You are shadowing a nurse in the emergency room of a local hospital. An orderly wheels in a patient who has..?

Question

You are shadowing a nurse in the emergency room of a local hospital. An orderly wheels in a patient who has been in a very serious accident and has had severe bleeding. The nurse quickly explains to you that in a case like this, the patient's bed will be tilted with the head downward to make sure the brain gets enough blood. She tells you that, for most patients, the largest angle that the bed can be tilted without the patient beginning to slide off is 32.0 degrees from the horizontal.

a. on what factor does this angle of tilting depend?
b. find the coefficient of static friction between a typical patient and the bed's sheets.

This problem is giving me trouble.
Please help me to understand it.

I have asked this question before, and have got confusing results.

Answer 1

a) the angle is determined by the coefficient of static friction.

b) Since the patient is in equilibrium with the angle at 32.0 degrees,
Ffs = W*sin(32.0)
where Ffs is the force of static friction, and W is the patient's weight. This is because W*sin(32.0) is the component of the patient's weight that points down the slope and Ffs is the frictional force opposing it leaving the net force = 0.

The force of friction Ffs is calculated as
Ffs = mu*N
where N is the component of the patient's weight that points perpendicular to the slope. N is W*cos(32.0).

So
mu*W*cos(32.0) = W*sin(32.0)
Simplifying
mu = sin(32.0)/cos(32.0) = tan(32.0)

Answer 2

nicely I wont do your homework for you yet the following is a clue make sure the rigidity of the affected human being sliding. you recognize the attitude, imagine of sin cos tan. now that you'll you take advantage of for that reason? draw out a diagram, label what you recognize and what you want now which equation provides you with the rigidity of the affected human being even as he starts sliding? hint : that is going to likely be an equation. a) what does it count number on? nicely how about this style of garments the affected human being wears, of route brilliant plastic dance clothing might want to slip more effective than say a velcro healthful. what about the mattress sheets, silk sheets might want to be extra slipery than say flannel. b) in case you recognize the rigidity the affected human being will exert even as he starts to slip you recognize the coefficient of static will precisely equivalent this rigidity at 32 ranges. any extra and the affected human being slides, so it overcomes friction, and any a lot less and friction is a lot more effective than the rigidity.