Example: Pushing a Safe up an Incline A new safe is being delivered to the Corne

Question

Example: Pushing a Safe up an Incline A new safe is being delivered to the Corner Book Store. It is to be placed in the wall at a height of 1.5m above the floor. The delivery people have a portable ramp, which they plan to use to help them push the safe upand into position. The mass of the safe is 510kg, the coefficient of static friction along the incline is ,-042, and the coefficient of kinetic friction along the incline is k = 0.33. The ramp forms an angle = 15° above the horizontal. (a) How hard do the movers have to push to start the safe moving up the incline? Assume that they push in a direction parallel to the incline. (b) To slide the safe up push? at a constant speed, with what magnitude force must the movers

Explanation / Answer

here,

mass , m = 510 kg

coefficient of kinetic friction , uk = 0.33

coefficient of static friction , us = 0.42

theta = 15 degree

a)

the force required by the movers to start the safe moving up , F = m * g * sin(theta) + us * m * g * cos(theta)

F = 510 * 9.81 * ( sin(15) + 0.42 * cos(15)) N

solving for F

F = 3324.6 N

b)

the force required by the movers to slide the safe up at constant speed , F = m * g * sin(theta) + uk * m * g * cos(theta)

F = 510 * 9.81 * ( sin(15) + 0.33 * cos(15)) N

solving for F

F = 2889.66 N

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