PROBLEM 11.124 Knowing that at the instant shown block A has a velocity of 8 in./s and an acceleration of 6 in./s both directed down the incline, determine (a) the velocity of block B. (b) the acceleration of block B. B メ。= Sinls yさ25 15° %3D Xp = 6 in /s? y > 25 Xg = ? Xg = ? 25° 40 L= XA + XA (xg-Xx) 16 %3D 25 = xA + XA + - 2 - 2(8) = -16 in/s O = 40 2* A 16 cos 40° 8 cos 25° B/A %3D ×6- ×。マ Xe= X8%% + xA ion) ( Now just ned direct %3D A - -16 cos 40° + 8 cos 25° = - 12.258 + 7.250
PROBLEM 11.124 Knowing that at the instant shown block A has a velocity of 8 in./s and an acceleration of 6 in./s both directed down the incline, determine (a) the velocity of block B. (b) the acceleration of block B. B メ。= Sinls yさ25 15° %3D Xp = 6 in /s? y > 25 Xg = ? Xg = ? 25° 40 L= XA + XA (xg-Xx) 16 %3D 25 = xA + XA + - 2 - 2(8) = -16 in/s O = 40 2* A 16 cos 40° 8 cos 25° B/A %3D ×6- ×。マ Xe= X8%% + xA ion) ( Now just ned direct %3D A - -16 cos 40° + 8 cos 25° = - 12.258 + 7.250
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Problem 11.124**
Knowing that at the instant shown block A has a velocity of 8 in/s and an acceleration of 6 in/s² both directed down the incline, determine (a) the velocity of block B, (b) the acceleration of block B.
### Diagram Explanation
A diagram shows block A on an incline making an angle of 25° with the horizontal. Block B is connected via pulleys and is at another incline of 15°. The angle between the two pulleys is 40°.
### Solution
Given:
- Velocity of block A, \( \dot{x}_A = 8 \, \text{in/s} \) down the incline.
- Acceleration of block A, \( \ddot{x}_A = 6 \, \text{in/s}^2 \) down the incline.
- \( x_B = ? \)
- \( \dot{x}_B = ? \)
- \( \ddot{x}_B = ? \)
Steps:
1. **Length Equation:**
\[
L = x_A + x_A + (x_B - x_A)
\]
2. **Differentiating:**
\[
0 = \dot{x}_A + \dot{x}_A + \dot{x}_{B/A}
\]
3. **Substitution:**
\[
\dot{x}_{B/A} = -2 \dot{x}_A = -2(8) = -16 \, \text{in/s}
\]
4. **Velocity of B:**
\[
\dot{x}_B = \dot{x}_{B/A} + \dot{x}_A
\]
\[
= -16 \cos 40^\circ + 8 \cos 25^\circ
\]
\[
= -12.258 + 7.250 = -5.008 \, \text{in/s}
\]
(Now just need direction)
### Graphs and Calculations
Two right-angled triangles are shown for calculating the components:
- One with hypotenuse 16 and angle 40°.
- Second with hypotenuse 8 and angle 25°.
The calculations involve:
\[
16 \cos 40^\circ
\]
\[
8 \cos 25^\circ
\]
Conclusion:
- Compute the exact](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86798898-a53e-4bc3-9be6-9ee38aec03ed%2Fcd844b35-2c81-414a-974b-6086036b51d7%2Fvvc2d4r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 11.124**
Knowing that at the instant shown block A has a velocity of 8 in/s and an acceleration of 6 in/s² both directed down the incline, determine (a) the velocity of block B, (b) the acceleration of block B.
### Diagram Explanation
A diagram shows block A on an incline making an angle of 25° with the horizontal. Block B is connected via pulleys and is at another incline of 15°. The angle between the two pulleys is 40°.
### Solution
Given:
- Velocity of block A, \( \dot{x}_A = 8 \, \text{in/s} \) down the incline.
- Acceleration of block A, \( \ddot{x}_A = 6 \, \text{in/s}^2 \) down the incline.
- \( x_B = ? \)
- \( \dot{x}_B = ? \)
- \( \ddot{x}_B = ? \)
Steps:
1. **Length Equation:**
\[
L = x_A + x_A + (x_B - x_A)
\]
2. **Differentiating:**
\[
0 = \dot{x}_A + \dot{x}_A + \dot{x}_{B/A}
\]
3. **Substitution:**
\[
\dot{x}_{B/A} = -2 \dot{x}_A = -2(8) = -16 \, \text{in/s}
\]
4. **Velocity of B:**
\[
\dot{x}_B = \dot{x}_{B/A} + \dot{x}_A
\]
\[
= -16 \cos 40^\circ + 8 \cos 25^\circ
\]
\[
= -12.258 + 7.250 = -5.008 \, \text{in/s}
\]
(Now just need direction)
### Graphs and Calculations
Two right-angled triangles are shown for calculating the components:
- One with hypotenuse 16 and angle 40°.
- Second with hypotenuse 8 and angle 25°.
The calculations involve:
\[
16 \cos 40^\circ
\]
\[
8 \cos 25^\circ
\]
Conclusion:
- Compute the exact
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