hey everyone

 

sorry i just got back from a big night out last night and yeah hard to think, so that sort of explains the title

 

anyways.... my query (this is not a homework question of anything, just a general th0ouoght i had when reading a physics text)

 

why is it that when a pendulum is swinging that you can assume it has maximum KE at the bottom of its swinging arc?

 

Cheers

 

Sarah

i think it may be because that if you set the "zero" position for PE to be at the bottom of the swing, therefore Emech will be just .5mv^2 because PE at this point is zero. so the formula Emech = PE + KE, is just Emech = KE

 

what do you guys think?

 

man bad hangover and not much sleep

why is it that when a pendulum is swinging that you can assume it has maximum KE at the bottom of its swinging arc?

 

Cheers

 

Sarah

 

Because it's a conservative system.

 

Rev Prez

oh ok thanks

Well if

 

KE = 1/2 x m x v^2

 

then when it's at the bottom it will be going fastest (as soon as it starts going up gravity acts against it and it slows down), threfore it has it's biggest velocity, so using:

KE = 1/2 x m x v^2

1/2 is constant, m is constant, velocity is the variant, so when the velocity is at its greatest so is the KE.

But...because we can't have a perfect closed system on earth, wouldn't it be impossible to have max KE...wouldn't energy be lossed to the environment?

um, [math]E=mgh+\frac{1}{2}mv^2[/math]. the energy in all positions is the same(neglecting friction which somewhat steals energy by the movement through the air). at the highest point, gravitational potential energy is high, so kinetic is low. at the bottom, gravitational potential is 0 so [math]E=\frac{1}{2}mv^2[/math].

But...because we can't have a perfect closed system on earth, wouldn't it be impossible to have max KE...wouldn't energy be lossed to the environment?

 

No, we can't have a "perfectly" closed system. But, for something like a pendulum, it makes life a whole bunch simpler if we neglect friction/air resistance/other annoying forces.

 

If we took into account every single factor when modelling a system, then the equations would be horribly complex (assuming we could even do it in the first place). The idea is to strike a balance between the model becoming completely inaccurate and having complex equations that may or may not have a solution.

hey everyone

 

sorry i just got back from a big night out last night and yeah hard to think' date=' so that sort of explains the title

 

anyways.... my query (this is not a homework question of anything, just a general th0ouoght i had when reading a physics text)

 

why is it that when a pendulum is swinging that you can assume it has maximum KE at the bottom of its swinging arc?

 

Cheers

 

Sarah[/quote']

 

When the air resistance matches the acceleration (due to gravity and the centripetal force) on the downward swing the maximum KE will be achieved.

This would be at the bottom in a vacuum, and before that otherwise with less KE at the bottom due to the friction component exceeding the force due to the PE.