Answers – Mechanical Equilibrium

Mechanical Equilibrium and Newton’s First Law

Which of these objects is at mechanical equilibrium:

  1. A seagull standing on top of a fence post: at equilibrium. It’s not moving.
  2. A car moving due south at 40 kilometers per hour: at equilibrium. It’s moving at constant velocity.
  3. A water drop from a kitchen tap, just before it hits the surface of the sink: not at equilibrium. It is accelerating due to gravity.
  4. A rain drop from the sky, just before it hits the ground: probably at equilibrium. It has fallen far enough that the air resistance has canceled out the pull of gravity and it is falling at a constant speed, like a parachuted person.
  5. A car as it enters the freeway, traveling from a surface road where the speed limit is 60 km/h to the freeway where the speed limit is 100 km/h. The driver’s foot is pressing the accelerator: not at equilibrium. The car is accelerating.
  6. A can in a factory on a straight flat conveyor belt moving at 0.1 m/s: at equilibrium. It’s moving at constant velocity.
  7. A bicycle wheel rolling in a straight line at 50 revolutions per second: the center of the wheel is at equilibrium, since it is moving in a straight line at constant speed. But the edge of the wheel is not at equilibrium. See problem 10.
  8. A coin after it is dropped from someone’s hand and before it hits the ground: not at equilibrium. Gravity accelerates the coin as it falls.
  9. A rock thrown up in the air, at the very top of its journey through the air: not at equilibrium, even though its speed is zero at the top of its journey. It is still pulled to the ground by gravity.
  10. The earth as it travels around the sun. (This is a trick question, something to think about. Assume that the earth travels around the sun in a circle, and assume that the earth’s speed is constant. The earth’s orbit is approximately circular and its speed is approximately constant – after all, it goes around pretty steadily once a year.)

The earth’s speed is constant as it goes around the sun. But its velocity is not constant, because the earth is continually changing direction as it moves in a circle. Its velocity is therefore changing. It is therefore being accelerated. The force that provides the acceleration is the gravitational pull from the sun. There is no counterbalance to this force (the seagull in problem 1 experiences a counterbalance to the force of gravity – a force upward from the fence post). The earth in space has no counterbalance.

The earth (and everything on it, including us) is a collection of particles that happened to be going at the right initial velocity around the sun, long ago when the solar system was formed, such that they gathered together into a stable orbit around the sun. Other particles that were around the sun at that time either fell into the sun, formed other planets or comets or asteroids, or flew away from the sun.