### Inclined Plane Friction CalculationA 19.0 kg box is placed at the top of an inclined plane and released to either move freely or sit at rest. The plane is at an angle of \(30^\circ\) above the ground and has a total length of \(d = 2.80\) m along the incline. The coefficient of static friction between the box and the plane is \(\mu_s = 0.40\) and the coefficient of kinetic friction is \(\mu_k = 0.30\). What kind of friction does the box experience once it is released, and what is its magnitude?#### Diagram DescriptionThe diagram accompanying the problem depicts:- An inclined plane with an angle \(\theta\) of \(30^\circ\).- A box of mass \(m\) placed on the inclined plane.- The length of the inclined plane (\(d\)) is shown as 2.80 meters.#### Answer Choices1. **Kinetic, \(F_{kf} = 55.9\) N**2. **Static, \(F_{sf} = 74.5\) N**3. **Static, \(F_{sf} = 64.5\) N**4. **Kinetic, \(F_{kf} = 48.4\) N**#### Solution AnalysisTo determine the kind of friction and its magnitude, we must first calculate the forces involved:1. **Calculate the component of gravitational force parallel to the incline:** \[ F_{parallel} = mg \sin(\theta) \] where \(m = 19.0\) kg, \(g = 9.8\) m/s\(^2\), and \(\theta = 30^\circ\).2. **Calculation:** \[ F_{parallel} = 19.0 \times 9.8 \times \sin(30^\circ) = 19.0 \times 9.8 \times 0.5 = 93.1 \, \text{N} \]3. **Calculate the component of gravitational force perpendicular to the incline:** \[ F_{perpendicular} = mg \cos(\theta) \] 4. **Calculation:** \[ F_{perpendicular} = 19.0 \times 9.

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Description: ### Inclined Plane Friction CalculationA 19.0 kg box is placed at the top of an inclined plane and released to either move freely or sit at rest. The plane is at an angle of \(30^\circ\) above the ground and has a total length of \(d = 2.80\) m alon

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A 19.0 kg box is placed at the top of an inclined plane and released to either move freely or sit at rest. The plane is at an angle of 30° above the ground and has a total length of d = 2.80 m along the incline. The coefficient of static friction between the box and the plane is us = 0.40 and the coefficient of kinetic friction is pk = 0.30. What kind of friction does the box experience once it is released, and what is its magnitude? m d Kinetic, Fkf - 55.9 N Static, Fsf = 74.5 N Static, Fsf = 64.5 N Kinetic, Fkf = 48.4 N

A 19.0 kg box is placed at the top of an inclined plane and released to either move freely or sit at rest. The plane is at an angle of 30° above the ground and has a total length of d = 2.80 m along the incline. The coefficient of static friction between the box and the plane is us = 0.40 and the coefficient of kinetic friction is pk = 0.30. What kind of friction does the box experience once it is released, and what is its magnitude? m d Kinetic, Fkf - 55.9 N Static, Fsf = 74.5 N Static, Fsf = 64.5 N Kinetic, Fkf = 48.4 N

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11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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