Work and Energy - Mission WE10 Detailed Help

A 50-kg skier starts from rest at the top of a 60-meter high practice slope (A). She uses her poles to propel her forward, doing 12 000 Joules of positive work until she gets to the bottom of the hill (B). Use g = 10 N/kg to perform an energy analysis and fill in all the blanks.

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

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. The amount of work done on the object by non-conservative forces is equal to the amount of change in mechanical energy.

Like all questions in this mission, the work done by non-conservative forces must be related to the changes in energy of the object (see Know the Law section). In the case of the skier on the practice hill, the potential energy equation (see Formula Frenzy section) can be used to determine the initial and final potential energy of the skier. Since the skier is at ground level in the final state, the height and potential energy can be regarded as zero. The initial kinetic energy is 0 J since the skier starts from rest. The final kinetic energy can be determined by using the relationship between work and energy. The change in total mechanical energy is caused by and equal to the work done upon the object. The work is stated in the question statement. This work value is equal to the difference between initial and final mechanical energy. In equation form
KEi + PEi + Wnc = KEf + PEf

The final kinetic energy can be calculated using the above equation.

The amount of kinetic energy (KE) possessed by an object depends upon its mass (m) and its velocity (v). The formula is
KE = 0.5 • m • v2

The amount of potential energy (PE) possessed by an object depends upon its mass (m) and its height (h). The formula is

   PE = m • g • h  

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