Problem II $(70$ Points$)$

On the basis of fundamental physics principles, conduct a thorough analysis of the

situation below, which shows an individual riding a water slide down an inclined surface

at a constant speed of $U=35f\frac{t}{s}.$ This person is sitting on a rectangular, $3ft4ft,$ rigid

board $($board weight & thickness are negligible$).$ Viscous fluid $(=0\mathrm{.}00002lb**\frac{s}{f}{t}^2)$

creates an extremely thin film $($thickness $=0\mathrm{.}0024in)$ between the moving board and the

stationary inclined surface. A linear velocity profile in such a small gap is assumed to be

an excellent approximation. Predict the weight of this individual using the British

Gravitational $($BG$)$ unit system $-$ show all work!

Name:

ID Number:

$6\mathrm{.}1$

Problem Statement:

You are designing a dock for your lake house. You are going to use pine, which has an

allowable stress of $1620$ psi $.$ You have $10$ friends that may be there for the summer that

could produce a distributed load of $250$ pounds per foot. Waves traveling at $1\mathrm{.}75$ ft per

second strike the front of the buoy supporting the dock. These waves apply a distributed

load onto the buoy that is $5$ ft $.$ deep into the water of $191$ pounds per foot. The dock is

simply supported at the land $($there is no reaction moment.$)$ Given the above, and the

diagram below, determine the following:

Problem Queries:

$20$ pts$.$

a$)$ Draw a free body diagram of JUST the dock $($not the buoy$).$ Include the full distributed

load from your friends but consider the external forces at the buoy as point loads from the

buoy support, $R_{B,y},$ and the moment produced by the wave, $M_{B,y}.$

$20$ pts$.$ b$)$ Determine the reaction forces at the land $R_{A,y},$ and forces and moments at the buoy, $R_{B,y},$

and $M_{B,y}.$

$20$ pts$.$ c$)$ Draw the shear and moment diagram for the dock.

$20$ pts$.$ d$)$ Determine the section modulus needed to support the loaded configuration.

$20$ pts$.$ e$)$ Since you are building this structure on a lake, and the water will deteriorate the wood, you

decide to use a factor of safety of $3.$ What should the section modulus be now?

Name:

ID Number:

$6\mathrm{.}1$

Problem Statement:

You are designing a dock for your lake house. You are going to use pine, which has an

allowable stress of $1620$ psi $.$ You have $10$ friends that may be there for the summer that

could produce a distributed load of $250$ pounds per foot. Waves traveling at $1\mathrm{.}75$ ft per

second strike the front of the buoy supporting the dock. These waves apply a distributed

load onto the buoy that is $5$ ft $.$ deep into the water of $191$ pounds per foot. The dock is

simply supported at the land $($there is no reaction moment.$)$ Given the above, and the

diagram below, determine the following:

Problem Queries:

$20$ pts$.$

a$)$ Draw a free body diagram of JUST the dock $($not the buoy$).$ Include the full distributed

load from your friends but consider the external forces at the buoy as point loads from the

buoy support, $R_{B,y},$ and the moment produced by the wave, $M_{B,y}.$

$20$ pts$.$ b$)$ Determine the reaction forces at the land $R_{A,y},$ and forces and moments at the buoy, $R_{B,y},$

and $M_{B,y}.$

$20$ pts$.$ c$)$ Draw the shear and moment diagram for the dock.

$20$ pts$.$ d$)$ Determine the section modulus needed to support the loaded configuration.

$20$ pts$.$ e$)$ Since you are building this structure on a lake, and the water will deteriorate the wood, you

decide to use a factor of safety of $3.$ What should the section modulus be now?