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No, force and energy are not the same dimension to start with. Gravitational force on an object is equal to mass*(gravitational acceleration) {dimensions Mass*Length/Time²}

Kinetic energy is (1/2)*mass*(velocity)² {dimensions Mass*Length²/Time²}. If you look at these, Force, multiplied by length has the same dimension as Energy. And in fact you have other forms of energy:

  • Work is Force times distance;
  • Potential energy = mass*(gravitational accel)*height = (Force due to gravity)*(height), height is a distance or length.
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