How Much Should a Person Weigh to Depress a Diving Board by 4cm?

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A diving board experiences a vertical depression of 15cm when a 60kg person stands 3m from the fulcrum. The discussion focuses on calculating the weight needed to create a 4cm depression when another person stands 2m from the fulcrum. Two experiments established relationships between weight and depression, resulting in linear and logarithmic equations. The user attempted to apply these equations to find the necessary weight but encountered difficulties. Clarification was provided regarding the relevance of the second equation, suggesting it may not apply to the current scenario.
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Homework Statement



A diving board has a vertical depression of 15cm when a 60kg person stands on it 3m from the fulcrum.

If another person was to stand on the same diving board, 2m from the fulcrum, how much would they have to weight to create 4cm of depression?

In class we did 2 experiments:

1st - Find out the relationship between depression and weight. Noted the depression of a ruler when numerous weights were suspended from it, plotted the data and got the straight line equation:
y = 1.35x - 1.3

2nd - Looked at how the depression changed in relation to the length of the ruler when 1kg was suspended from the tip. Got a power graph that using logs turned into a straight line graph as well:
log(y) = 2.5*log(mass) - 3.87


Homework Equations


y = 1.35x - 1.3
log(y) = 2.5*log(mass) - 3.87


The Attempt at a Solution



d= depression
m= mass
K = constant
n = exponent of power equation
L= length of board

K=?
d=15cm
m= 60kg
n= 2.5
L= 300cm

d=KmL^n

(15cm)/(60kg)(300cm)^2.5 = K

Then since I had K, I could input the second set of values and find out m... didn't work though :(.

Would love some help!
Thanks a bagillion! :D
 
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Welcome to PF!

Hi haroldtreen! Welcome to PF! :smile:

Why are you using the 2nd equation? That was for the fulcrum moving nearer the tip. :wink:
 

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