Obtaining kinetic energy equation.

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SUMMARY

The discussion centers on deriving the kinetic energy equation for a mass represented by its position in two dimensions, specifically using the coordinates (2rsin(a) - rsin(b), 2rcos(a) + rcos(b)). To find the speed of the mass, participants emphasize the necessity of applying Pythagoras' theorem rather than simply summing the velocities in the x and y directions. The correct approach involves calculating the kinetic energies in each direction separately and then combining them to obtain the total kinetic energy.

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  • Understanding of basic calculus, specifically differentiation
  • Familiarity with Pythagorean theorem applications in physics
  • Knowledge of kinetic energy formula: KE = (1/2)mv²
  • Concept of vector addition in two-dimensional motion
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  • Explore vector calculus for understanding motion in multiple dimensions
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The question is about 2 sticks standing above each other, but i have a more general question.

The position of my mass is described by: (2rsin(a) - rsin(b) , 2rcos(a)+rcos(b))

the goal is to get a formula for the kinetic energy, so i need the speed of the mass.

If i take the derivatives of both functions i get the speed in x and y direction.

So my question is: is it allowed for the v in (mv^2)/2 to summ up the velocities in both directions and to use it as the formula of v in the kinetic energy equationThis is my first post on this forum, so sorry for the lay-out of this question which is probably wrong...
 
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Welcome to PF!

You can't just sum them, you have to use Pythagoras' theorem.
 
sk1105 said:
you have to use Pythagoras' theorem.
From which it follows that what you can do is calculate the KEs in the two directions separately and add those.
 

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