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Home Minds On Work and Energy Mission WE7 Mechanical Energy Conservation Help Help 5

Mission WE7 Mechanical Energy Conservation

The Question

An object starts at rest from a height of 40 meters. It's total amount of mechanical energy is 400 Joules. The object begins a free-falling motion; there is no air resistance. When it has fallen to a height of one-fourth of its original height, its potential energy will be ____ Joules and its total amount of mechanical energy will be ____ Joules.

(Note: Your numbers are randomly selected and likely different from the numbers listed here.)

Physics Rules

Work - Mechanical Energy Relationships:
If non-conservative forces do net work upon an object, then the total mechanical energy of that object is changed. The sum of the kinetic and potential energies will change as work is done upon the object. If non-conservative forces do NOT do net work, then the total mechanical energy will be conserved.

Formula Fix

The potential energy is the energy stored in an object due to its vertical position above (or below) the ground or some zero level. The amount of kinetic energy (PE) possessed by an object depends upon its mass (m) and its height (h). The formula for calculating the potential energy is
 
PE = m • g • h  

where g is the gravitational field strength (9.8 N/kg on Earth).

Minds On Time

The object is said to be in free-fall. The only force acting AND doing work upon the object is gravity. Gravity is a conservative force and so the total amount of mechanical energy is conserved. It is the same at every point during its fall as it is initially. See Know the Law section.
Potential energy is the stored energy of position. In the case of the falling object, its height (i.e., vertical position above the ground) is decreasing. In fact, it decreases to one-fourth its original value. The object starts at rest, so there is no kinetic energy in the initial state. The initial potential energy is the same as the total amount of energy. Once the object has fallen to one-fourth its original height, its potential energy is one fourth its original value. See Formula Frenzy section.

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