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Monday, August 17, 2026

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Question 1 of 5 Score: 0 / 0

1.7.5 - Energy, work and power Core

An electric motor is used to raise a load of mass $60\ \text{kg}$ through a vertical height of $15\ \text{m}$ at a steady speed. The motor draws electrical power from the supply at a rate of $500\ \text{W}$ and is $40\%$ efficient. Taking $g = 10\ \text{N/kg}$ , how long does the lift take?

Detailed Explanation

The motor must supply more energy than it usefully delivers because it is only 40% efficient, so divide the lifting work (mgh) by the efficiency to get the input energy, then divide by the input power to get the time (45 s).

1.2.2 - Motion Core

A car starts from rest and accelerates uniformly at $2.5\ \text{m/s}^2$ for $8.0\ \text{s}$ . It then travels at constant speed for $12\ \text{s}$ , and finally decelerates uniformly to rest in a further $5.0\ \text{s}$ . What is the total distance travelled by the car?

Detailed Explanation

Break the motion into three phases and add the distances; the accelerating and decelerating phases cover only half of (max speed x time) because the speed is changing, so each is a triangle on a speed-time graph while the middle phase is a rectangle.

4.5.4 - Force on a current-carrying conductor Core

A current-carrying wire is placed in a uniform magnetic field. State the three factors that determine the magnitude of the force on the wire.

Detailed Explanation

Force on a Current-Carrying Wire in a Magnetic Field

Why the correct answer is right: The magnetic force on a wire follows the equation: F = BIL

B = magnetic field strength (Tesla)
I = current in the wire (Amperes)
L = length of wire in the field (meters)

These three factors directly multiply together to give the force magnitude.

Key concept: When electric current flows through a wire in a magnetic field, the moving charges experience a force that transfers to the wire itself.

Helpful tips:

Remember "BIL" as your formula
All three factors must be present - no current means no force, no magnetic field means no force, no wire length means no force
The force is maximized when the wire is perpendicular to the magnetic field
This principle is used in electric motors and loudspeakers

Note: The angle between wire and field affects force direction but these three factors determine the magnitude.

1.5.2 - Turning effect of forces Core

A uniform beam of length 4.0 m is balanced on a pivot at its center. A 60 N force acts downward at a distance of 1.5 m from the pivot. The diagram shows the setup. What does the calculation show for the balancing force F needed at the opposite end of the beam?

Detailed Explanation

Why 45 N is correct: For a balanced beam the clockwise and anticlockwise moments about the pivot must be equal (the principle of moments: force × perpendicular distance). The 60 N force acts 1.5 m from the pivot, giving a moment of 60 × 1.5 = 90 N·m. The balancing force F acts at the far end, which is half of the 4.0 m beam = 2.0 m from the pivot, so F × 2.0 = 90, giving F = 45 N.

Common mistakes: Answering 60 N comes from assuming the two forces must be equal and forgetting that they act at different distances. Getting 80 N comes from inverting the distance ratio (multiplying 60 by 2.0/1.5 instead of balancing the moments). Getting 180 N comes from using the full 4.0 m length, or multiplying the 90 N·m moment by 2.0 m instead of dividing by it.

4.5 - Electromagnetic effects Extended

A rectangular coil of $3$ turns is connected in series with a $2.0\,\Omega$ resistor to a $12\,\text{V}$ supply of negligible internal resistance. The coil wire itself has a total resistance of $4.0\,\Omega$ . One side of the coil, of length $0.25\,\text{m}$ , lies at right angles to a uniform magnetic field of flux density $0.40\,\text{T}$ . What is the total magnetic force acting on that side of the coil?

Detailed Explanation

First use the series resistance (4.0 + 2.0 = 6.0 ohm) and Ohm's law to find I = 2.0 A, then apply F = BIL for one wire and multiply by the 3 turns to get 0.60 N. Skipping the series resistor or the number of turns each lands you on a wrong but plausible value.

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