Problem 6: At a post office, a parcel that is an m kg box slides down a ramp inclined at an angle θ with the horizontal, as shown. The coefficient of kinetic friction between the box and the ramp is μK, and the coefficient of static friction for the same is μS. Notice that the coordinate axes have been chosen with the x axis directed up the incline, as shown. Part (e) Input an expression for the acceleration of the box in the x direction consistent with the coordinate axes on the diagram. Express your answer in terms of the mass of the box, m, the acceleration due to gravity, g, the angle of the incline, θ, and appropriate coefficients of friction. The coefficient of kinetic friction between the box and the ramp is μK, and the coefficient of static friction for the same is μS. Part (f) Enter a numeric answer for the magnitude of the acceleration in meters per squared seconds when the angle of the incline is 28° and the coefficient of kinetic friction is 0.035. Part (g) Using the numbers from the previous step, give a numeric answer for the time in seconds that elapse when the package, initially at rest, travels a distance of 2.25 m down the ramp. Part (h) Using the numbers from the previous steps, give a numeric answer for the speed of the package at the moment it has traveled a distance of 2.25 m down the ramp.

College Physics

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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Problem 6: At a post office, a parcel that is an m kg box slides down a ramp inclined at an angle θ with the horizontal, as shown. The coefficient of kinetic friction between the box and the ramp is μ_K, and the coefficient of static friction for the same is μ_S. Notice that the coordinate axes have been chosen with the x axis directed up the incline, as shown.

Part (e) Input an expression for the acceleration of the box in the x direction consistent with the coordinate axes on the diagram. Express your answer in terms of the mass of the box, m, the acceleration due to gravity, g, the angle of the incline, θ, and appropriate coefficients of friction. The coefficient of kinetic friction between the box and the ramp is μ_K, and the coefficient of static friction for the same is μ_S.

Part (f) Enter a numeric answer for the magnitude of the acceleration in meters per squared seconds when the angle of the incline is 28° and the coefficient of kinetic friction is 0.035.

Part (g) Using the numbers from the previous step, give a numeric answer for the time in seconds that elapse when the package, initially at rest, travels a distance of 2.25 m down the ramp.

Part (h) Using the numbers from the previous steps, give a numeric answer for the speed of the package at the moment it has traveled a distance of 2.25 m down the ramp.

Expert Solution

Step 1: Free-body diagram

Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts for you. To get the remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.

The free-body diagram of the system is given below-

Where,

$m$ is the mass of the box,

$theta$ is the inclination angle of the ramp,

$g$ is the acceleration due to gravity,

$N$ is the normal force, and

$f subscript k$ is the force due to kinetic friction.

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