do all steps and make sure the signs and the answer is correct pleaseYou are pushing a box of mass m up a rough ramp of incline angleθ (see figure). Your applied constant force F is to the right ( parallel to the floor, not the ramp). There is friction between the box and the ramp and you push with just enough force to keep the box moving at a constant velocity.a) Draw a free-body diagram for the box (don’t rotate the FBD).b) Derive an expression for the magnitude of force F in terms of μk, g, θ, and m. The image depicts a diagram of a block on an inclined plane, often used in physics to illustrate concepts of force and motion.- The inclined plane is shown with an angle \( \theta \).- A block is placed on the slope.- An arrow labeled \( F \) represents a force being applied horizontally to the block.- The angle \( \theta \) indicates the incline of the plane relative to the horizontal baseline.This setup is typically used to analyze the components of forces acting on the block, such as gravitational force, normal force, and friction, and to explore concepts like equilibrium and acceleration on an inclined plane.

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Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 16OQ

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do all steps and make sure the signs and the answer is correct please

You are pushing a box of mass m up a rough ramp of incline angleθ (see figure). Your applied constant force F is to the right ( parallel to the floor, not the ramp). There is friction between the box and the ramp and you push with just enough force to keep the box moving at a constant velocity.

a) Draw a free-body diagram for the box (don’t rotate the FBD).

b) Derive an expression for the magnitude of force F in terms of μk, g, θ, and m.

The image depicts a diagram of a block on an inclined plane, often used in physics to illustrate concepts of force and motion.

- The inclined plane is shown with an angle \( \theta \).
- A block is placed on the slope.
- An arrow labeled \( F \) represents a force being applied horizontally to the block.
- The angle \( \theta \) indicates the incline of the plane relative to the horizontal baseline.

This setup is typically used to analyze the components of forces acting on the block, such as gravitational force, normal force, and friction, and to explore concepts like equilibrium and acceleration on an inclined plane.

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