Part A The initial and final states of the toolbox are illustrated in the figure. Identify the initial speed v; of the toolbox and the vertical distance h through which the toolbox moves.(Figure 1) Enter the initial speed and the height symbolically in terms of the variables given in the problem introduction (m a A fi n and d
Part A The initial and final states of the toolbox are illustrated in the figure. Identify the initial speed v; of the toolbox and the vertical distance h through which the toolbox moves.(Figure 1) Enter the initial speed and the height symbolically in terms of the variables given in the problem introduction (m a A fi n and d
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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This homework question has really been stumping me. Help would be greatly appreciated, thanks!
![**Learning Goal:**
To practice Problem-Solving Strategy 7.3 Conservation of energy with nonconservative forces.
**Problem Statement:**
While a roofer is working on a roof that slants at \(\theta = 36.0\) degrees above the horizontal, he accidentally nudges his \(m = 8.50 \, \text{kg}\) toolbox, causing it to start sliding downward, starting from rest. A frictional force of magnitude \(f_k = 22.0 \, \text{N}\) acts on the toolbox as it slides. If the box starts \(d = 4.25 \, \text{m}\) from the lower edge of the roof, how fast \(v\) will the toolbox be moving just as it reaches the edge of the roof? Assume that the acceleration due to gravity is \(g = 9.80 \, \text{m/s}^2\).
**Figure Explanation:**
The figure illustrates a toolbox on a slanted roof. The roof has an angle \(\theta\) relative to the horizontal. The toolbox starts from an initial state at a distance \(d\) from the edge and slides down to the final state. The vertical height from the roof's starting to the ending point is labeled \(h\).
---
**Problem Solving Strategy 7.3: Conservation of energy with nonconservative forces**
**SET UP**
1. Identify the system you will analyze and decide on the initial and final states (positions and velocities) you will use in solving the problem. Draw one or more sketches showing the initial and final states.
2. Define your coordinate system, particularly the zero points for gravitational and elastic potential energies (the point at which \(y = 0\)).
3. List the initial and final kinetic and potential energies \((K_i, K_f, U_i, \text{ and } U_f)\) and identify any nonconservative forces. Write an expression for the work, \(W_{\text{other}}\), done by the nonconservative forces.
**SOLVE**
4. Use the general expression
\[
U_i + K_i + W_{\text{other}} = U_f + K_f
\]
for conservation of energy and solve to find the unknown quantity.
**REFLECT**
5. Does your answer make sense? Did friction slow the object down? Did any pushing forces speed](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03d19364-d2f4-4703-a72b-e46c5aa833e9%2Ff4c31e25-9d90-4720-86f9-4537707a4c2e%2F517n4v_processed.png&w=3840&q=75)
Transcribed Image Text:**Learning Goal:**
To practice Problem-Solving Strategy 7.3 Conservation of energy with nonconservative forces.
**Problem Statement:**
While a roofer is working on a roof that slants at \(\theta = 36.0\) degrees above the horizontal, he accidentally nudges his \(m = 8.50 \, \text{kg}\) toolbox, causing it to start sliding downward, starting from rest. A frictional force of magnitude \(f_k = 22.0 \, \text{N}\) acts on the toolbox as it slides. If the box starts \(d = 4.25 \, \text{m}\) from the lower edge of the roof, how fast \(v\) will the toolbox be moving just as it reaches the edge of the roof? Assume that the acceleration due to gravity is \(g = 9.80 \, \text{m/s}^2\).
**Figure Explanation:**
The figure illustrates a toolbox on a slanted roof. The roof has an angle \(\theta\) relative to the horizontal. The toolbox starts from an initial state at a distance \(d\) from the edge and slides down to the final state. The vertical height from the roof's starting to the ending point is labeled \(h\).
---
**Problem Solving Strategy 7.3: Conservation of energy with nonconservative forces**
**SET UP**
1. Identify the system you will analyze and decide on the initial and final states (positions and velocities) you will use in solving the problem. Draw one or more sketches showing the initial and final states.
2. Define your coordinate system, particularly the zero points for gravitational and elastic potential energies (the point at which \(y = 0\)).
3. List the initial and final kinetic and potential energies \((K_i, K_f, U_i, \text{ and } U_f)\) and identify any nonconservative forces. Write an expression for the work, \(W_{\text{other}}\), done by the nonconservative forces.
**SOLVE**
4. Use the general expression
\[
U_i + K_i + W_{\text{other}} = U_f + K_f
\]
for conservation of energy and solve to find the unknown quantity.
**REFLECT**
5. Does your answer make sense? Did friction slow the object down? Did any pushing forces speed
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