You lean your chair back against the (frictionless) wall to read your physics te

Question

You lean your chair back against the (frictionless) wall to read your physics textbook, but you fall asleep because of how late you were up studying the night before. The center of mass of the person-chair system is 50 cm from the feet of the chair resting on the ground (along the diagonal and 105 cm from the top of the chair (along the diagonal). The coefficient of static friction between your chair and the floor is u=0.80 Your chair makes an angle theta=21.7° with the floor. Will you get to dream through class or will you wake up after hitting the floor first?

You lean your chair back against the (frictionless) wall to read your physics textbook, but you fall asleep because of how late you were up studying the night before. The center of mass of the person-chair system is 50 cm from the feet of the chair resting on the ground (along the diagonal and 105 cm from the top of the chair (along the diagonal). The coefficient of static friction between your chair and the floor is u=0.80 Your chair makes an angle theta=21.7A degree with the floor. Will you get to dream through class or will you wake up after hitting the floor first?

Explanation / Answer

along Y axis

N = M*g

f = mue*N

x axis

-F + f = 0

F= f

Force on top

F = mue*M*g
Torque Q1 due to F = F*L*sin21.7 = mue*M*g*L*sin21.7= 0.8*M*9.8*1.55*sin21.7 = 4.493*M Nm Anti clock wise

Torque Q2 due to combined weight Q2 = M*g*L*sin21.7 = M*9.8*0.50*cos21.7 = 4.552*M Nm clock wise

Q1 in not equal Q2

Q2 > Q1
you wake up after hitting the floor first

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