Hospital patient. A 83.0 kg patient is suspended in a raised hospital bed as sho

Question

Hospital patient. A 83.0 kg patient is suspended in a raised hospital bed as shown in the figure. The wire is attached to a brace on the patient's neck and pulls parallel to the bed, and the coefficients of kinetic and static friction between the patient and the bed are 0.500 and 0.800, respectively.(Figure 1) What is the maximum mass m can be without the patient sliding up the bed? Express your answer with the appropriate units. If the wire suddenly breaks, what's the patient's acceleration?

Explanation / Answer

T - m*g*sin(50) - us * m*g*cos(50) = 0
T = m*g*sin(50) + us * m*g*cos(50)
T = 83.0 * 9.8 * sin(50) + 0.800 * 83.0 *9.8*cos(50)
T =  1041.4

Now,
T = m*g
m = T/g
m = 1041.4/9.8 Kg
m = 106.3 Kg
Maximum mass of m = 106.3 Kg

If wire suddenly breaks,
m*g*sin(50) - uk * m*g*cos(50) = m*a
9.8*sin(50) - 0.5 * 9.8 * cos(50) = a
a = 4.36 m/s^2
Acceleration of the patient, a = 4.36 m/s^2

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