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Kinetic and potential energy, work and power calculator

Kinetic energy (½mv²), potential energy (mgh), spring energy, work (Fd cos θ) and power (W/t), solved for any variable, plus the speed after a drop.

হালনাগাদ যাচাই করা উদাহরণ: ৮

চেষ্টা করুন
Energy or work
J
Energy or work: 200,000 J
সার্থক অঙ্ক: ৬; নিকটতম; সমান দূরত্বে শূন্য থেকে দূরে
ভর
1,000kg
দ্রুতি
20m/s
Energy or work
0.0555556kWh

1,000 kg moving at 20 m/s carries 200,000 J of kinetic energy; doubling the speed would quadruple it.

Kinetic energy against speed

0100,000200,000300,000400,0000102030Speed (m/s)Energy (J)200,000 J
যেভাবে হিসাব করা হয় S

  1. Kinetic energy

    E=12mv2=12(1,000)(20)2=200,000 JE = \tfrac12 mv^2 = \tfrac12(1{,}000)(20)^2 = 200{,}000\ \mathrm{J}

Kinetic and potential energy, work and power calculator সম্পর্কে

Six formulas cover the common mechanical-energy problems: kinetic energy ½mv², gravitational potential energy mgh, spring energy ½kx², work Fd cos θ, average power W ÷ t, and the speed after a frictionless drop, √(v₀² + 2gh). Pick one, choose the variable to solve for, and the others become inputs.

Energy comes out in joules, with the kilowatt-hour equivalent beside it from 1 Wh (3,600 J) up; 1 kWh = 3.6 MJ. The default, a 1,000 kg car at 20 m/s (72 km/h), carries 200,000 J, or 0.0556 kWh; at 40 m/s it would carry four times as much.

Potential energy is measured from whichever level you call h = 0, so only differences in height matter. The drop mode ignores friction and air resistance, which makes its speeds an upper limit for real falls.

সমাধান করা উদাহরণ

1000 kg car at 20 m/s

Quantity
Kinetic energy ½mv²
Solve for
শক্তি
ভর
1000 kg
দ্রুতি
20 m/s
Energy or work
200,000 J
Energy or work
0.055556 kWh

যাচাইয়ের উৎস: Python 3.8 decimal: ½ × 1000 × 20² = 200000 J = 0.0555… kWh

Speed of a 0.145 kg ball carrying 100 J

Quantity
Kinetic energy ½mv²
Solve for
দ্রুতি
Energy or work
100 J
ভর
0.145 kg
দ্রুতি
37.1391 m/s

যাচাইয়ের উৎস: Python 3.8 decimal: v = √(2E/m) = √(200/0.145) = 37.1390676…

50 kg lifted 10 m

Quantity
Gravitational potential energy mgh
Solve for
শক্তি
ভর
50 kg
উচ্চতা
10 m
Energy or work
4,903.33 J

যাচাইয়ের উৎস: Python 3.8 decimal: 50 × 9.80665 × 10

Spring k = 200 N/m compressed 10 cm

Quantity
Spring energy ½kx²
Solve for
শক্তি
Spring constant k
200 N/m
Extension or compression x
10 cm
Energy or work
1 J

যাচাইয়ের উৎস: Python 3.8 decimal: ½ × 200 × 0.1² = 1 J

প্রশ্ন

What is the formula for kinetic energy?

Kinetic energy is KE = ½mv²; with mass in kilograms and speed in metres per second the result is in joules. Because speed is squared, doubling it quadruples the energy: a 1,000 kg car has 200 kJ at 20 m/s and 800 kJ at 40 m/s. Rearranged for speed, v = √(2KE ÷ m), so a 0.145 kg ball carrying 100 J moves at 37.1 m/s.

What is the difference between work and power?

Work is energy transferred by a force, W = Fd cos θ, measured in joules; power is how fast that transfer happens, P = W ÷ t, measured in watts, where 1 W = 1 J/s. Lifting 50 kg through 10 m takes 4,903 J however it is done; doing it in 5 s needs 981 W, and spreading it over 60 s needs 81.7 W.

How many joules are in a kilowatt-hour or a kilocalorie?

One kilowatt-hour is 3,600,000 J, because it is 1,000 W sustained for 3,600 s. One kilocalorie, the food Calorie, is 4,184 J, using the thermochemical calorie of exactly 4.184 J listed in NIST SP 811. The 200,000 J carried by a 1,000 kg car at 20 m/s is therefore 0.0556 kWh, or about 47.8 kcal.

How fast does an object hit the ground when dropped?

Without air resistance the impact speed is v = √(2gh), whatever the mass. A drop from 20 m ends at 19.81 m/s (71.3 km/h); a drop from 5 m ends at 9.90 m/s. Speed grows with the square root of height, so four times the height only doubles the speed. Air drag makes real speeds lower, most of all for light objects and long falls.

How much energy does a spring store?

A spring stores E = ½kx², where k is the spring constant in N/m and x the extension or compression in metres. A 200 N/m spring compressed by 10 cm stores 1 J; compressed by 20 cm it stores 4 J. The formula holds only within the elastic range, where Hooke's law F = kx applies and the spring returns to its original length.

“Kinetic and potential energy, work and power calculator” কতটা নির্ভুল?

নির্ভুলতা আপনার ইনপুট ও পদ্ধতির অনুমানের ওপর নির্ভর করে। দশমিক গণনায় 50টি সার্থক অঙ্ক ব্যবহৃত হয়, কিন্তু আনুমানিক হিসাব, সংখ্যাগত পদ্ধতি ও উৎসের তথ্য কম নির্ভুল হতে পারে; প্রদর্শিত মান রাউন্ড করলে এই সীমাবদ্ধতাগুলি দূর হয় না। স্বতন্ত্র উৎসের সমাধানের সঙ্গে যাচাই করা উদাহরণ: ৮। যেমন, “1000 kg car at 20 m/s” উদাহরণটি Python 3.8 decimal: ½ × 1000 × 20² = 200000 J = 0.0555… kWh-এর সঙ্গে যাচাই করা হয়।

এই পদ্ধতির উৎস কী?

OpenStax University Physics Volume 1, ch. 7 Work and kinetic energy; ch. 8 Potential energy and conservation of energy; HyperPhysics — Work, energy and power.

এই ক্যালকুলেটর সম্পর্কে

KE=12mv2,PE=mgh,Es=12kx2,W=Fdcos⁡θ,P=Wt,vb=v02+2ghKE = \tfrac12 mv^2,\quad PE = mgh,\quad E_s = \tfrac12 kx^2,\quad W = Fd\cos\theta,\quad P = \frac{W}{t},\quad v_b = \sqrt{v_0^2 + 2gh}

উৎস

  1. OpenStax University Physics Volume 1, ch. 7 Work and kinetic energy; ch. 8 Potential energy and conservation of energy
  2. HyperPhysics — Work, energy and power

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