Falling and keeping the total

The idea

As an object moves under the gravitational force with no other external forces acting, the potential energy it loses becomes kinetic energy, so its mechanical energy stays constant.

A falling ball

A ball is dropped from a height. As it falls it goes faster, so it gains energy of motion.

Where do you think that extra energy of motion comes from?

• From the energy it had because of its height
• From nowhere
• From the air pushing it down

Drop the ball

The ball falls 20 m. We take g = 10 m s⁻² and ignore the air. Press Drop.

A swap, not a loss

While the ball fell, its potential energy decreased and its kinetic energy increased by exactly the same amount. The sum, the mechanical energy, stayed constant. Writing it out with the equations of motion gives mgh for the total at every moment.

As an object moves under the gravitational force with no other external forces acting, the potential energy it loses becomes kinetic energy, so its mechanical energy stays constant. This is the conservation of mechanical energy.

Notes

When only gravity acts, the potential energy lost becomes kinetic energy and the mechanical energy stays constant: conservation of mechanical energy.

Check yourself

A ball falls freely. Its potential energy decreases. What happens to its kinetic energy?

The mechanical energy of a freely falling object, with no other external forces acting, is…

A ball has a mechanical energy of 400 J at the top. During its fall its potential energy is 300 J at one moment. What is its kinetic energy then, in J? (No other forces act.)

Answer: 100 J

K = 400 J − 300 J = 100 J.

What is the name of the idea that the mechanical energy stays constant when only gravity does work?

• It decreases too. The potential energy it loses is converted into kinetic energy, so the kinetic energy increases.
• It increases by the same amount — correct. Yes!
• It stays the same. The ball speeds up as it falls, so its kinetic energy increases.
• increasing, since the ball speeds up. The kinetic energy increases, but the potential energy decreases by the same amount, so the sum is constant.
• decreasing, since the ball loses height. The potential energy decreases, but the kinetic energy increases by the same amount, so the sum is constant.
• constant — correct. Yes!
• The conservation of mechanical energy — correct. Yes!
• The work-energy theorem. That theorem says the work done on an object equals the change in its energy.
• The definition of power. Power is the rate at which work is done.