This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Task 1 1. Transpose the Young's Modulus formula E = (FL)/(A L) to make Extension ( L) the subject. Step 1: Start with the given formula. E = (FL)/(A L) Step 2: Multiply both sides by A L. E A L = FL Step 3: Divide both sides by EA to isolate L. L = (FL)/(EA) The transposed formula is L = (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. Step 1: Identify the given values and convert them to SI units. • Length of cable, L = 20 m • Maximum load (Force), F = 5000 N • Modulus of elasticity, E = 210 GPa = 210 × 10^9 Pa • Cross-sectional area of cable, A = 50 mm^2 = 50 × (10^-3 m)^2 = 50 × 10^-6 m^2 Step 2: Substitute the values into the transposed formula. L = (FL)/(EA) L = (5000 N)(20 m)(210 × 10^9 Pa)(50 × 10^-6 m^2) Step 3: Calculate the extension in meters. L = 100000 N·m10500 × 10^3 N L = (100000)/(10500000) m L ≈ 0.0095238 m Step 4: Convert the extension to millimeters. L = 0.0095238 m × 1000 mm1 m L ≈ 9.5238 mm The total extension of the cable is approximately 9.52 mm. 3. The system operates on a 48 V DC supply with a total circuit resistance of 2.4 . Calculate the current flowing during the motor's operation. Step 1: Identify the given values. • Voltage, V = 48 V • Resistance, R = 2.4 Step 2: Use Ohm's Law to calculate the current. I = (V)/(R) I = 48 V2.4 I = 20 A The current flowing during the motor's operation is 20 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). Step 1: Identify the given values. • Motor input power, P = 3.5 kW (from the case scenario) • Time of operation, t = 2 hours Step 2: Calculate the energy consumed using the formula E = P × t. E = (3.5 kW) × (2 hours) E = 7.0 kWh The total electrical energy consumed is 7.0 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 + (1)/(2)at^2 meters. Calculate the time the train takes to travel a distance of 6m. Step 1: Identify the given values. • Initial velocity, u = 5 m/s • Acceleration, a = 2 m/s^2 • Distance, S = 6 m Step 2: Substitute the values into the given equation. S = ut + (1)/(2)at^2 6 = (5)t + (1)/(2)(2)t^2 Step 3: Simplify the equation to form a quadratic equation. 6 = 5t + t^2 t^2 + 5t - 6 = 0 Step 4: Solve the quadratic equation for t. We can factor the quadratic equation. (t+6)(t-1) = 0 This gives two possible solutions for t: t+6 = 0 t = -6 s t-1 = 0 t = 1 s Step 5: Choose the physically meaningful solution. Time cannot be negative. Therefore, t = 1 s. The time the train takes to travel a distance of 6m is 1 s. Send me the next one 📸