Work and Energy - Mission WE2 Detailed Help

Mac and Tosh run up the same hill. Mac has twice the mass as Tosh. Tosh climbs up the hill in one-half the time as Mac. In this situation, _____.


 
Definition of Work:
When a force acts upon an object to cause (or to hinder) a displacement, work is done upon the object. Mathematically, work is the dot product of the force and displacement for such a situation.


Definition of Power:
Power is the rate at which work is done upon an object.


   
Work (W) is calculated from knowledge of the force (F) that acts upon an object, the displacement (d), and the angle (Θ) between the F and d vectors. The formula is
 
W = F • d • cosine(Θ).
 

Power (P) is calculated from knowledge of the work done upon an object (W) and the time (t) required to do this work. The formula is

P = W / t


 
Take some time to ponder the two definitions in the Dictionary section and the two formulas in the Formula Frenzy section. These are the key to understanding the answer to this question. The work that Mac and Tosh do is dependent upon the force they must exert and the distance they climb up the hill. Both Mac and Tosh climb the same distance (it's the same hill) but the twice-as-massive Mac must apply twice the force to lift his body (the applied force is proportional to his weight). This should allow you to compare the work of Mac to Tosh.

Power is the rate at which work is done. It depends on two variables - the amount of work that is done and the rate at which the work is done. The previous paragraph compares the work done by Mac to the work done by Tosh. This amount of work was done in different times. Mac takes twice the time as Tosh in doing his work. To compare their power, the work-to-time ratio must be taken. Doing twice the work in twice the time might be more work, but it is the same amount of power.