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You push downward on a trunk at an angle 25° below the horizontal with a force of 500 N. If the trunk is on a flat surface and the coefficient of static friction is 0.61, what is the most massive trunk you will be able to move? [4 pts] for a Free Body Diagram correctly labeled​

Sagot :

Cricetus

Answer:

The correct response is "54.19 kg".

Explanation:

The given values are:

Force,

F = 500 N

Coefficient of static friction,

μ = 0.61

Angle,

[tex]\Theta = 25^{\circ}[/tex]

As we know,

⇒  [tex]F_x=F= \mu_s.N[/tex]

then,

⇒  [tex]FCos \Theta=\mu_s(mg+FSin \Theta)[/tex]

On substituting the given values, we get

⇒  [tex]500Cos(25^{\circ})=0.61[m(9.81)+500 Sin25^{\circ}][/tex]

On substituting the values of Cos and Sin, we get

⇒  [tex]453.154=0.61(9.81m+211.31)[/tex]

⇒  [tex]453.154=5.9842m+128.8991[/tex]

⇒  [tex]453.154-128.8991=5.9842m[/tex]

⇒                  [tex]324.2549=5.9842m[/tex]

⇒                            [tex]m=\frac{324.2549}{5.9842}[/tex]

⇒                            [tex]m=54.19 \ kg[/tex]

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