### Problem 5: Determining the Normal Force on a BoxA large box is pulled by a person with a force $ \vec{F} $ as illustrated in the figure below. The angle $ \theta $ between the force vector and the horizontal surface is $ 25^\circ $. Given that the mass of the box is $ m = 23.5 $ kg and the coefficient of static friction between the box and the floor is $ 0.64 $, calculate the magnitude of the normal force exerted on the box at the moment when it is just about to move.#### Details and Diagram- **Mass of the box (m)**: 23.5 kg- **Coefficient of static friction ($ \mu_s $)**: 0.64- **Angle ($ \theta $)**: $ 25^\circ $![Diagram Showing Force $ \vec{F} $ Applied at an Angle $ \theta $](image_link)In the diagram, the force $ \vec{F} $ is applied at an angle $ \theta $ of $ 25^\circ $ above the horizontal. The forces acting on the box need to be analyzed to determine the normal force acting on it just as it is about to move.To find the normal force,\[ N = mg - F \sin(\theta) \]Where:- $ N $ is the normal force.- $ m $ is the mass of the box.- $ g $ is the acceleration due to gravity (approximately $ 9.81 \, \text{m/s}^2 $).- $ F $ is the applied force.- $ \theta $ is the angle of the applied force from the horizontal.Given this setup, the applied force $ \vec{F} $ can be further analyzed including its horizontal and vertical components. The normal force can be precisely determined by resolving all the vertical components acting on the box including the effect of $ \vec{F} $. This equation explains the reduction in normal force due to the vertical component of the applied force $ F $.This problem is an excellent example of static equilibrium and the application of Newton's laws in two dimensions. Students should consider breaking down the forces into their components and applying the equilibrium conditions to solve for the normal force.

Given: The pulling force is F. The direction of the pulling force with horizontal is 25o. The mass…

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Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter6: Applications Of Newton’s Laws Of Motion

Section: Chapter Questions

Problem 43PQ: Your sailboat has capsized! Fortunately, you are no longer aboard the boat. Instead, you are hanging...

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