We know that the work (W) done by a force vector F applied to an object over a displacement ?x is given byW = F(cos?) ?x,where F is the magnitude of the force, and ? is the angle between the applied force and the direction of the displacement. This expression assumes that the force is constant over the displacement ?x. If F is not constant, it can be shown that the work done is equal to the area under the curve force versus position.Based on what above said, calculate the work done by the force versus position represented in each graph (a), (b), and (c) in the figure below.
We know that the work (W) done by a force vector F applied to an object over a displacement ?x is given byW = F(cos?) ?x,where F is the magnitude of the force, and ? is the angle between the applied force and the direction of the displacement. This expression assumes that the force is constant over the displacement ?x. If F is not constant, it can be shown that the work done is equal to the area under the curve force versus position.Based on what above said, calculate the work done by the force versus position represented in each graph (a), (b), and (c) in the figure below.
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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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We know that the work (W) done by a force vector F applied to an object over a displacement ?x is given byW = F(cos?) ?x,where F is the magnitude of the force, and ? is the angle between the applied force and the direction of the displacement. This expression assumes that the force is constant over the displacement ?x. If F is not constant, it can be shown that the work done is equal to the area under the curve force versus position.Based on what above said, calculate the work done by the force versus position represented in each graph (a), (b), and (c) in the figure below.
Transcribed Image Text:The image presents three graphs labeled (a), (b), and (c), each depicting force \( F \) in newtons (N) versus displacement \( x \) in meters (m).
### Graph (a)
- **Description**: The graph shows a horizontal line indicating a constant force.
- **Axis**:
- \( x \)-axis ranges from 0 to 8 meters.
- \( F \)-axis ranges from 0 to 20 N.
- **Details**:
- The force is constant at 10 N from 0 to 4 meters.
- The area under the curve forms a rectangle shaded in beige, representing work done by the force.
### Graph (b)
- **Description**: The graph presents a linearly increasing force.
- **Axis**:
- \( x \)-axis ranges from 0 to 8 meters.
- \( F \)-axis ranges from 0 to 20 N.
- **Details**:
- The force increases linearly from 0 to 20 N between 0 and 8 meters.
- The beige-shaded area under the curve forms a right triangle, representing work done by the force.
### Graph (c)
- **Description**: The graph consists of a piecewise function showing a step change in force.
- **Axis**:
- \( x \)-axis ranges from 0 to 8 meters.
- \( F \)-axis ranges from 0 to 20 N.
- **Details**:
- The force is 20 N from 0 to 4 meters, and then it decreases linearly to 10 N at 8 meters.
- The beige-shaded area under the curve includes a rectangle and a right triangle, representing work done.
**Figure Problem 1** provides these graphs to illustrate the relationship between force and displacement in different scenarios of force application, highlighting the concept of work done through the areas under the force-displacement curves.
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