Part G Let the proton be released instead at x1 = 3α/β....

Jerrah Biggerstaff and 65 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Key Concept

Premium Feature

Explore the core concept behind this problem.

Key Concept

Premium Feature

Explore the core concept behind this problem.

Recommended Videos

A proton with mass $m$ moves in one dimension. The potential-energy function is $U(x)=\left(\alpha / x^{2}\right)-(\beta / x),$ where $\alpha$ and $\beta$ are positive constants. The proton is released from rest at $x_{0}=\alpha / \beta$. (a) Show that $U(x)$ can be written as $$ Graph $U(x) .$ Calculate $U\left(x_{0}\right)$ and thereby locate the point $x_{0}$ on the graph. (b) Calculate $v(x)$, the speed of the proton as a function of position. Graph $v(x)$ and give a qualitative description of the motion. (c) For what value of $x$ is the speed of the proton a maximum? What is the value of that maximum speed? (d) What is the force on the proton at the point in part (c)? (e) Let the proton be released instead at $x_{1}=3 \alpha / \beta .$ Locate the point $x_{1}$ on the graph of $U(x) .$ Calculate $v(x)$ and give a qualitative description of the motion. (f) For each release point $\left(x=x_{0}\right.$ and $\left.x=x_{1}\right),$ what are the maximum and minimum values of $x$ reached during the motion? U(x)=\frac{\alpha}{x_{0}^{2}}\left[\left(\frac{x_{0}}{x}\right)^{2}-\frac{x_{0}}{x}\right] $$

A proton with mass $m$ moves in one dimension. The potential-energy function is $U(x) = (\alpha/x^2) - (\beta/x)$, where $\alpha$ and $\beta$ are positive constants. The proton is released from rest at $x_0$ = $\alpha$/$\beta$. (a) Show that $U(x)$ can be written as $$U(x) = \frac{\alpha}{x^2_0}\ \Big[ \Big( \frac{x_0}{x}\ \Big)^2 - \frac{x_0}{x}\ \Big] $$ Graph $U(x)$. Calculate $U(x_0)$ and thereby locate the point $x_0$ on the graph. (b) Calculate $v(x)$, the speed of the proton as a function of position. Graph $v(x)$ and give a qualitative description of the motion. (c) For what value of $x$ is the speed of the proton a maximum? What is the value of that maximum speed? (d) What is the force on the proton at the point in part (c)? (e) Let the proton be released instead at $x_1 = 3\alpha / \beta$. Locate the point $x_1$ on the graph of $U(x)$. Calculate $v(x)$ and give a qualitative description of the motion. (f) For each release point ($x = x_0$ and $x = x_1$), what are the maximum and minimum values of $x$ reached during the motion?

A proton with mass $m$ moves in one dimension. The potential-energy function is $U(x)=\alpha / x^{2}-\beta / x,$ where $\alpha$ and $\beta$ are positive constants. The proton is released from rest at $x_{0}=\alpha / \beta$ (a) Show that $U(x)$ can be written as $$ U(x)=\frac{\alpha}{x_{0}^{2}}\left[\left(\frac{x_{0}}{x}\right)^{2}-\frac{x_{0}}{x}\right] $$ Graph $U(x)$ . Calculate $U\left(x_{0}\right)$ and thereby locate the point $x_{0}$ on the graph. (b) Calculate $v(x),$ the speed of the proton as a function of position. Graph $v(x)$ and give a qualitative description of the motion. (c) For what value of $x$ is the speed of the proton a maximum? What is the value of that maximum speed? (d) What is the force on the proton at the point in part (c)? (e) Let the proton be released instead at $x_{1}=3 \alpha / \beta$ . Locate the point $x_{1}$ on the graph of $U(x)$ . Calculate $v(x)$ and give a qualitative description of the motion. (f) For each release point $\left(x=x_{0} \text { and } x=x_{1}\right),$ what are the maximum and minimum values of $x$ reached during the motion?

Transcript

00:01 We're given a proton that's moving in one dimension with a given potential energy function.

00:06 And we have alpha and beta as our positive constants.

00:10 So it's just asking us to rewrite that potential energy function.

00:15 So the first thing is we have this proton right here that is moving.

00:24 And we are given that its starting point x -not is alpha over beta.

00:34 So we're given the potential energy function is equal to u of x is alpha over x squared minus beta over x.

00:44 And we'll call this equation 1.

00:47 So from the given x not, we can rearrange that to solve for beta...

Question

Part G Let the proton be released instead at $x_1 = 3\alpha/\beta$. Calculate $v(x)$. Express your answer in terms of the variables $\alpha$, $x_0$, $m$, and $x$.

Question

Part G Let the proton be released instead at $x_1 = 3\alpha/\beta$. Calculate $v(x)$. Express your answer in terms of the variables $\alpha$, $x_0$, $m$, and $x$.

Please give Ace some feedback