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Two boxes of masses m and 3m are stacked. The surface between the more massive box and the horizontal surface is smooth and the surface between the boxes is rough. If the less massive box does not slide on the more massive box, what is the static friction force on the less massive box?

Respuesta :

Hagrid
If the less massive box does not slide on the more massive box, the static friction force on the less massive box is (D) F/4.
F = ma
F=(3m+m)a
a = F/4m 

Here are the following choices:
A) F
B) F/2
C) F/3
D) F/4

Answer:

The friction coefficient is [tex]\dfrac{F}{4mg}[/tex].

Explanation:

Given that,

Mass of first box = m

Mass of second box = 3m

Let the static friction force on the less massive box is [tex]F_{1}[/tex].

Since the small box is not slide, they have the same acceleration.

We need to calculate the acceleration

Using balance equation

[tex]F-F_{1}=3ma[/tex]....(I)

[tex]F_{1}=ma[/tex]....(II)

Adding both the equation

[tex]F=4 ma[/tex]

[tex]a=\dfrac{F}{4m}[/tex]

Put the value of a in equation (II)

[tex]F_{1}=m\times\dfrac{F}{4m}[/tex]

[tex]F_{1}=\dfrac{F}{4}[/tex]

We need to calculate the friction coefficient

Using formula of frictional force

[tex]F=\mu mg[/tex]

[tex]\mu=\dfrac{F}{4mg}[/tex]

Hence, The friction coefficient is [tex]\dfrac{F}{4mg}[/tex].

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