Q25E - University Physics with Modern Physics

Question

After emergencies with major blood loss, a patient is placed in the Trendelen burg position, in which the foot of the bed is raised to get maximum blood flow to the brain. If the coefficient of static friction between atypical patient and the bed sheets is 1.20, what is the maximum angle at which the bed can be tilted with respect to the floor before the patient begins to slide?

Step-by-Step Solution

Answer

The maximum angle at which the bed can tilted is, $50.19°$. 

Step 1: identification of given data

The given data can be listed below as,

• The coefficient of static friction is ${\mu }_s=1.2$.

 

Step 2: Significance of fictional force

The opposing force which resists one surface to slide over another surface when the two surfaces are in contact is known as frictional force.

Step 3: Determination of maximum angle.

The expression for the frictional force from the free body diagram can be expressed as,

 $$\begin{gathered} f_r=m g \sin \theta \\ {\mu }_s N=m g \sin \theta \end{gathered}$$

Here ${\mu }_s$is the coefficient of static friction, N is the normal force, m is the mass of the body, and g is the acceleration due to gravity.

 Substitute,$m g \cos \theta$ for N , 1.2 for ${\mu }_s$in the above equation.

$$\begin{gathered} (1.2) m g \cos \theta =m g \sin \theta \\ (1.2)=\frac{\sin \theta }{\cos \theta } \\ \tan \theta =1.2 \\ \theta ={\tan }^{-1} (1.2) \\ =50.19° \end{gathered}$$

Hence, the required maximum angle is, $50.19°$.