Answer :
Answer: B. Concrete
Explanation:
Let N = reacting force pressing the bodies in context together (units in Newtons),
The question stated that the force pressing the two mounted/stacked objects together is equal to the weight of the object on top.
We need to start by finding the weight of the piece of wood.
friction is given by
f = μN
The value of f is 22.5,
and from the chart reference the coefficient of friction between wood and stone, μ is 0.30.
22.5 = 75. 0.30
Putting the values into the equation: 22.5 = 0.30N.
Divide both sides by 0.30 to find the value of N:
N= 22.5/0.3 = 75
Now that the piece of wood will be placed on another surface, its weight of 75 Newton is the force pressing the two bodies together.
To determine the new surface, you should find the new coefficient of friction by using the new value of the force of friction given 46.5:
46.5 = µ(75).
Divide both sides by 75 to isolate μ.
The refer chart also indicates that the coefficient of friction equals 0.62 between wood and concrete, so the new surface corresponding to 0.62 is the concrete, which is (B).
The second surface could be brick.
The given parameters:
- Friction, Ff = 22.5 N
- Second friction, Ff = 46.5 N
Let the weight of the wood = W
The normal force on the stone surface is calculated as follows;
[tex]F_n = W\\\\ [/tex]
The static frictional force between the stone surface and the wood is calculated as follows;
[tex]F_s = \mu_s F_n\\\\ [/tex]
where;
- [tex]\mu_s [/tex] is coefficient of static friction on stone surface = 0.3.
[tex]22.5 = 0.3 W \\\\ W = \frac{22.5}{0.3} \\\\ W = 75 \ N[/tex]
When the wood is placed on the second surface, the coefficient of static friction is calculated as follows;
[tex]F_s = \mu_s W\\\\ \mu_s = \frac{F_s}{W} \\\\ \mu_s = \frac{46.5}{75} \\\\ \mu_s = 0.62[/tex]
The coefficient of static friction between wood and brick is 0.6. Thus, the second surface is brick.
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