Solution Found!
A 10 g particle has the potential energy shown in
Chapter 11, Problem 39P(choose chapter or problem)
A 10 g particle has the potential energy shown in Figure P11.39.
a. Draw a force-versus-position graph from\(x = 0 cm\) to\(x = 8 cm\).
b. How much work does the force do as the particle moves from \(x = 2 cm\) to \(x = 6 cm\)?
c. What speed does the particle need at \(x = 2 cm\) to arrive at \(x = 6 cm\) with a speed of 10 m/s?
Equation Transcription:
Text Transcription:
x = 0 cm
x = 8 cm
x = 2 cm
x = 6 cm
x = 2 cm
x = 6 cm
Questions & Answers
QUESTION:
A 10 g particle has the potential energy shown in Figure P11.39.
a. Draw a force-versus-position graph from\(x = 0 cm\) to\(x = 8 cm\).
b. How much work does the force do as the particle moves from \(x = 2 cm\) to \(x = 6 cm\)?
c. What speed does the particle need at \(x = 2 cm\) to arrive at \(x = 6 cm\) with a speed of 10 m/s?
Equation Transcription:
Text Transcription:
x = 0 cm
x = 8 cm
x = 2 cm
x = 6 cm
x = 2 cm
x = 6 cm
ANSWER:
Step 1 of 4
(a)
From the given potential energy graph for a particle with mass \(m=10 \mathrm{~g}=0.01 \mathrm{~kg}\), we need to draw a force versus position graph.
- To derive a relation between force and potential energy,
From the work-energy theorem, we know that work done during the process will be equal to the negative change in potential energy.
That is,
\(W=-\Delta U\)
Using work done as a product of force and displacement \(W=F \Delta x\)
\(F \Delta x=-\Delta U\)
\(F=-\frac{\Delta U}{\Delta x}\)
\(F=-\text { Slope of potential energy curve........ }\)