Next, imagine the rather than sliding down the hill, the skier holds onto a rope that is connected to a tree at the top of the hill, and that the force of the rope holds the skier in place. How would you modify your force diagram now? Hint: The rope is parallel to the surface of the hill. Show that the net force is zero, again by using the parallelogram rule to show that any 2 forces add up to exactly cancel the 3rd force. Note that tension force is always along the direction of the rope but is not drawn equal to the length of the rope. What must be true for an object in equilibrium is that vector sum of the forces in any and every direction must equal zero. Though, we only need to show that along our chosen coordinate axes. Here it is okay to use the "usual" x- and y- directions
Next, imagine the rather than sliding down the hill, the skier holds onto a rope that is connected to a tree at the top of the hill, and that the force of the rope holds the skier in place. How would you modify your force diagram now? Hint: The rope is parallel to the surface of the hill. Show that the net force is zero, again by using the parallelogram rule to show that any 2 forces add up to exactly cancel the 3rd force. Note that tension force is always along the direction of the rope but is not drawn equal to the length of the rope. What must be true for an object in equilibrium is that vector sum of the forces in any and every direction must equal zero. Though, we only need to show that along our chosen coordinate axes. Here it is okay to use the "usual" x- and y- directions
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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2. Next, imagine the rather than sliding down the hill, the skier holds onto a rope that is connected to a tree at the top of the hill, and that the force of the rope holds the skier in place. How would you modify your force diagram now?
Hint:
The rope is parallel to the surface of the hill. Show that the net force is zero, again by using the parallelogram rule to show that any 2 forces add up to exactly cancel the 3rd force. Note that tension force is always along the direction of the rope but is not drawn equal to the length of the rope. What must be true for an object in equilibrium is that vector sum of the forces in any and every direction must equal zero. Though, we only need to show that along our chosen coordinate axes. Here it is okay to use the "usual" x- and y- directions
Transcribed Image Text:**Free Body Diagram Analysis**
A free body diagram includes all the forces acting on an object with direction. In this scenario, we consider:
- The x-axis is along the plane of the hill.
- The y-axis is perpendicular to the inclined plane.
### Diagram Explanation:
1. **Inclined Plane Force Diagram**
- An object is represented on an inclined plane.
- Two forces are shown:
- **F (Force of gravity):** Points downward along the y-axis.
- **N (Normal force):** Perpendicular to the surface of the inclined plane.
2. **Parallelogram Diagram**
- Vectors are used to showcase forces and their components.
- The diagonal represents the resultant vector according to the parallelogram law.
### Key Concepts:
- **Parallelogram Law**: The diagonal of the parallelogram represents the resultant vector of two vectors.
- By using logical reasoning, the object will move along the plane, which implies movement along the x-axis. Therefore, acceleration should be along the x-axis.
- **Diagram Analysis (ABCD)**
- Points A and B form the diagonal.
- AB is the diagonal along the inclined plane or along the x-axis.
- The diagonal has a non-zero length, indicating a non-zero acceleration.
Understanding these diagrams and concepts demonstrates how forces act on objects on inclined planes and how resulting vectors determine the motion and acceleration of the objects.
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