Physics Mechanics Calculator

On flat ground with no air resistance, 45 degrees gives the maximum horizontal range. A projectile launched at 20 m/s at 45 degrees travels about 40.8 meters. In practice, air drag makes the optimal angle slightly lower - typically 38 to 42 degrees depending on the object's shape and speed.

Use the formula KE = 0.5 times mass times velocity squared. A 1 kg ball moving at 10 m/s has 50 joules of kinetic energy. Doubling the speed quadruples the energy to 200 J, which is why vehicle crash severity increases so dramatically with speed.

A simple pendulum with a length of 1 meter swings with a period of about 2.006 seconds at sea level where g = 9.81 m/s squared. The formula is T = 2 pi times the square root of L/g. The period depends only on length and gravity - not on the mass of the bob or the amplitude for small angles under about 15 degrees.

Total momentum before a collision equals total momentum after. If a 2 kg cart moving at 3 m/s hits a stationary 1 kg cart and they stick together, the combined 3 kg mass moves at 2 m/s. Momentum is conserved (6 kg m/s) but kinetic energy drops from 9 J to 6 J - the missing 3 J becomes heat and sound.

Divide the applied force by the displacement from the spring's natural length. A spring that stretches 0.05 m under a 10 N force has a spring constant of 200 N/m. This linear relationship (Hooke's law) holds until the spring reaches its elastic limit, typically at 1-3% strain for steel springs.