Work, Energy & Gravitation
Every work, energy & gravitation calculator on CalcEngines — each with its formula, a worked example, the standard it follows and the assumptions it makes.
8 calculators in this section
- Escape Velocity and Orbital Velocity CalculatorPick a body and an altitude and you get the escape speed, the circular orbital speed, the orbital period and the field strength at that height — with the √2 that is always between the first two. Built on GM rather than on a mass, because GM is the quantity that is actually known.
- Hooke’s Law and Elastic Potential Energy CalculatorEnergy stored and energy released. ½kx² is the area under the force–extension line, so it goes as the square of the extension — and the page takes the stored energy back out again as the launch speed and the height a given mass reaches, then tells you when the extension has gone past the limit of proportionality and the formula no longer applies.
- mgh or −GMm/r: Which Gravitational Potential Energy Formula AppliesTwo formulas for one quantity, and exams punish the wrong choice. Tell me how far you moved and how big the body is, and this page tells you which form to use and by exactly how much the easy one is wrong — because the fractional error in mgh is precisely h/R, which is a closed result and not an estimate.
- Newton’s Law of Gravitation and Field Strength CalculatorF = Gm₁m₂/r² and g = GM/r² from the same inputs, with the choice of G made explicit — the published 6.674 30 × 10−11, or the three-figure 6.67 your textbook prints — and what that choice costs in the answer.
- Power and Efficiency Calculator (Two-Stage Chain)Efficiency across a chain, which is what a real machine has: two stages multiply rather than average, so 85 per cent and 92 per cent give 78.2 and never 88.5. The page compares the efficiency your quoted stages predict against the one your measured output actually shows, and says what a figure over 100 per cent means.
- Simple Pendulum and SHM CalculatorT = 2π√(L/g) with the amplitude put back in, because the small-angle result that the period does not depend on the swing is only true for small angles — and the page tells you how wrong it is at yours. Plus the choice of g, which is where three different school numbers compete.
- Work Done by a Force at an Angle CalculatorGive me a force, how far the thing moved, the angle between the two, and whatever is resisting. You get the work the force did, the work friction took back, and the net work — which is the only one the work–energy theorem will accept. Including the 90° case, where a force does nothing at all.
- Work–Energy Theorem Calculator (Final Speed and Stopping Distance)Net work equals the change in kinetic energy, so give me a mass, a starting speed, the net force and the distance and you get the final speed — plus the stopping distance, the acceleration, and the cross-check against v² = u² + 2as that must agree with it.