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When a 40N force, parallel to and directed up the incline, is applied to a block on a frictionless incline that is 30o above the horizontal, the acceleration of the block is 2.0 m/s2, up the incline. Find the mass of the block.

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lublana

Answer:

5.8 kg

Explanation:

We are given that

Force,F=40 N

[tex]\theta=30^{\circ}[/tex]

Acceleration,a=[tex]2 m/s^2[/tex]

We have to find the mass of block.

[tex]F_{net}=ma[/tex]

[tex]F-mgsin\theta=ma[/tex]

[tex]F=mgsin\theta+ma=m(gsin\theta+a)[/tex]

[tex]40=m(9.8sin30+2)[/tex]

Where

[tex]g=9.8m/s^2[/tex]

[tex]40=6.9m[/tex]

[tex]m=\frac{40}{6.9}=5.8 kg[/tex]

Answer:

[tex]m=5.797\ kg[/tex]

Explanation:

GIVEN:

applied force up the inclined plane, [tex]F=40\ N[/tex]

angle of the plank from the horizontal, [tex]\theta=30^{\circ}[/tex]

acceleration of the body up the plane, [tex]a=2\ m.s^{-2}[/tex]

Now from the  schematic we balance the forces:

[tex]F-mg\sin\theta=m.a[/tex]

[tex]F=m(g\sin\theta +a)[/tex]

[tex]40=m(9.8\times0.5+2)[/tex]

[tex]m=5.797\ kg[/tex]

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