The commercial unit for measurement of electrical energy consumption is the kilowatt-hour (kWh).
This economics question tests your understanding of economic models and analysis. The step-by-step answer below applies the relevant framework and explains the reasoning.
ScanSolve AI Answer
Here are the solutions to the questions.
1. a)
The commercial unit for measurement of electrical energy consumption is the kilowatt-hour (kWh).
1. b)
Step 1: Calculate the energy consumed by the heater per day.
Power of heater $P = 1000 \text{ W} = 1 \text{ kW}$.
Time used per day $t = 5 \text{ hours}$.
Energy consumed per day $E_{\text{day}} = P \times t = 1 \text{ kW} \times 5 \text{ h} = 5 \text{ kWh}$.
Step 2: Calculate the total energy consumed for 30 days.
Total energy $E_{\text{total}} = E_{\text{day}} \times 30 \text{ days} = 5 \text{ kWh/day} \times 30 \text{ days} = 150 \text{ kWh}$.
Step 3: Calculate the total cost.
Cost per kWh = 50 frs.
Total cost = $E_{\text{total}} \times \text{Cost per kWh} = 150 \text{ kWh} \times 50 \text{ frs/kWh} = \boxed{7500 \text{ frs}}$.
1. c)
Step 1: Calculate the current drawn by the heater.
Power $P = 1000 \text{ W}$.
Voltage $V = 220 \text{ V}$.
Current $I = \frac{P}{V}$.
$$I = \frac{1000 \text{ W}}{220 \text{ V}}$$
$$I \approx 4.55 \text{ A}$$
Step 2: Determine a suitable fuse value.
A fuse should have a rating slightly higher than the normal operating current to prevent it from blowing unnecessarily, but low enough to protect the circuit in case of a fault. Common fuse values are 1 A, 2 A, 3 A, 5 A, 10 A, 13 A.
The next standard fuse value above 4.55 A is 5 A.
The fuse value that would be good for the heater is $\boxed{5 \text{ A}}$.
2. a)
The forces acting on the bucket are:
• Weight (W): Acting vertically downwards from the center of mass of the sand and bucket.
• Tension (T): Acting vertically upwards along the string.
`
Support
|
| T (Tension)
|
-----
| |
| | Bucket of sand
|-----|
|
| W (Weight)
|
Center of Mass
`
2. b)
Step 1: Identify the given mass.
Mass of sand $m = 25 \text{ kg}$.
Step 2: Use the acceleration due to gravity $g = 10 \text{ m/s}^2$.
Step 3: Calculate the weight of the sand.
Weight $W = m \times g$.
$$W = 25 \text{ kg} \times 10 \text{ m/s}^2$$
$$W = \boxed{250 \text{ N}}$$
2. c)
One difference between weight and mass is that mass is a measure of the amount of matter in an object and is constant everywhere, while weight is the force of gravity acting on an object and varies with gravitational field strength.
2. d)
Step 1: The system is in equilibrium, meaning the net force is zero.
Step 2: Neglecting the weight of the bucket, the upward force (support provided by the string, which is tension T) must balance the downward force (weight of the sand W).
$$T = W$$
Step 3: From part b), the weight of the sand is 250 N.
$$T = 250 \text{ N}$$
The support provided by the string is $\boxed{250 \text{ N}}$.
3. a)
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