Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
37 (a) A dc power line for a light-rail system carries 1000 A at an angle of 30.0º to Earth's 5.0×10−5T field. What is the force on a 100-m section of this line? (b) Discuss practical concerns this presents, if any.
![**Example Problem: Calculating Magnetic Force on a Current-Carrying Wire**
**Given:**
- Current (\( I \)) = 1000 A
- Angle (\( \theta \)) = 30°
- Magnetic field (\( B \)) = \( 5 \times 10^{-5} \) T
- Length of wire (\( \ell \)) = 100 m
**Problem:**
Calculate the magnetic force (\( \vec{F}_B \)) on the wire.
**Diagram:**
The diagram shows a wire placed at an angle (\( \theta \)) with respect to the magnetic field \( \vec{B} \). The wire carries a current \( I \). The magnetic field lines are illustrated as parallel arrows crossing the path of the wire at an angle.
**Solution:**
1. **Formula for Magnetic Force:**
\[
\vec{F}_B = I \cdot \vec{\ell} \times \vec{B}
\]
2. **Magnitude of Magnetic Force:**
\[
|\vec{F}_B| = I \cdot |\vec{\ell}| \cdot |\vec{B}| \cdot \sin \theta
\]
3. **Substitute the Given Values:**
\[
|\vec{F}_B| = 1000 \, \text{A} \cdot 100 \, \text{m} \cdot 5 \times 10^{-5} \, \text{T} \cdot \sin 30^\circ
\]
4. **Calculation:**
\[
|\vec{F}_B| = 1000 \cdot 100 \cdot 5 \times 10^{-5} \cdot 0.5
\]
5. **Result:**
The expression for \( |\vec{F}_B| \) is written, but calculation steps to reach the final numeric answer are expected to be completed.
**Note:** The student should complete the numeric calculation to find the exact magnitude of the magnetic force.
This problem demonstrates how to apply the formula for the magnetic force on a current-carrying conductor in a magnetic field. It highlights the effect of the angle and magnetic field on the force experienced by the wire.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F183a4de2-60b8-4988-9fb9-0a70f8d6fd02%2F7c9312e6-b1cf-4e77-9ce9-181469e87216%2Fbfy53qk_processed.png&w=3840&q=75)
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