7.35 **Exercise 7.35**A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces a potential energy \( U(x) \) given by \( U(x) = \alpha x^4 \) where \( \alpha = 1.31 \, \text{J/m}^4 \).### Part A**Question:**What is the force when the particle is at position \( x = -0.740 \, \text{m} \)?**Answer:**To find the force \( F_x \) at the given position, you need to first understand the relationship between force and potential energy. The force \( F_x \) can be determined using the gradient (or derivative) of the potential energy function:\[ F_x = -\frac{dU}{dx} \]Given the potential energy function:\[ U(x) = \alpha x^4 \]To find \( F_x \), we take the derivative of \( U(x) \) with respect to \( x \):\[ \frac{dU}{dx} = 4\alpha x^3 \]Thus,\[ F_x = -4\alpha x^3 \]Substitute \( \alpha = 1.31 \, \text{J/m}^4 \) and \( x = -0.740 \, \text{m} \):\[ F_x = -4 (1.31) (-0.740)^3 \]To complete this calculation and find the numerical value of \( F_x \), input these values into the calculation.#### Graph/Diagram Description:No graphs or diagrams are depicted in this exercise. The focus is on textual and mathematical analysis. Click on the 'Submit' button to insert your calculated force value in \( F_x = \text{_____} \, \text{N} \). For additional help or to see the answer, you can click on 'Request Answer'.

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Description: 7.35 **Exercise 7.35**A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces a potential energy \( U(x) \) given by \( U(x) = \alpha x^4 \) where \( \alpha = 1.31 \, \text{J/m}^4 \).### Part A**Question:**What

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A force parallel to the z-axis acts on a particle moving along the z-axis. This force produces a potential energy U(z) given by U(x) = ax¹ where a =1.31 J/m¹ Part A What is the force when the particle is at position a = -0.740 m ? 15. ΑΣΦΑ p ? F₂ = N

A force parallel to the z-axis acts on a particle moving along the z-axis. This force produces a potential energy U(z) given by U(x) = ax¹ where a =1.31 J/m¹ Part A What is the force when the particle is at position a = -0.740 m ? 15. ΑΣΦΑ p ? F₂ = N

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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