Dynamics

Use this for “A car at 20 m/s speeds up at 3 m/s² on a curve of radius 100 m. Find its normal and total acceleration.”

Use this for “A ball is launched at 45° and must land 40 m away on level ground. How fast must it leave the ground?”

Use this for “Car A drives north at 20 m/s and car B west at 15 m/s. Find B’s velocity relative to A.”

Use this for “A highway curve of radius 50 m is banked at 20°. What speed needs no friction, and how fast can a car take it if μₛ = 0.25?”

Use this for “A hoist raises a 500 kg crate 12 m at a steady 0.8 m/s, and its motor is 85% efficient (η = 0.85). What output power lifts the crate, and what input power does the motor draw?”

Use this for “A 0.145 kg ball reaches the bat at 40 m/s and leaves at 30 m/s the other way after 2 ms of contact. What impulse does the bat give, and what average force?”

Use this for “A 2 kg cart at 6 m/s runs into a 3 kg cart moving the same way at 1 m/s, with e = 0.5. How fast is each cart moving after the impact, and how much kinetic energy is lost?”

Use this for “A solid ball rolls without slipping down a 30° slope. Find its acceleration.”

Use this for “A 5 m ladder slides with its foot moving out at 2 m/s when it makes 60° with the floor. Find ω and the top’s speed.”

Use this for “A flywheel with I = 2 kg·m² spins at 3000 rpm. How much kinetic energy does it store?”