The 60 kg climber in Fig. 4-52 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.82 and 0.58, respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum.
See:
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wfd
To find the minimum normal force the climber must exert, we need to analyze the forces acting on him in the "chimney".
First, let's draw a free body diagram of the climber:
```
|
|
|
|--------| N |--------|
| |_____| |
| |
| |
| Weight |
|_ _ _ _ _ _ _ _ _ _ _ _|
```
Here, N represents the normal force exerted by the climber on the wall, and Weight represents the gravitational force acting downwards on the climber.
Since the climber is not accelerating vertically, the sum of the vertical forces is zero. This means the normal force N is equal to the weight of the climber:
N = mg
where m is the mass of the climber and g is the acceleration due to gravity (9.8 m/s^2).
In this case, the mass of the climber is given as 60 kg. Therefore:
N = 60 kg * 9.8 m/s^2
N ≈ 588 N
So, the minimum normal force the climber must exert is approximately 588 Newtons.