Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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### Physics Problem on Impulse-Momentum and Braking Force Calculation

**Problem Statement:**
A 13,129-pound truck enters an emergency exit ramp at an initial speed of 112.4 feet per second (ft/s). It travels for 7.9 seconds before its speed is reduced to 24.5 ft/s. The task is to determine the braking force exerted by the truck, assuming the acceleration is constant. This problem uses the Impulse-Momentum concepts.

**Assumptions:**
- The angle \( \theta \) of the ramp is 21.4 degrees.

**Objective:**
- Calculate the braking force (in pounds of force, lbf) to two decimal places.

**Diagram Description:**
- The diagram illustrates a truck labeled "Rail Lines Cross Country Movers" ascending an inclined ramp.
- The initial velocity \( v_0 \) is shown as a green arrow pointing in the direction of the ramp's slope.
- The ramp has an indicated angle \( \theta \) with the horizontal plane, specified as 21.4 degrees.

**Steps for Calculation:**
1. **Extract Given Data:**
    - Mass of the truck: 13,129 lb
    - Initial velocity (\( v_0 \)): 112.4 ft/s
    - Final velocity (\( v_f \)): 24.5 ft/s
    - Time (\( t \)): 7.9 s
    - Ramp angle (\( \theta \)): 21.4 degrees

2. **Use Impulse-Momentum Theorem:**
    - Impulse (\( J \)) is the change in momentum (\( \Delta p \)) of the truck.
    - \( J = \Delta p = m \cdot \Delta v \)
    - Impulse is also equal to the braking force (\( F \)) times the time (\( t \)): \( J = F \cdot t \)

3. **Calculate Change in Velocity:**
    - \( \Delta v = v_f - v_0 = 24.5 \text{ ft/s} - 112.4 \text{ ft/s} = -87.9 \text{ ft/s} \)

4. **Calculate Momentum Change:**
    - Since \( m \) is given in pounds (force), ensure units are consistent.
    - Using \( m \) directly (assuming weight and mass conversion factors
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Transcribed Image Text:### Physics Problem on Impulse-Momentum and Braking Force Calculation **Problem Statement:** A 13,129-pound truck enters an emergency exit ramp at an initial speed of 112.4 feet per second (ft/s). It travels for 7.9 seconds before its speed is reduced to 24.5 ft/s. The task is to determine the braking force exerted by the truck, assuming the acceleration is constant. This problem uses the Impulse-Momentum concepts. **Assumptions:** - The angle \( \theta \) of the ramp is 21.4 degrees. **Objective:** - Calculate the braking force (in pounds of force, lbf) to two decimal places. **Diagram Description:** - The diagram illustrates a truck labeled "Rail Lines Cross Country Movers" ascending an inclined ramp. - The initial velocity \( v_0 \) is shown as a green arrow pointing in the direction of the ramp's slope. - The ramp has an indicated angle \( \theta \) with the horizontal plane, specified as 21.4 degrees. **Steps for Calculation:** 1. **Extract Given Data:** - Mass of the truck: 13,129 lb - Initial velocity (\( v_0 \)): 112.4 ft/s - Final velocity (\( v_f \)): 24.5 ft/s - Time (\( t \)): 7.9 s - Ramp angle (\( \theta \)): 21.4 degrees 2. **Use Impulse-Momentum Theorem:** - Impulse (\( J \)) is the change in momentum (\( \Delta p \)) of the truck. - \( J = \Delta p = m \cdot \Delta v \) - Impulse is also equal to the braking force (\( F \)) times the time (\( t \)): \( J = F \cdot t \) 3. **Calculate Change in Velocity:** - \( \Delta v = v_f - v_0 = 24.5 \text{ ft/s} - 112.4 \text{ ft/s} = -87.9 \text{ ft/s} \) 4. **Calculate Momentum Change:** - Since \( m \) is given in pounds (force), ensure units are consistent. - Using \( m \) directly (assuming weight and mass conversion factors
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