Depression of a Diving Board

[haroldtreen]

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

 

[tiny-tim]

Welcome to PF!

Hi haroldtreen! Welcome to PF!

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

 

[tomcue]

I would first like to commend you for conducting two experiments to gather data and find a relationship between depression and weight in the first experiment, and between depression and length in the second experiment. This shows a thorough and scientific approach to solving the problem at hand.

Based on the data and equations provided, I can see that there is a linear relationship between depression and weight (y = 1.35x - 1.3) and a power relationship between depression and length (log(y) = 2.5*log(mass) - 3.87). This means that as weight and length increase, the depression also increases, but at different rates.

To solve the problem, we can use the first equation to find the constant, K, by plugging in the values given (d=15cm, m=60kg). This gives us K = 0.025.

Then, using the second equation, we can calculate the weight needed to create a depression of 4cm by plugging in the values (d=4cm, n=2.5, L=200cm). This gives us log(mass) = 0.92, which can be solved for mass, giving us a weight of approximately 9.6kg.

Therefore, the second person would need to weigh approximately 9.6kg to create a depression of 4cm on the diving board, assuming all other factors remain constant. This solution is based on the data and equations provided, and may vary in real-life scenarios due to other factors such as the strength and flexibility of the diving board.