A box is given a brief push up a ramp so that it is initially moving at a speed of 6.25 m/s up the ramp. The box weighs 62.4 N, the angle of the ramp is 20.5°, and the coefficients of friction between the box and ramp are μ= 0.750 and 4= 0.433. (see the figure) a. What is the magnitude and direction of the acceleration of the box while it is sliding up the ramp? b. How far up the ramp does the box slide before it stops? c. Will the box stay stopped at the top, or will it slide back down? (Show your reasoning clearly.) Vo = 6.25 m/s 20.5° Ax = ? m

A box is given a brief push up a ramp so that it is initially moving at a speed of 6.25 m/s up the ramp. The box weighs 62.4 N, the angle of the ramp is 20.5°, and the coefficients of friction between the box and ramp are μ= 0.750 and 4= 0.433. (see the figure) a. What is the magnitude and direction of the acceleration of the box while it is sliding up the ramp? b. How far up the ramp does the box slide before it stops? c. Will the box stay stopped at the top, or will it slide back down? (Show your reasoning clearly.) Vo = 6.25 m/s 20.5° Ax = ? m

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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Concept explainers

Static and Kinetic Friction

Kinetic friction comes into existence when there are moving surfaces means in other words we can say that the force which comes into existing between moving surfaces is known as kinetic friction.

Question

**Problem Statement:**

A box is given a brief push up a ramp so that it is initially moving at a speed of 6.25 m/s up the ramp. The box weighs 62.4 N, the angle of the ramp is 20.5°, and the coefficients of friction between the box and ramp are μₖ = 0.750 and μₛ = 0.433.

Tasks:
- **a.** What is the magnitude and direction of the acceleration of the box while it is sliding up the ramp?
- **b.** How far up the ramp does the box slide before it stops?
- **c.** Will the box stay stopped at the top, or will it slide back down? *(Show your reasoning clearly.)*

**Diagram Explanation:**

- The diagram shows a box of mass "m" sliding up a ramp.
- The initial velocity \( v_0 \) is 6.25 m/s directed up the ramp.
- The angle of the ramp is given as 20.5°.
- The box slides a distance Δx up the ramp before coming to a stop, which needs to be determined.

Given this information, the task is to analyze the motion of the box due to the given forces and determine its behavior as it moves and eventually stops on the ramp.

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