Hospital patient. A 71.0kg patient is suspended in a raised hospital bed as show
ID: 1394464 • Letter: H
Question
Hospital patient. A 71.0kg 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)
Part A
What is the maximum mass m can be without the patient sliding up the bed?
Express your answer with the appropriate units.
Part B
If the wire suddenly breaks, what's the patient's acceleration?
Express your answer with the appropriate units.
Mass 50.0°Explanation / Answer
A)
Let Mmax is the maximum mass.
Net force acting on patient = 0
Mmax*g - m*g*sin(50) - mue_s*m*g*cos(50) = 0
Mmax = m*sin(50) + mue_s*m*cos(50)
= m*sin(50) + mue_s*m*cos(50)
= 71*sin(50) + 0.8*71*cos(50)
= 90.9 kg <<<<<<<-------------Answer
B) Net force in downward direction.
Fnet = m*g*sin(50) - mue_s*m*g*cos(50)
m*a = m*g*sin(50) - mue_s*m*g*cos(50)
a = g*sin(50) - mue_s*g*cos(50)
= 9.8*sin(50) - 0.8*9.8*cos(50)
= 2.47 m/s^2 <<<<<<<-------------Answer
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