A force acting on a particle moving in the \(xy\) plane is given by \(\vec{F} = (2y\hat{i} + x^2\hat{j})\), where \(\vec{F}\) is in newtons and \(x\) and \(y\) are in meters. The particle moves from the origin to a final position having coordinates \(x = 4.00 \, \text{m}\) and \(y = 4.00 \, \text{m}\), as shown in the figure below.**Diagram Explanation:**- The diagram is a graph with axes labeled \(x \, (\text{m})\) and \(y \, (\text{m})\).- Three paths are indicated: - The **purple path** (\(O \to A \to C\)) consists of a straight line from the origin \(O\) to point \(A\) along the x-axis, then from \(A\) to \(C\) vertically. - The **red path** (\(O \to B \to C\)) consists of a straight line from the origin \(O\) to point \(B\) along the y-axis, then from \(B\) to \(C\) horizontally. - The **blue path** (\(O \to C\)) is a direct diagonal line from the origin \(O\) to point \(C\).**Questions:**(a) Calculate the work done by \(\vec{F}\) on the particle as it moves along the purple path (\(O \rightarrow A \rightarrow C\)).\[\boxed{\phantom{J}}\](b) Calculate the work done by \(\vec{F}\) on the particle as it moves along the red path (\(O \rightarrow B \rightarrow C\)).\[\boxed{\phantom{J}}\](c) Calculate the work done by \(\vec{F}\) on the particle as it moves along the blue path (\(O \rightarrow C\)).\[\boxed{\phantom{J}}\](d) Is \(\vec{F}\) conservative or nonconservative?- \( \circ \) conservative- \( \circ \) nonconservative(e) Explain your answer to part (d).\[\boxed{}\]

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Description: A force acting on a particle moving in the \(xy\) plane is given by \(\vec{F} = (2y\hat{i} + x^2\hat{j})\), where \(\vec{F}\) is in newtons and \(x\) and \(y\) are in meters. The particle moves from the origin to a final position having coordinates

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A force acting on a particle moving in the xy plane is given by F = (2yî + x²ĵ), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = 4.00 m and y = 4.00 m, as shown in the figure below. y (m) # (x, y) x (m) (a) Calculate the work done by F on the particle as it moves along the purple path (OAC J (b) Calculate the work done by F on the particle as it moves along the red path (OⓇBC). J (c) Calculate the work done by on the particle as it moves along the blue path (OC). J

A force acting on a particle moving in the xy plane is given by F = (2yî + x²ĵ), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = 4.00 m and y = 4.00 m, as shown in the figure below. y (m) # (x, y) x (m) (a) Calculate the work done by F on the particle as it moves along the purple path (OAC J (b) Calculate the work done by F on the particle as it moves along the red path (OⓇBC). J (c) Calculate the work done by on the particle as it moves along the blue path (OC). J

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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Question

A force acting on a particle moving in the \(xy\) plane is given by \(\vec{F} = (2y\hat{i} + x^2\hat{j})\), where \(\vec{F}\) is in newtons and \(x\) and \(y\) are in meters. The particle moves from the origin to a final position having coordinates \(x = 4.00 \, \text{m}\) and \(y = 4.00 \, \text{m}\), as shown in the figure below.

**Diagram Explanation:**

- The diagram is a graph with axes labeled \(x \, (\text{m})\) and \(y \, (\text{m})\).
- Three paths are indicated:
- The **purple path** (\(O \to A \to C\)) consists of a straight line from the origin \(O\) to point \(A\) along the x-axis, then from \(A\) to \(C\) vertically.
- The **red path** (\(O \to B \to C\)) consists of a straight line from the origin \(O\) to point \(B\) along the y-axis, then from \(B\) to \(C\) horizontally.
- The **blue path** (\(O \to C\)) is a direct diagonal line from the origin \(O\) to point \(C\).

**Questions:**

(a) Calculate the work done by \(\vec{F}\) on the particle as it moves along the purple path (\(O \rightarrow A \rightarrow C\)).
\[
\boxed{\phantom{J}}
\]

(b) Calculate the work done by \(\vec{F}\) on the particle as it moves along the red path (\(O \rightarrow B \rightarrow C\)).
\[
\boxed{\phantom{J}}
\]

(c) Calculate the work done by \(\vec{F}\) on the particle as it moves along the blue path (\(O \rightarrow C\)).
\[
\boxed{\phantom{J}}
\]

(d) Is \(\vec{F}\) conservative or nonconservative?
- \( \circ \) conservative
- \( \circ \) nonconservative

(e) Explain your answer to part (d).
\[
\boxed{}
\]

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