Help with thermal/kinetic friction energy?

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AI Thread Summary
A child weighing 269 N slides down a 6.80 m slide at a 41.0° angle, with a kinetic friction coefficient of 0.190. The energy transferred to thermal energy was initially calculated as 228 J, but the calculation was incorrect due to using the sine function instead of the cosine for the normal force. The correct formula for thermal energy involves using the normal force calculated with mgCOS41. The discussion confirms that energy lost to friction converts to thermal energy, which is a key concept in solving such problems. The correct approach to find thermal energy is crucial for accurate homework answers.
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Homework Statement


A child whose weight is 269 N slides down a 6.80 m playground slide that makes an angle of 41.0° with the horizontal. The coefficient of kinetic friction between slide and child is 0.190. (a) How much energy is transferred to thermal energy? (b) If she starts at the top with a speed of 0.314 m/s, what is her speed at the bottom?


Homework Equations


ke=1/2 mv2
thermal energy = fkd = fnUkd


The Attempt at a Solution



for b I used 1/2mvi2 + mgh - fkd = fnUkd = 1/2mvf2
and got it correct...
I missed the class where the teacher explained thermal energy and frictional energy so I assumed that the energy lost to friction is turned into thermal energy and i used
thermal energy = fkd = fnUkd
plugged everything in and got 228 J...
but maybe i have the relationship wrong?
 
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hi dorkymichelle! :smile:

(have a mu: µ :wink:)
dorkymichelle said:
I missed the class where the teacher explained thermal energy and frictional energy so I assumed that the energy lost to friction is turned into thermal energy …

yes, that's correct …

kinetic energy and potential energy are called "mechanical energy", and any "missing" energy (in questions like this) is thermal energy :smile:
 
so for a, I should just use equation thermal energy = fnUkd
and I got 228 J but when I put in the answer,(my homework is online) its wrong...
am i reading the question in correctly somehow?
but I got b right.
 
hi dorkymichelle! :smile:
dorkymichelle said:
so for a, I should just use equation thermal energy = fnUkd
and I got 228 J but when I put in the answer,(my homework is online) its wrong...

i make it the same as you, 228 J (= 269*6.8*sin41°*0.19) :confused:
 
tiny-tim said:
hi dorkymichelle! :smile:


i make it the same as you, 228 J (= 269*6.8*sin41°*0.19) :confused:

oops, found the mistake, in finding normal force, its mgCOS41 not Sin. =d silly mistake!
 
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