8. You push downward on a box with a force of 750 N. The box is on a flat horizontal surface for which the coefficient of static friction with the box is 0.74. The angle between the force you exert and the horizontal surface is 25 degrees. What is the mass of the heaviest box you will be able to move

The mass of the heaviest box you will be able to move with this applied force = 61.4 kg

Explanation:

From the diagram attached, the forces acting on the box include the weight of the box, applied force on the box, normal reaction of the surface on the box and the Frictional force in the opposite direction to the applied force.

For the box to be able to move, the applied force must have a horizontal component that at least matches the Frictional force between the box and the surface. This is the force balance in the horizontal direction.

Resolving the applied force into horizontal and vertical components,

Fₓ = 750 cos 25° = 679.73 N

Fᵧ = 750 sin 25° = 316.96 N

Doing a force balance in the vertical axis,

N = (mg + 316.96)

Frictional force = μN = μ (mg + 316.96)

μ = 0.74, g = 9.8 m/s²

Frictional force = Fᵧ

μ (mg + 316.96) = 679.73

0.74(9.8m + 316.96) = 679.73

7.252m + 234.5504 = 679.73

7.252m = 679.73 - 234.5504 = 445.1796

m = (445.1796/7.252)

m = 61.4 kg

Hope this Helps!!!

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