A metal rod of mass m slides without friction along two parallel horizontal rails, separated by a distance e and connected by a resistor R, as shown in the figure below. A uniform vertical magnetic field of magnitude B is applied perpendicular to the plane of the paper. The applied force shown in the figure acts only for a moment, to give the rod a speed v. In terms of m, e, R, B, and v, find the distance the rod will then slide as it coasts to a stop. d = R Fapp

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Chapter1: Units, Trigonometry. And Vectors
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A metal rod of mass \( m \) slides without friction along two parallel horizontal rails, separated by a distance \( \ell \) and connected by a resistor \( R \), as shown in the figure below. A uniform vertical magnetic field of magnitude \( B \) is applied perpendicular to the plane of the paper. The applied force shown in the figure acts only for a moment, to give the rod a speed \( v \). In terms of \( m \), \( \ell \), \( R \), \( B \), and \( v \), find the distance the rod will then slide as it coasts to a stop.

\[ d = \boxed{ \ \ \ \ \ } \]

**Diagram Explanation:**

The diagram shows:
- Two parallel horizontal orange rails.
- A blue rod sliding on these rails.
- The distance between the rails is labeled as \( \ell \).
- A resistor \( R \) is connected across the rails.
- A force \( F_{\text{app}} \) is applied horizontally to the rod.
- The magnetic field is directed into the plane of the paper, perpendicular to the rod.
Transcribed Image Text:A metal rod of mass \( m \) slides without friction along two parallel horizontal rails, separated by a distance \( \ell \) and connected by a resistor \( R \), as shown in the figure below. A uniform vertical magnetic field of magnitude \( B \) is applied perpendicular to the plane of the paper. The applied force shown in the figure acts only for a moment, to give the rod a speed \( v \). In terms of \( m \), \( \ell \), \( R \), \( B \), and \( v \), find the distance the rod will then slide as it coasts to a stop. \[ d = \boxed{ \ \ \ \ \ } \] **Diagram Explanation:** The diagram shows: - Two parallel horizontal orange rails. - A blue rod sliding on these rails. - The distance between the rails is labeled as \( \ell \). - A resistor \( R \) is connected across the rails. - A force \( F_{\text{app}} \) is applied horizontally to the rod. - The magnetic field is directed into the plane of the paper, perpendicular to the rod.
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