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A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively:

1. 0.6 and 0.5
2. 0.5 and 0.6
3. 0.4 and 0.3
4. 0.6 and 0.6

Correct answer: 0.6 and 0.5

Solution

The box starts to slip at 30°, so the coefficient of static friction is μs = tan(30°) = 0.6. Using the equation of motion and the kinetic friction force, the coefficient of kinetic friction is calculated as μk = 0.5.

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