Unit 8: Continued

This is my friend Brian, who has just raced up two flights of stairs with my friend Cathryn. She is a really good sprinter...so obviously, she won. Let's find out the amount of work he does and how much power he exerts using what we learned in class today. He weighs around 130 pounds, while she weights about 105. To convert this to kilograms we divide it by 2.2 kg. Gravity is about 10 meters per second, so we can now find the force by using the equation F=ma.
130 lbs x 1 kg/2.2 lb = 59.09 kg ---> 59.09 kg(10m/s) = 590.9 N
105 lbs x 1 kg/2.2 lb = 47.73 kg ---> 47.73 kg(10m/s) = 477.3 N
They both ran the same amount of distance (two flights of stairs, about 10 meters?), but who did the most work? Who exerted the most power? We can solve for this using these equations:
work (joules) = force • distance
power (watts) = work/time
Cat beat Brian up the stairs, so we know she took less time than him to travel the same distance. She took about seven seconds, while he took around fifteen (Brian is lazy).
Brian's
     Work: 590.9 N • 10m = 5909 J
     Power: 5909 J / 15 s = 393.93 watts

Cat's
     Work: 477.3 N • 10m = 4773 J
     Power: 4773 J / 7 s = 681.86 watts
So what can we conclude? Even if Cat beat Brian up the stairs, Brian still worked more than she did! Why? Because work is any change in energy, while power is the rate at which work is done. This is why Cat exerted more power than Brian.