2. A 5 kg body resting on a 30° inclined plane is pulled up the plane by a 40N force acting at an angle of 20° with respect to the surface of the plane. The coefficient of the friction is 0.1 a) Draw a free body diagram identifying all the forces acting on the body. F.B.D. Explanations b) Reconstruct the F.B.D. so as to reflect all the forces in terms of x' and y' (parallel and perpendicular) components. F.B.D. Explanations c) Find an expression for the frictional force. Then, indicate all forces that directly affect the motion of the body on the final rendition of the F.B.D. (i.e. x' component). F.B.D. Explanations

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**Problem Statement:**

A 5 kg body resting on a 30° inclined plane is pulled up the plane by a 40 N force acting at an angle of 20° with respect to the surface of the plane. The coefficient of friction is 0.1.

**Tasks:**

a) Draw a free body diagram (F.B.D.) identifying all the forces acting on the body.

   **Explanation:** 
   - Show the gravitational force acting downward.
   - Indicate the normal force perpendicular to the inclined plane.
   - Display the applied force at a 20° angle to the plane.
   - Include the frictional force opposing the motion.

b) Reconstruct the F.B.D. to reflect all the forces in terms of x’ and y’ (parallel and perpendicular) components.

   **Explanation:** 
   - Resolve the gravitational force into components parallel and perpendicular to the plane.
   - Resolve the applied force into parallel and perpendicular components.
   - Show the frictional force acting parallel to the plane.

c) Find an expression for the frictional force. Then, indicate all forces that directly affect the motion of the body on the final rendition of the F.B.D. (i.e., x’ component).

   **Explanation:** 
   - Calculate the frictional force using the formula \( f = \mu \times N \), where \( \mu \) is the coefficient of friction and \( N \) is the normal force.
   - Identify and label the forces affecting motion along the plane, such as parallel components of the gravitational and applied forces and the frictional force.

**Graphs/Diagrams:**

- F.B.D. for part (a): A diagram showing all the forces with appropriate labels and directions.
- F.B.D. for part (b): The same diagram with forces resolved into components, including vectors along the x’ and y’ axes.
- F.B.D. for part (c): Forces affecting motion are highlighted, showing the resultant force along the plane.
Transcribed Image Text:**Problem Statement:** A 5 kg body resting on a 30° inclined plane is pulled up the plane by a 40 N force acting at an angle of 20° with respect to the surface of the plane. The coefficient of friction is 0.1. **Tasks:** a) Draw a free body diagram (F.B.D.) identifying all the forces acting on the body. **Explanation:** - Show the gravitational force acting downward. - Indicate the normal force perpendicular to the inclined plane. - Display the applied force at a 20° angle to the plane. - Include the frictional force opposing the motion. b) Reconstruct the F.B.D. to reflect all the forces in terms of x’ and y’ (parallel and perpendicular) components. **Explanation:** - Resolve the gravitational force into components parallel and perpendicular to the plane. - Resolve the applied force into parallel and perpendicular components. - Show the frictional force acting parallel to the plane. c) Find an expression for the frictional force. Then, indicate all forces that directly affect the motion of the body on the final rendition of the F.B.D. (i.e., x’ component). **Explanation:** - Calculate the frictional force using the formula \( f = \mu \times N \), where \( \mu \) is the coefficient of friction and \( N \) is the normal force. - Identify and label the forces affecting motion along the plane, such as parallel components of the gravitational and applied forces and the frictional force. **Graphs/Diagrams:** - F.B.D. for part (a): A diagram showing all the forces with appropriate labels and directions. - F.B.D. for part (b): The same diagram with forces resolved into components, including vectors along the x’ and y’ axes. - F.B.D. for part (c): Forces affecting motion are highlighted, showing the resultant force along the plane.
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