problem below A) A student moves a box of books by attaching a rope to the box and pulling with a force of 90 N at an angle of 30 in respect to the sidewalk. The box of books has a mass of 20.0 kg, and the kinetic friction is 0.50. find the acceleration of the book    

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You must apply Newton's 2nd Law to the book.

In the horizontal direction -

90 (cos 30) - Ff = ma

77.9 - mu*Fn = m*a

77.9 - (0.5)*Fn = 20 a

You must find Fn from the vertical forces

90 (sin 30) + Fn = mg

45 + Fn...

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You must apply Newton's 2nd Law to the book.

In the horizontal direction -

90 (cos 30) - Ff = ma

77.9 - mu*Fn = m*a

77.9 - (0.5)*Fn = 20 a

You must find Fn from the vertical forces

90 (sin 30) + Fn = mg

45 + Fn = (20)(9.8)

Fn = 196 - 45 = 154 N

Sub that into horizontal equation

77.9 - (0.5)(154) = 20 a

77.9 - 77 = 20 a

0.9 = 20 a

a = 0.9/20 = 0.045 m/s^2

 

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