D) Determine the true magnitude and direction of the forces acting on the cylinder
Plane Trusses
It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure where the force is applied only at two points. The point of contact of joints of truss are known as nodes. They are generally made up of triangular patterns. Nodes are the points where all the external forces and the reactionary forces due to them act and shows whether the force is tensile or compressive. There are various characteristics of trusses and are characterized as Simple truss, planar truss or the Space Frame truss.
Equilibrium Equations
If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the resultant force on a system is null, where the system remains to be at rest or moves at uniform motion. It is when the rate of the forward reaction is equal to the rate of the backward reaction.
Force Systems
When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.
![**Educational Content on Free Body Diagrams and Hand Calculations**
**Problem 4-3: Analyzing Forces on a Cylinder**
**Figure 4.3 Description:**
A cylinder resting on a smooth 45° incline is depicted. The cylinder has a weight of 200 lb. Two forces are labeled: one is the tension (T), directed at an angle of 40° above the horizontal, and the other is a reaction force at the point of contact, inclined at 25° to the horizontal plane.
**Diagram Explanation:**
The diagram shows a cylinder on an incline with two external forces impacting it. The tension force T is making an angle of 40° with the vertical while the inclined contact angle made by the reaction force is 25°.
**Instructions:**
a) **Free Body Diagram**
- Apply all known and unknown forces to the free body diagram provided below the description.
- The diagram illustrates the cylindrical object with a circle, awaiting annotation of force vectors.
b) **Hand Calculations**
- Determine the true magnitude and direction of the forces acting on the cylinder.
- A coordinate system is provided for clarity, with x-y axes depicted both in positive and negative directions (+x, +y, -x, -y).
c) **Balanced Free Body Diagram**
- Revise the initial free body diagram to reflect the true magnitude and direction of all forces. This includes a balanced arrangement following the calculation in part (b).
This exercise aims to develop a comprehensive understanding of force dynamics through the visualization and calculation of force vectors on a cylindrical object resting on an inclined plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedc85e3b-dc2d-4f8b-a097-9d7c53c76aad%2Fd978ddac-d100-4a15-95a2-fae2f572dc7d%2Fy8qhn2j.jpeg&w=3840&q=75)
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