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Q. 16 of 75
A 56kg climber is supported in
the 'chimney' by the friction
forces exerted on his shoes and
back as shown in fig. The static
coefficients of friction between
his shoes and the wall, and
between his back and the wall
are 0.80 and 0.60 respectively.
Assume the walls are vertical
and that frictional forces are
maximum. The minimum normal
force (in Newton) he must exerts
is (take g = 10 m/s2)​

Answer 1

Given:

A 56kg climber is supported inthe 'chimney' by the friction forces exerted on his shoes and back as shown in fig. The static coefficients of friction between his shoes and the wall, and between his back and the wall are 0.80 and 0.60 respectively.

Assume the walls are vertical and that frictional forces are maximum.

To find:

The minimum normal force (in Newton) he must exerts is (take g = 10 m/s2)

Calculation:

Let the minimum normal force that has to be applied be N ;

Now , net frictional force due to shoes and back will be :

$\rm{f = \mu1(N) + \mu2(N)}$

Now , this upward frictional force should be equal to the downward acting weight due to gravity.

$\therefore \: \rm{f =mg}$

$\rm{ = > \mu1(N) + \mu2(N) = mg}$

$\rm{ = > ( \mu1+ \mu2)N = mg}$

$\rm{ = > (0.8 + 0.6)N = 56 \times 10}$

$\rm{ = > (0.8 + 0.6)N = 560}$

$\rm{ = > (1.4)N = 560}$

$\rm{ = > N = \dfrac{560}{1.4}}$

$\rm{ = > N = \dfrac{5600}{14}}$

$\rm{ = > N = 400 \: newton}$

So, minimum normal force to be applied is 400N.