Work and Energy - Mission WE10 Detailed Help

A 75-kg skier starts from rest at the top of a 60-meter high practice slope (A). He uses his poles to propel himself forward, doing 10000 Joules of positive work from the top of the hill to the halfway point on 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 slope, the potential energy equation (see Formula Frenzy section) can be used to determine the initial and final potential energy of the skier. The initial height is stated and the final height is said to be one-half the initial height. The skier is said to start from rest so the initial kinetic energy is 0 J (see Formula Frenzy section). 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).


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