The 210-kg crate rests on the ground for which the coefficients of static and kinetic friction are u, = 0.5 and Hk = 0.4, respectively. The winch delivers a horizontal towing force T to its cable at A which varies as shown in the graph. Originally the tension in the cable is zero. (Figure 1) Part A Determine the speed of the crate when t = 3.8 s. Hint: First determine the force needed to begin moving the crate. Express your answer to three significant figures and include the appropriate units. > View Avallable Hint(s) Value Units Submit Figure 1 of 1> Provide Feedback T (N) 800 T- 400 (s)
The 210-kg crate rests on the ground for which the coefficients of static and kinetic friction are u, = 0.5 and Hk = 0.4, respectively. The winch delivers a horizontal towing force T to its cable at A which varies as shown in the graph. Originally the tension in the cable is zero. (Figure 1) Part A Determine the speed of the crate when t = 3.8 s. Hint: First determine the force needed to begin moving the crate. Express your answer to three significant figures and include the appropriate units. > View Avallable Hint(s) Value Units Submit Figure 1 of 1> Provide Feedback T (N) 800 T- 400 (s)
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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![### Physics Problem: Speed of a Crate
**Context:**
In this problem, you will find the speed of a 210-kg crate under the influence of a variable horizontal force exerted by a winch.
**Given Data:**
- The mass of the crate: \( 210 \) kg
- Coefficient of static friction (\(\mu_s\)): \( 0.5 \)
- Coefficient of kinetic friction (\(\mu_k\)): \( 0.4 \)
- The winch delivers a variable horizontal towing force \( T \) to its cable at point \( A \).
**Objective:**
Determine the speed of the crate at \( t = 3.8 \) seconds.
**Part A:**
First, determine the force needed to begin moving the crate. Then, compute its speed.
**Instructions:**
Express your answer to three significant figures and include the appropriate units.
---
#### Diagram Description:
The diagram depicts a crate being pulled by a winch. The tension \( T \) in the cable varies over time as described by the function \( T = 400t^{1/2} \). The tension \( T \) (in Newtons) increases from \( 0 \) to \( 800 \) N as the time \( t \) (in seconds) increases from \( 0 \) to \( 4 \) s.
**Figure 1:**
- A crate is shown on a flat surface.
- Cable attached to the crate is linked to a winch at point \( A \).
- A graph above illustrates the tension \( T \) in Newtons (N) over time \( t \) in seconds (s).
---
**Example Calculation:**
1. **Determine the force needed to overcome static friction:**
\[
F_{\text{static}} = \mu_s \cdot m \cdot g
\]
where \( g \) is the acceleration due to gravity (\( 9.8 \text{ m/s}^2 \)).
2. **Determine kinetic friction force once the crate starts moving:**
\[
F_{\text{kinetic}} = \mu_k \cdot m \cdot g
\]
3. **Calculate the net force and eventually the acceleration:**
\[
F_{\text{net}} = T - F_{\text{kinetic}}
\]
\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2d7e9b1-7208-47e7-acf1-5a4d04c3ff3b%2F79ed6f48-6410-40c4-a283-bf3f740d613b%2Ffg9ra1n_processed.png&w=3840&q=75)
Transcribed Image Text:### Physics Problem: Speed of a Crate
**Context:**
In this problem, you will find the speed of a 210-kg crate under the influence of a variable horizontal force exerted by a winch.
**Given Data:**
- The mass of the crate: \( 210 \) kg
- Coefficient of static friction (\(\mu_s\)): \( 0.5 \)
- Coefficient of kinetic friction (\(\mu_k\)): \( 0.4 \)
- The winch delivers a variable horizontal towing force \( T \) to its cable at point \( A \).
**Objective:**
Determine the speed of the crate at \( t = 3.8 \) seconds.
**Part A:**
First, determine the force needed to begin moving the crate. Then, compute its speed.
**Instructions:**
Express your answer to three significant figures and include the appropriate units.
---
#### Diagram Description:
The diagram depicts a crate being pulled by a winch. The tension \( T \) in the cable varies over time as described by the function \( T = 400t^{1/2} \). The tension \( T \) (in Newtons) increases from \( 0 \) to \( 800 \) N as the time \( t \) (in seconds) increases from \( 0 \) to \( 4 \) s.
**Figure 1:**
- A crate is shown on a flat surface.
- Cable attached to the crate is linked to a winch at point \( A \).
- A graph above illustrates the tension \( T \) in Newtons (N) over time \( t \) in seconds (s).
---
**Example Calculation:**
1. **Determine the force needed to overcome static friction:**
\[
F_{\text{static}} = \mu_s \cdot m \cdot g
\]
where \( g \) is the acceleration due to gravity (\( 9.8 \text{ m/s}^2 \)).
2. **Determine kinetic friction force once the crate starts moving:**
\[
F_{\text{kinetic}} = \mu_k \cdot m \cdot g
\]
3. **Calculate the net force and eventually the acceleration:**
\[
F_{\text{net}} = T - F_{\text{kinetic}}
\]
\
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