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Solved: An object has several forces acting on it. One
Chapter 7, Problem 85P(choose chapter or problem)
An object has several forces acting on it. One force is \(\vec{F}=\alpha x y \hat{i}\) a force in the \(x \text {-direction }\) whose magnitude depends on the position of the object. (See Problem 6.98.) The constant is
\(\alpha=2.00 \mathrm{~N} / \mathrm{m}^{2}\). The object moves along the following path: (1) It starts at the origin and moves along the y-axis to the point \(x=0, y=1.50 \mathrm{~m}\); (2) it moves parallel to the x-axis to the point
\(x=1.50 \mathrm{~m}, y=1.50 \mathrm{~m}\);(3) it moves parallel to the y-axis to the point
\(x=1.50 \mathrm{~m}, y=0\); (4) it moves parallel to the x-axis back to the origin.
(a) Sketch this path in the xy-plane.
(b) Calculate the work done on the object by \(\vec{F}\) for each leg of the path and for the complete round trip.
(c) Is \(\vec{F}\) conservative or nonconservative? Explain.
Equation Transcription:
Text Transcription:
Vec F=axy î
x-direction
Beta =2.00 N/m2
y-axis
x=0, y=1.50 m
x-axis
x=1.50 m, y=1.50 m
x=1.50 m, y=0
Vec F
Vec F
Questions & Answers
QUESTION:
An object has several forces acting on it. One force is \(\vec{F}=\alpha x y \hat{i}\) a force in the \(x \text {-direction }\) whose magnitude depends on the position of the object. (See Problem 6.98.) The constant is
\(\alpha=2.00 \mathrm{~N} / \mathrm{m}^{2}\). The object moves along the following path: (1) It starts at the origin and moves along the y-axis to the point \(x=0, y=1.50 \mathrm{~m}\); (2) it moves parallel to the x-axis to the point
\(x=1.50 \mathrm{~m}, y=1.50 \mathrm{~m}\);(3) it moves parallel to the y-axis to the point
\(x=1.50 \mathrm{~m}, y=0\); (4) it moves parallel to the x-axis back to the origin.
(a) Sketch this path in the xy-plane.
(b) Calculate the work done on the object by \(\vec{F}\) for each leg of the path and for the complete round trip.
(c) Is \(\vec{F}\) conservative or nonconservative? Explain.
Equation Transcription:
Text Transcription:
Vec F=axy î
x-direction
Beta =2.00 N/m2
y-axis
x=0, y=1.50 m
x-axis
x=1.50 m, y=1.50 m
x=1.50 m, y=0
Vec F
Vec F
ANSWER:
Solution 85P
Step 1:
(a).The object moves parallel to the force and so the dot product between the vectors is trivial.it's just the product of the vectors themselves.Therefore, the work done here is just