Question

The 78 kg climber here is supported in the "chimney" by the friction forces exerted on her shoes and back. The static coefficients of friction between her shoes and the wall, and between her back and the wall, are 0.88 and 0.63, respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum.

Answer 1

N = 516.56 N

Step-by-step explanation:

By the means of a sum of forces on the x-axis:

`N_b-N-f=0`

Where
`N_b` is the force on her back and
`N_f` is the force on her feet:

`N_b=N-f = N`

On the y-axis:

`Ff_b+Ff_f-m*g=0`

`\mu_b*N_b+\mu_f*N_f-m*g=0`

`\mu_b*N+\mu_f*N=m*g`

`(\mu_b+\mu_f)*N=m*g`

`N=(m*g)/(\mu_b+\mu_f)` using
`g=10m/s^2`

N = 516.56N