Physics - Mechanics and Energy
This domain covers motion, forces, work, and energy as tested in the Niigata public high school entrance examination. Questions typically require reading distance–time and velocity–time graphs, combining forces, calculating work and power, and applying energy conservation to carts, springs, and falling objects. State units and directions explicitly.
Motion
- Average speed = total distance ÷ total time; instantaneous speed is the slope of a distance–time graph.
- Velocity includes direction. Acceleration = change in velocity ÷ time; on a velocity–time graph, slope = acceleration and area under the line = displacement.
- In free fall with negligible air resistance, acceleration is about 9.8 m/s² downward and is independent of mass.
Forces
- Newton’s first law: if net force is zero, an object stays at rest or moves at constant velocity.
- Newton’s second law: acceleration is proportional to net force and inversely proportional to mass (F = ma).
- Newton’s third law: forces act in equal and opposite pairs on different objects.
- Weight = mass × gravitational acceleration; normal force and friction act at surfaces.
Work and energy
- Work = force × displacement in the force direction (J). A force perpendicular to motion does no work.
- Kinetic energy = ½mv²; gravitational potential energy = mgh.
- Without friction, mechanical energy is conserved; friction converts mechanical energy to thermal energy.
- Power = work ÷ time (W).
Worked example
A 2.0 kg cart at 3.0 m/s is pushed by a constant 4.0 N force over 5.0 m. Find its final speed. Work done = 4.0 × 5.0 = 20 J. Initial KE = ½ × 2.0 × 3.0² = 9 J. Final KE = 29 J. Since KE = ½mv², v² = 2 × 29 ÷ 2.0 = 29, so v ≈ 5.4 m/s. The work–energy route avoids finding time and rounding twice.
Traps
- Using distance instead of displacement.
- Adding forces in different directions as scalars.
- Reading area under a distance–time graph as displacement.
- Saying energy disappears when friction acts; it becomes thermal energy.
- Forgetting to square speed in kinetic energy.