A 60-kg woman holds a 9-kg package as she stands within an elevator which briefly accelerates upward at a rate of g/4. Determine the force R which the elevator floor exerts on her feet and the lifting force L which she exerts on the package during the acceleration in-travel. If the elevator supports cables suddenly and completely fail, what values would R and L acquire

force R = 846.11 N

lifting force L = 110.36 N

if cable fail complete both R and L will be zero

Explanation:

given data

mass woman mw = 60 kg

mass package mp = 9 kg

accelerates rate a = g/4

to find out

force R and lifting force L and if cable fail than what values would R and L acquire

solution

we calculate here first reaction R force

we know elevator which accelerates upward

so now by direction of motion, balance the force that is express as

R - (mw + mp) * g = (mw + mp) * a

here put all these value and a = g/4 and use g = 9.81 m/s²

R - (60 + 9) * 9.81 = (60 + 9) * g/4

R = (69) * 9.81/4 + (69) 9.81

R = 69 (9.81 + 2.4525)

force R = 846.11 N

and

lifting force is express as here

lifting force = mp (g + a)

put here value

lifting force = 9 (9.81 + 9.81/4)

lifting force L = 110.36 N

and

we know if cable completely fail than body move free fall and experience no force

so both R and L will be zero