Mechanics in Motion: From Newton to Propulsion

Apply Newton's first, second, and third laws to problems like a 2 kg book on a frictionless table under 5 N for 3 s and a 1500 kg car accelerating.

Explore how position, velocity, and acceleration relate through problems, calculating instantaneous velocity, average velocity, and distance from position-time and velocity-time graphs.

Learn motion with constant acceleration in a line by solving final velocity and distance problems, and apply the v^2 = v0^2 + 2 a s formula to a vertical throw.

Explore forces and moments on a bicycle, solving for support force in straight line motion and the centripetal demand, lean angle, and safe speed in turns using friction and gravity.

Learn how lift balances the weight of a 150 kg single-person rowing boat at rest, and how hull friction drag depends on velocity, wetted area, and water density.

Compute hot air balloon lift with the lifting force equation and the ideal gas law for a 2500 m³ balloon, and buoyancy for a 1000 m³ helium balloon.

Explore how level flight requires lift equal to weight, here 9800 newtons for a 1000 kg aircraft, and how thrust balances drag to yield 500 watts at 10 m/s.

Analyze force vectors and their components for a cyclist on a 15-degree incline, resolving weight 800 N, pedaling 200 N, headwind 50 N to determine deceleration or acceleration.

Learn how to compute moments and couples using moment = F times d, assess single and multiple forces on a beam, and analyze opposite, parallel forces forming a couple.

Explore boat stability through buoyancy, density, and displaced water, derive the center of buoyancy and metacenter, and compute righting moments for a barge.

Compute rotational kinetic energy, angular momentum, translational kinetic energy, and angular acceleration for a wheel using 1/2 I ω^2, I ω, 1/2 m v^2, and torque divided by inertia.

Analyze bicycle brake dynamics under friction and rotational motion. Compute stop time, revolutions, and the change in rotational kinetic energy using moment of inertia and angular acceleration.

Explore work, energy, and power through problems on a frictionless incline and a roller coaster, applying the work-energy theorem, gravity components parallel to the plane, and height-based energy changes.

Explore work, kinetic energy, and power through three problems with variable and constant forces, using integration, the work-energy theorem, and instantaneous and average power.

Examine elastic potential energy in springs using Hooke's law, calculate forces to fully compress bike suspensions, and analyze parallel spring systems with energy conservation.

Investigate friction by comparing dry and wet surfaces, calculate force and work to move a block, then analyze incline friction with static and kinetic coefficients and pulley effects.

Explore bicycle bearing mechanics in a hub with ten 5 mm steel balls, 15 and 26 mm diameters, rotating at 300 rpm, computing outer and surface speeds, ball angular velocity.

Analyze two lubrication problems: a thin film between moving plates calculating shear rate, shear stress, viscosity, and force; and a rotating circular-plate system determining edge shear rate, torque, and power.

Explore rolling resistance and its energy dissipation in wheel systems by calculating the resistance force, the power to overcome it, and the energy dissipated over 5 km at 15 km/h.

Explore the torque and power loss due to rolling resistance for a rigid wheel on soft ground, with a 0.5 m radius, 0.2 m depression, and 5 m/s speed.

Assess rolling and air resistance in bicycles by comparing wheel sizes (26 and 29 inch) and how power to overcome these forces scales with speed, air density, and frontal area.

Learn how to determine pressure in fluids using a u-shaped water manometer, with density 1000 kg/m3 and a 15 cm height difference, applying rho g h to find a delta p of 1,471.5 pa. Add this to atmospheric pressure p1 of 101.3 kpa to obtain p2 of about 102.8 kpa.

Compute liquid's volume, density, and specific gravity in a cylindrical tank (radius 0.5 m, height 2 m, mass 2356 kg) using pi r square h and water density 998.2 kg/m^3.

Apply the ideal gas equation PV = nRT to calculate volume and show that at pressure volume scales with temperature, then note carbon dioxide liquefaction limits from the critical temperature.

Compute the oil viscosity between parallel plates and the velocity at 0.3 mm from the bottom plate, illustrating a Newtonian fluid with a linear profile.

Compute Reynolds numbers for an airfoil in air and water via rho u d / mu, and assess lift changes with CL across angles of attack at 50 m/s.

Apply continuity and Bernoulli's equation to a horizontal pipe narrowing from 0.05 m² to 0.03 m² with Q=0.2 m³/s, deriving v1, v2, and P2, illustrating velocity rises as area narrows.

Explore boundary layers and drag by solving a flat-plate flow in a wind tunnel, calculating Reynolds number, turbulent friction coefficient, and the total skin friction drag.

Compute wing area, dynamic pressure q, and lift and drag from CL and CD; relate lift-to-drag ratio to CL/CD for a rectangular wing.

Calculate jet engine propulsion with the thrust equation, mass flow rate times change in velocity, using 80 kg/s and a 400 m/s exit velocity to yield 32,000 N of thrust.