Go back to question 6 but this time assume uk=0.2. a) How much time elapses before the block reaches its maximum height up the plane?b) How much time elapses from the point it reaches maximum height up the plaane to the point where it was launched? **Education Website: Physics Lesson****Title: Analyzing Motion on an Inclined Plane****Introduction:**This section explores the physics involved when an object moves along an inclined plane, focusing on breaking down the forces and calculating the motion using constant acceleration formulas.**Step-by-Step Breakdown:**1. **Coordinate System Setup:** - Align the coordinate system with the inclined plane. - Break forces into components: - *x-direction*: \( N - W \cos \theta = 0 \) - *y-direction*: \( -W \sin \theta = ma \Rightarrow a = -g \sin \theta \) (constant acceleration)2. **Using Constant Acceleration Formulas:** - Formula: \( V_f^2 - V_o^2 = 2a \Delta s \) - Rearrangement for \(\Delta s\): \[ 0 - V_o^2 = -2g \sin \theta \Delta s \Rightarrow \Delta s = \frac{V_o^2}{2g \sin \theta} = 2.18 \, m \] - The object travels 2.18 meters before stopping.3. **Calculating Time to Stop (Forward and Return):** - Velocity-Time relation: \( V_f = V_o + at \) - Substituting for complete stop: \[ 0 = \frac{4 \, m/s}{5} - g \sin \theta t \Rightarrow t = \frac{4 \, m/s}{g \sin \theta} \approx 1.09 \, sec \] - Total time for round trip: \[ \text{Total time} = 2 \times 1.09 \, sec = 2.18 \, sec \]**Note:**Friction was neglected in this analysis. If friction were considered, the time up would not equal the time down, which will be explored further in later sections. **Illustration:**- A diagram showing an angled plane with a distance of 2.18 meters.This example provides insights into the dynamics involved when analyzing motion on inclined planes, emphasizing the importance of component forces and kinematic equations in predicting motion. The problem involves a block on an inclined plane. The block is given an initial speed of 4 meters per second up the plane, which is inclined at an angle of \( \theta = 22^\circ \). Friction is ignored in this scenario.**Questions:**(a) How far up the plane will the block go?(b) How much time elapses before it returns to its starting point?**Diagram Explanation:**- The diagram shows a right triangle representing the inclined plane. The angle of elevation is \( 22^\circ \).- A block with mass \( m \) is placed on the incline and has an initial velocity of 4 m/s directed up the plane.- The problem investigates the motion of the block under these conditions, ignoring friction.

This question belongs to friction.

Go back to question 6 but this time assume uk=0.2. a) How much time elapses before the block reaches its maximum height up the plane? b) How much time elapses from the point it reaches maximum height up the plaane to the point where it was launched?

Go back to question 6 but this time assume uk=0.2. a) How much time elapses before the block reaches its maximum height up the plane? b) How much time elapses from the point it reaches maximum height up the plaane to the point where it was launched?

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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Question

Go back to question 6 but this time assume uk=0.2.

a) How much time elapses before the block reaches its maximum height up the plane?

b) How much time elapses from the point it reaches maximum height up the plaane to the point where it was launched?

**Education Website: Physics Lesson**

**Title: Analyzing Motion on an Inclined Plane**

**Introduction:**
This section explores the physics involved when an object moves along an inclined plane, focusing on breaking down the forces and calculating the motion using constant acceleration formulas.

**Step-by-Step Breakdown:**

1. **Coordinate System Setup:**
- Align the coordinate system with the inclined plane.
- Break forces into components:
- *x-direction*: \( N - W \cos \theta = 0 \)
- *y-direction*: \( -W \sin \theta = ma \Rightarrow a = -g \sin \theta \) (constant acceleration)

2. **Using Constant Acceleration Formulas:**
- Formula: \( V_f^2 - V_o^2 = 2a \Delta s \)
- Rearrangement for \(\Delta s\):
\[
0 - V_o^2 = -2g \sin \theta \Delta s \Rightarrow \Delta s = \frac{V_o^2}{2g \sin \theta} = 2.18 \, m
\]
- The object travels 2.18 meters before stopping.

3. **Calculating Time to Stop (Forward and Return):**
- Velocity-Time relation: \( V_f = V_o + at \)
- Substituting for complete stop:
\[
0 = \frac{4 \, m/s}{5} - g \sin \theta t \Rightarrow t = \frac{4 \, m/s}{g \sin \theta} \approx 1.09 \, sec
\]
- Total time for round trip:
\[
\text{Total time} = 2 \times 1.09 \, sec = 2.18 \, sec
\]

**Note:**
Friction was neglected in this analysis. If friction were considered, the time up would not equal the time down, which will be explored further in later sections.

**Illustration:**
- A diagram showing an angled plane with a distance of 2.18 meters.

This example provides insights into the dynamics involved when analyzing motion on inclined planes, emphasizing the importance of component forces and kinematic equations in predicting motion.

The problem involves a block on an inclined plane. The block is given an initial speed of 4 meters per second up the plane, which is inclined at an angle of \( \theta = 22^\circ \). Friction is ignored in this scenario.

**Questions:**

(a) How far up the plane will the block go?

(b) How much time elapses before it returns to its starting point?

**Diagram Explanation:**

- The diagram shows a right triangle representing the inclined plane. The angle of elevation is \( 22^\circ \).
- A block with mass \( m \) is placed on the incline and has an initial velocity of 4 m/s directed up the plane.
- The problem investigates the motion of the block under these conditions, ignoring friction.

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