An object with a mass of 10 kg is initially at rest at the top of a frictionless inclined plane that rises at 30° above the horizontal. At the top, the object is initially 8.0 m from the bottom of the incline, as shown in the figure. When the object is released from this position, it eventually stops at a distance d from the bottom of the inclined plane along a horizontal surface, as shown. The coefficient of kinetic friction between the horizontal surface and the object is 0.20, and air resistance is negligible. Find the distance d. In the image above, we have a diagram depicting a right triangle formed by a horizontal ground line and an inclined line that makes a 30-degree angle with the horizontal. Here are several key elements illustrated within this diagram:1. **Inclined Line:** This line represents the hypotenuse of the right triangle, measuring 8.0 meters in length.2. **Ground Line:** A horizontal line at the base of the triangle.3. **Distance (d):** Marked along the ground line, this represents the length of the base of the triangle from the starting point (on the left) to the point where the inclined line meets the ground.4. **Angle:** The angle formed between the ground line and the inclined line is 30 degrees.This diagram can be used in various educational circumstances such as trigonometry lessons to teach students how to calculate the lengths and angles in right triangles. Using trigonometric ratios, students could determine the value of the base (d) of the triangle, for example, by applying the cosine function to the given angle and hypotenuse:\[\cos(30^\circ) = \frac{\text{d}}{8.0 \text{ m}}\]By solving this, students can find the length of the base \(d\).

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Answered: An object with a mass of 10 kg is…

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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An object with a mass of 10 kg is initially at rest at the top of a frictionless inclined plane that rises at 30° above the horizontal. At the top, the object is initially 8.0 m from the bottom of the incline, as shown in the figure. When the object is released from this position, it eventually stops at a distance d from the bottom of the inclined plane along a horizontal surface, as shown. The coefficient of kinetic friction between the horizontal surface and the object is 0.20, and air resistance is negligible. Find the distance d.

In the image above, we have a diagram depicting a right triangle formed by a horizontal ground line and an inclined line that makes a 30-degree angle with the horizontal. Here are several key elements illustrated within this diagram:

1. **Inclined Line:** This line represents the hypotenuse of the right triangle, measuring 8.0 meters in length.

2. **Ground Line:** A horizontal line at the base of the triangle.

3. **Distance (d):** Marked along the ground line, this represents the length of the base of the triangle from the starting point (on the left) to the point where the inclined line meets the ground.

4. **Angle:** The angle formed between the ground line and the inclined line is 30 degrees.

This diagram can be used in various educational circumstances such as trigonometry lessons to teach students how to calculate the lengths and angles in right triangles. Using trigonometric ratios, students could determine the value of the base (d) of the triangle, for example, by applying the cosine function to the given angle and hypotenuse:

\[
\cos(30^\circ) = \frac{\text{d}}{8.0 \text{ m}}
\]

By solving this, students can find the length of the base \(d\).

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