### Problem DescriptionA machine part consists of a thin, uniform horizontal bar and a vertical bar connected at a hinge:1. **Horizontal Bar**: - Mass: 4.00 kg - Length: 1.50 m - Positioned horizontally with its hinge on the left.2. **Vertical Bar**: - Mass: 3.00 kg - Length: 1.80 m - Positioned vertically with its hinge at the top.3. **Ball**: - Mass: 2.00 kg - Attached to the bottom end of the vertical bar. The objective is to find the center of mass of this system relative to the hinge.### Steps to Solve the Problem**a. Center of Mass of the Top Bar**- **X-component:** Since the bar is horizontal, the center of mass is at \( \frac{1.50 \, \text{m}}{2} = 0.75 \, \text{m} \) from the hinge.- **Y-component:** There is no vertical displacement, so it is \( 0 \, \text{m} \).**b. Center of Mass of the Vertical Bar**- **X-component:** There is no horizontal displacement, so it is \( 0 \, \text{m} \).- **Y-component:** The center of mass is at \( \frac{1.80 \, \text{m}}{2} = 0.90 \, \text{m} \) downward from the hinge.**c. Center of Mass of the Ball**- **X-component:** Since the ball is directly below the hinge along the vertical bar, it is \( 0 \, \text{m} \).- **Y-component:** The ball is \( 1.80 \, \text{m} \) downward from the hinge.**d. Center of Mass of the Entire Machine Part**To find the overall center of mass, calculate the weighted average of the components from parts (a), (b), and (c).- **X-component Calculation:** \[ \text{Total mass} = 4.00 \, \text{kg} + 3.00 \, \text{kg} + 2.00 \, \text{kg} = 9.00 \, \text{kg}

Introduction: Centre of mass of a body is defined as a point where whole mass of a body is…

4. A machine part consists of a thin, uniform 4.00-kg bar that is 1.50 m long, hinged perpendicular to a similar vertical bar of mass 3.00 kg and length 1.80 m. The longer bar has a small but dense 2.00-kg ball at one end (see figure). -1.50 m- 4.00 kg a. Find the position of the center of mass of the top bar relative to the hinge. Write out its x- and y-components. b. Find the position of the center of mass of the vertical bar relative to the hinge. Write out its x- and y-components. c. Find the center of mass of the ball relative to the hinge. Write out its x- and y-components. d. Use your answers to parts (a)-(c) to find the center of mass of the entire machine part relative to the hinge. Write out its x- and y-components. Hinge 3.00 kg 1.80 m 2.00 kg

4. A machine part consists of a thin, uniform 4.00-kg bar that is 1.50 m long, hinged perpendicular to a similar vertical bar of mass 3.00 kg and length 1.80 m. The longer bar has a small but dense 2.00-kg ball at one end (see figure). -1.50 m- 4.00 kg a. Find the position of the center of mass of the top bar relative to the hinge. Write out its x- and y-components. b. Find the position of the center of mass of the vertical bar relative to the hinge. Write out its x- and y-components. c. Find the center of mass of the ball relative to the hinge. Write out its x- and y-components. d. Use your answers to parts (a)-(c) to find the center of mass of the entire machine part relative to the hinge. Write out its x- and y-components. Hinge 3.00 kg 1.80 m 2.00 kg

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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