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A force is applied to a block to move it up a 30° incline. The incline is frictionless, the block is initially at rest, F= 65.0 N and M=5.00 kg. If the block starts from rest, how far will it move in 0.550 s? Also, indicate whether the block moves up or down the incline.

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lublana

Answer:

0.96 m, upward

Explanation:

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

[tex]F=65 N[/tex]

[tex]M=5 kg[/tex]

Initial velocity, u=0

[tex]t=0.550 s[/tex]

[tex]Fcos\theta-Mgsin\theta=Ma[/tex]

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

Substitute the values

[tex]65cos30-5\times 9.8sin30=5a[/tex]

[tex]31.8=5a[/tex]

[tex]a=\frac{31.8}{5}=6.36 m/s^2[/tex]

[tex]S=ut+\frac{1}{2}at^2[/tex]

[tex]S=0+\frac{1}{2}(6.36)(0.55)^2=0.96 m[/tex]

Hence,the block moves upward because displacement is positive.

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