**Problem No. 5****Objective:** Determine the location \( y \) of the center of mass \( G \) of the assembly and then calculate the moment of inertia about an axis perpendicular to the page and passing through \( G \). The block has a mass of 3 kg and the semi-cylinder has a mass of 5 kg.**Description of Diagram:**The diagram features a composite shape made up of a rectangular block and a semi-cylinder. The dimensions are as follows:- **Rectangular Block:** Width = 400 mm, Height = 300 mm.- **Semi-Cylinder:** The radius of the semi-cylinder is 200 mm.The point \( G \) represents the center of mass for the entire assembly. Point \( O \) is located on the base line beneath the semi-cylinder.In the diagram:- The overall width of the block and semi-cylinder together is given as 400 mm.- The overall height from the base of the semi-cylinder to the top of the rectangular block is 300 mm.- The semi-cylinder's radius is 200 mm, indicating its curvature starts from the 200 mm mark vertically from the base.**Tasks:**1. Calculate the location \( y \) of the center of mass \( G \) for the entire shape.2. Calculate the moment of inertia about an axis perpendicular to the page that passes through \( G \).This problem involves understanding the concept of the center of mass in composite bodies and calculating the moment of inertia for such assemblies.

Data given- Mass of block m1 = 3 kg Mass of semicylinder m2 = 5 kg Let the block be the 1 and the semicylinder be the 2 Then, center of mass G of the assembly is given as - the mass moment of inertia of the rectangular block about point G by use of parallel axis theorem mass moment of inertia of the semi-cylinderical block about point G by use of parallel axis theorem.

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Mechanical Engineering

Determine the location y of the center of mass G of the assembly and then calculate the moment of inertia about an axis perpendicular to the page and passing through G. The block has a mass of 3 kg and the semi-cylinder has a mass of 5 kg.

Determine the location y of the center of mass G of the assembly and then calculate the moment of inertia about an axis perpendicular to the page and passing through G. The block has a mass of 3 kg and the semi-cylinder has a mass of 5 kg.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.63P

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Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

Question

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**Problem No. 5**

**Objective:** Determine the location \( y \) of the center of mass \( G \) of the assembly and then calculate the moment of inertia about an axis perpendicular to the page and passing through \( G \). The block has a mass of 3 kg and the semi-cylinder has a mass of 5 kg.

**Description of Diagram:**

The diagram features a composite shape made up of a rectangular block and a semi-cylinder. The dimensions are as follows:

- **Rectangular Block:** Width = 400 mm, Height = 300 mm.
- **Semi-Cylinder:** The radius of the semi-cylinder is 200 mm.

The point \( G \) represents the center of mass for the entire assembly. Point \( O \) is located on the base line beneath the semi-cylinder.

In the diagram:
- The overall width of the block and semi-cylinder together is given as 400 mm.
- The overall height from the base of the semi-cylinder to the top of the rectangular block is 300 mm.
- The semi-cylinder's radius is 200 mm, indicating its curvature starts from the 200 mm mark vertically from the base.

**Tasks:**
1. Calculate the location \( y \) of the center of mass \( G \) for the entire shape.
2. Calculate the moment of inertia about an axis perpendicular to the page that passes through \( G \).

This problem involves understanding the concept of the center of mass in composite bodies and calculating the moment of inertia for such assemblies.

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