1.7.2 Work (3)
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1.
A 10 A current flows through a resistor of 10 ohms. Calculate the electrical power dissipated by the resistor. Explain how this electrical power relates to the energy transferred in a circuit. Include a brief explanation of the relationship between power, energy, and time.
Answer:
- Calculate the electrical power: P = I2R = (10 A)2 × 10 Ω = 100 W.
- The electrical power dissipated by the resistor is equal to the rate at which electrical energy is converted into heat. This is a direct consequence of the fundamental relationship between power, energy, and time: Energy = Power × Time. In a circuit, the power dissipated by a resistor is the electrical energy transferred to the resistor per unit time. The electrical energy is transferred from the source through the circuit and is dissipated as heat in the resistor.
- The electrical power is directly proportional to the energy transferred in a circuit. A higher power means more energy is transferred in a given time. The relationship is clearly expressed in the formula Energy = Power × Time.
2.
A student applies a force of 25 N to a block of wood, moving it 0.5 m across a level surface. Calculate the amount of mechanical work done by the student.
Given:
- Force (F) = 25 N
- Distance (d) = 0.5 m
Equation: Mechanical Work (W) = F d = ΔE
Calculation:
W = 25 N × 0.5 m = 12.5 J
Answer: The student does 12.5 J of mechanical work.
3.
A student pushes a box across a rough floor with a constant force of 20 N for a distance of 5 metres. The coefficient of kinetic friction between the box and the floor is 0.3. Calculate the amount of work done by the student on the box. Show your working.
Answer:
- Calculate the force of friction: Ffriction = μN = μmg, where μ = 0.3, m is the mass of the box, and g is the acceleration due to gravity (9.8 m/s2). We don't know the mass, so we can't calculate the exact friction force. However, the question asks for the work done by the student, which is the energy transferred to the box. The work done by the student is equal to the change in kinetic energy of the box. Since the box starts from rest, the work done by the student is equal to the final kinetic energy of the box.
- The work done by the student is given by: W = Fd = 20 N × 5 m = 100 J. This is the work done by the student.
- The work done by the student is equal to the energy transferred to the box. Therefore, the energy transferred to the box is 100 J.