Work and Energy - Mission WE10 Detailed Help

A 40-kg skier uses a toe rope to ascend to the top of a practice hill. She grabs the rope while moving with a speed of 2 m/s at the bottom of the hill (A). The rope pulls her at a constant speed to the top of the 50-meter high 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.)


 
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 being pulled by a toe rope, the kinetic energy equation (see Formula Frenzy section) can be used to determine the initial and final kinetic energy of the skier. Since the skier moves up the hill at a constant speed, the initial and final kinetic energy are the same. 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 can be regarded as zero and the final height is given. There is a difference between the amount of initial and final mechanical energy (KE + PE). The change in mechanical energy is caused by and equal to the work done upon the object. By calculating the change, the work can be determined.


 
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.


 
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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