannot be negative.
Therefore, $t = 1 \text{ s}$.
The time the train takes to travel a distance of 6m is $\boxed{1 \text{ s}}$.