The initially stationary 24-kg block is subjected to the time-varying force whose magnitude P is shown in the plot. Note that the force is zero for all times greater than 5 s. Determine the time to at which the block comes to rest. H₂=0.43 Hs = 0.51 Answe: ts= i 24 kg 4.181 P 26° P. N 173 0 5 t, s

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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**Problem Statement:**

The initially stationary 24-kg block is subjected to the time-varying force whose magnitude \(P\) is shown in the plot. Note that the force is zero for all times greater than 5 s. Determine the time \(t_s\) at which the block comes to rest.

**Given Values:**

\[
\mu_k = 0.43 \quad \mu_s = 0.51 \quad 26^\circ\quad 24\, \text{kg}
\]

**Diagrams:**

1. **Diagram of Block with Forces:**
   - A block weighing 24 kg is placed on a surface inclined at an angle of 26 degrees.
   - The coefficient of kinetic friction (\(\mu_k\)) is 0.43.
   - The coefficient of static friction (\(\mu_s\)) is 0.51.
   - There is a force \(P\) applied upwards along the ramp.

2. **Plot of Force \(P\) Against Time \(t\):**
   - A graph is shown with Force \(P\) (in N) on the vertical axis and Time \(t\) (in s) on the horizontal axis.
   - From \(t = 0\) to \(t = 5\) seconds, the force \(P\) increases linearly from 0 N to 173 N.
   - For times greater than 5 seconds, the force \(P\) is constant at 0 N.

**Answer:**

\[
t_s = \boxed{4.181} \, \text{s}
\]
Transcribed Image Text:**Problem Statement:** The initially stationary 24-kg block is subjected to the time-varying force whose magnitude \(P\) is shown in the plot. Note that the force is zero for all times greater than 5 s. Determine the time \(t_s\) at which the block comes to rest. **Given Values:** \[ \mu_k = 0.43 \quad \mu_s = 0.51 \quad 26^\circ\quad 24\, \text{kg} \] **Diagrams:** 1. **Diagram of Block with Forces:** - A block weighing 24 kg is placed on a surface inclined at an angle of 26 degrees. - The coefficient of kinetic friction (\(\mu_k\)) is 0.43. - The coefficient of static friction (\(\mu_s\)) is 0.51. - There is a force \(P\) applied upwards along the ramp. 2. **Plot of Force \(P\) Against Time \(t\):** - A graph is shown with Force \(P\) (in N) on the vertical axis and Time \(t\) (in s) on the horizontal axis. - From \(t = 0\) to \(t = 5\) seconds, the force \(P\) increases linearly from 0 N to 173 N. - For times greater than 5 seconds, the force \(P\) is constant at 0 N. **Answer:** \[ t_s = \boxed{4.181} \, \text{s} \]
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