art A A box of textbooks of mass 25.4 kg rests on a loading ramp that makes an a

Question

art A A box of textbooks of mass 25.4 kg rests on a loading ramp that makes an angle with the horizontal. The coefficient of kinetic friction is 0.24 and the coefficient of static friction is 0.37 As the angle is increased, find the minimum angle at which the box starts to slip Express your answer using two significant figures. Submit My Answers Give Up Part B At this angle, find the magnitude of the acceleration once the box has begun to move. Express your answer using two significant figures. m/s Submit My Answers Give Up Part c At this angle, how fast will the box be moving after it has slid a distance 5.1 m along the loading ramp? Express your answer using two significant figures. m/s

Explanation / Answer

component of weight acting along the ramp = m*g*sin

component of weight acting perpendicular the ramp = m*g*cos

PART A

Balancing forces along the ramp,

component of weight along the ramp = friction

m*g*sin = s*m*g*cos

The box starts to slip when,

m*g*sin > s*m*g*cos

=> Tan > 0.37

=> > 20.30o

PART B

m*g*sin(20.3o) - k*m*g*cos(20.3o) = ma

=> a = g[sin(20.3o) - k*cos(20.3o)]

=> a = 1.20 m/s2

PART C

v2 - u2 = 2*a*s

=> v2 - 0 = 2*1.2*5.1

=> v2 = 12.24

=> v = 3.50 m/s

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