### Understanding Angular and Linear Velocity of a Rectangular Plate under Horizontal Impulses**Problem Statement:**A 29-pound rectangular plate is at rest on a smooth horizontal floor. It is subjected to horizontal impulses as illustrated in **Figure 1**. Assume impulse \(I = 20 \text{ lb} \cdot \text{s}\).#### Figure 1: Diagram and DimensionsThe diagram shows a rectangular plate with the following dimensions:- Length: 1 ft.- Width: 0.5 ft.Two forces are applied:- A 5 lb・s impulse at a point 0.5 ft from the right edge and 60 degrees downwards to the right.- A 20 lb・s impulse acting horizontally to the left at a point 0.5 ft from the left edge.### Part A: Determine Angular Velocity**Objective:**To calculate the angular velocity (ω) of the rectangular plate in radians per second (rad/s).**Attempted Solution:**An attempt was made to input the angular velocity as 37.747 rad/s, but this answer was marked incorrect.**Steps to Determine Angular Velocity:**1. Identify the center of mass and distribution of impulses.2. Calculate the moments generated by the impulses about the center of mass.3. Apply the principle of angular impulse and momentum to solve for angular velocity.### Part B: Determine Linear Velocity of Mass Center**Objective:**To calculate the linear velocity (\(v_G\)) of the mass center of the plate in feet per second (ft/s).**Attempted Solution:**An attempt was made to input the linear velocity as 22.2 ft/s, which seems to be correct (indicated by the checkmark).**Steps to Determine Linear Velocity:**1. Apply the principle of linear impulse and momentum.2. Sum the horizontal components of the impulses.3. Use the mass of the plate to find the resulting velocity.### Conclusion:- For Part A, revisit the approach used to calculate the moments and angular velocity to correct the error.- For Part B, the calculation of the linear velocity is confirmed to be accurate.Understanding the proper application of impulse and momentum principles is crucial for accurately determining both the angular and linear velocity of the system.

The 29-1b rectangular plate is at rest on a smooth horizontal floor. It is given the horizontal impulses as shown in (Eigure 1). Assume I = 20 lb-s. Figure 0.5 ft 5 lb-s -2 ft -0.5 ft- < 1 of 1 > I ft Part A Determine its angular velocity. Express your answer in radians per second to three significant figures. w=37.747 VE] ΑΣΦΙ1 | vec Submit Previous Answers Request Answer * Incorrect; Try Again; 4 attempts remaining Part B Submit Determine the magnitude of the velocity of the mass center. Express your answer in feet per second to three significant figures. VG = 22.2 ft/s ? Previous Answers rad/s

The 29-1b rectangular plate is at rest on a smooth horizontal floor. It is given the horizontal impulses as shown in (Eigure 1). Assume I = 20 lb-s. Figure 0.5 ft 5 lb-s -2 ft -0.5 ft- < 1 of 1 > I ft Part A Determine its angular velocity. Express your answer in radians per second to three significant figures. w=37.747 VE] ΑΣΦΙ1 | vec Submit Previous Answers Request Answer * Incorrect; Try Again; 4 attempts remaining Part B Submit Determine the magnitude of the velocity of the mass center. Express your answer in feet per second to three significant figures. VG = 22.2 ft/s ? Previous Answers rad/s

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

### Understanding Angular and Linear Velocity of a Rectangular Plate under Horizontal Impulses

**Problem Statement:**
A 29-pound rectangular plate is at rest on a smooth horizontal floor. It is subjected to horizontal impulses as illustrated in **Figure 1**. Assume impulse \(I = 20 \text{ lb} \cdot \text{s}\).

#### Figure 1: Diagram and Dimensions

The diagram shows a rectangular plate with the following dimensions:
- Length: 1 ft.
- Width: 0.5 ft.

Two forces are applied:
- A 5 lb・s impulse at a point 0.5 ft from the right edge and 60 degrees downwards to the right.
- A 20 lb・s impulse acting horizontally to the left at a point 0.5 ft from the left edge.

### Part A: Determine Angular Velocity

**Objective:**
To calculate the angular velocity (ω) of the rectangular plate in radians per second (rad/s).

**Attempted Solution:**
An attempt was made to input the angular velocity as 37.747 rad/s, but this answer was marked incorrect.

**Steps to Determine Angular Velocity:**
1. Identify the center of mass and distribution of impulses.
2. Calculate the moments generated by the impulses about the center of mass.
3. Apply the principle of angular impulse and momentum to solve for angular velocity.

### Part B: Determine Linear Velocity of Mass Center

**Objective:**
To calculate the linear velocity (\(v_G\)) of the mass center of the plate in feet per second (ft/s).

**Attempted Solution:**
An attempt was made to input the linear velocity as 22.2 ft/s, which seems to be correct (indicated by the checkmark).

**Steps to Determine Linear Velocity:**
1. Apply the principle of linear impulse and momentum.
2. Sum the horizontal components of the impulses.
3. Use the mass of the plate to find the resulting velocity.

### Conclusion:
- For Part A, revisit the approach used to calculate the moments and angular velocity to correct the error.
- For Part B, the calculation of the linear velocity is confirmed to be accurate.

Understanding the proper application of impulse and momentum principles is crucial for accurately determining both the angular and linear velocity of the system.

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