You are riding in an elevator on the way to the eighteenth floor of your dormitory. the elevator's upward acceleration is a = 1.94 m/s2 . beside you is the box containing your new computer; box and contents have a total mass of 28.4 kg . while the elevator is accelerating upward, you push horizontally on the box to slide it at constant speed toward the elevator door. if the coefficient of kinetic friction between the box and elevator floor is μk = 0.35, what magnitude of force must you apply?

116.795N

Explanation:

Hello! to solve this problem the following steps are necessary

1. Find the total force to the box to the floor of the elevator, it is found remembering the second law of Newton that states that the sum of forces is a body is equal to the product of mass by acceleration.

Therefore, the downward force of the box would be equal to the sum of the weight and the effect of the product of the mass due to acceleration, the following equation is inferred.

F=ma+mg

F=total force

m=mass of box=28.4kg

g=gravity=9.81m/S^2

a=1.94m/S^2

F=(28.4kg)(1.94)+(28.4)(9.81)=333.7N

2.

Now we remember that the minimum force to move the box horizontally is the product of the friction coficient (μk = 0.35)by the total downward force found in the previous step

Fh=F(μk)

Fh=333.7N(0.35)=116.795N

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