A box of textbooks of mass 25.8 kg rests on a loading ramp that makes an angle w

Question

A box of textbooks of mass 25.8 kg rests on a loading ramp that makes an angle with the horizontal. The coefficient of kinetic friction is 0.25 and the coefficient of static friction is 0.35.

Part A

As the angle is increased, find the minimum angle at which the box starts to slip.

Express your answer using two significant figures.

Part B

At this angle, find the acceleration once the box has begun to move.

Express your answer using two significant figures.

Part C

At this angle, how fast will the box be moving after it has slid a distance 4.5 m along the loading ramp?

Express your answer using two significant figures.

Explanation / Answer

m = 25.8 Kg
uk = 0.25
us = 0.35

(A)
minimum angle at which the box starts to slip -
m*g*sin() = us * m*g*cos()
tan() = us
= tan^-1(0.35)
= 19.0o

(B)
m*g*sin(19.3) - uk * m*g* cos(19.3) = m*a
a = 9.8*sin(19.3) - 0.25 * 9.8 * cos(19.3)
a = 0.93 m/s^2

(C)
V^2 = u^2 + 2*a*s
V^2 = 0 + 2*0.926 * 4.5
V = 2.90 m/s

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