Amazon has hired you to help design a new fleet of robots to work in their warehouse. You are trying to decide how powerful the motor that allows the robots to climb vertically up the selves should be. assume that the robot itself will have a mass of 15 kg and needs to be able to carry an object with a mass of 5 kg up to the top of a 20 m shelf in 8 seconds. What minimum wattage should you use?

The work that needs to be done by the robot in order to climb the shelves is equal to the gain in gravitational potential energy of the robot + object, therefore:

[tex]W=mg \Delta h[/tex]

where

m = 15 kg + 5 kg = 20 kg is the total mass of the system

[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

[tex]\Delta h = 20 m[/tex] is the change in height

Substituting,

[tex]W=(20)(9.8)(20)=3,920 J[/tex]

Now we can calcualte the power (wattage) that the robot must have, using the equation

[tex]P=\frac{W}{t}[/tex]

where

W = 3,920 J is the work done

t = 8 s is the time interval

Substituting,

[tex]P=\frac{3920}{8}=490 W[/tex]

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