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Chapter 7: Problem 30

An incline makes an angle \(\theta\) with the horizontal. Find the gravitational potential energy associated with a mass \(m\) located a distance \(x\) measured along the incline. Take the zero of potential energy at the bottom of the incline.

Short Answer

Expert verified
The gravitational potential energy associated with the mass \(m\) at a distance \(x\) along the incline under gravity \(g\) and angle \(\theta\) with the horizontal is \(PE = m*g*x* \sin(\theta)\)

Step by step solution

01

Identify Given Information and Unknown

Firstly, identify all given values. Here, the mass \(m\), distance \(x\) and angle \(\theta\) are given. The zero point for potential energy is defined at the bottom of the incline. The goal is to find the gravitational potential energy associated with the mass \(m\) located on an incline of this distance.
02

Convert to Equivalant Vertical Height

To work with the gravitational potential energy, an equivalent vertical height needs to be determined. The height \(h\) of a right triangle (formed by the incline, height and the horizontal base), can be obtained from the function of sine of the angle. Therefore, \(h = x \sin(\theta)\).
03

Apply Gravitational Potential Energy Formula

Use the gravitational potential energy formula, which is \(PE = m*g*h\), where \(g\) is the acceleration due to gravity. Substituting height \(h\) from step 2, we get \(PE = m*g*x* \sin(\theta)\).

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Most popular questions from this chapter

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