Work done by gravity (path independent)| Work & Energy | Physics | Khan Academy
TLDRThe video script explores the concept of work done by gravity on two identical balls dropped from the same height, one falling straight down and the other rolling down a slide. It explains that work done is the product of force and displacement in the direction of the force. Despite the difference in paths, the work done by gravity is the same for both balls as it only depends on the vertical displacement, or the height from which they fall. The video emphasizes that the effect of a force decreases as the angle between the force and displacement increases, reaching zero when they are perpendicular.
Takeaways
- 📚 The concept of work done is explained as the product of the force acting on a body and the displacement of that body in the direction of the force.
- 🎾 In the example of two balls dropped from the same height, one falling straight down and the other rolling down a slide, the work done by gravity is the same in both cases because the force of gravity (mg) is the same and the vertical displacement (height) is the same.
- 🔄 The direction of displacement relative to the force matters in calculating work. When the force and displacement are not aligned, the work done is not simply the product of the force and the total displacement.
- 🧗♂️ The example of the ball rolling down a slide versus falling straight down illustrates that the path of motion does not affect the amount of work done by gravity, as long as the vertical displacement is the same.
- 📈 The work done by gravity can be visualized as the ball moving through a series of tiny steps (like a staircase), where only the vertical steps (displacements) contribute to the work done.
- 🚫 When the force and displacement are perpendicular to each other, the work done is zero because the force does not contribute to the displacement in that direction.
- 🌐 The principle that the work done by gravity is independent of the path and only depends on the vertical displacement is a fundamental concept in physics known as the conservation of mechanical energy.
- 🔄 The video script uses the analogy of a ball moving through increasingly smaller steps to illustrate that the work done by gravity remains constant, regardless of the path taken.
- 🤔 The script encourages critical thinking about the relationship between force, displacement, and work done, emphasizing the importance of considering the direction of these quantities.
- 📊 The examples provided in the script, such as pushing a mop forward and at an angle, help to reinforce the idea that the effect of a force decreases as the angle between the force and motion increases.
- 🎓 The video script is educational, aiming to clarify common misconceptions about how work is done in physical scenarios involving gravity and different paths of motion.
Q & A
What is the formula for calculating work done?
-The formula for calculating work done is the force acting on a body multiplied by the displacement of that body in the direction of the force.
Why is the gravitational force on both balls the same when dropped from the same height?
-The gravitational force on both balls is the same because they are identical in mass, and gravitational force is calculated as the product of mass (m) and gravitational acceleration (g), represented as mg.
How does the work done by gravity compare when a ball falls straight down versus when it rolls down a slide?
-Despite initial appearances, the work done by gravity in both cases is the same. This is because the work done by a force is only related to the component of displacement in the direction of the force, which in both cases is the vertical drop or height (h).
What is the importance of the direction of displacement when calculating work done by a force?
-The direction of displacement is crucial because work is only done by a force when there is displacement in the direction of the force. If the displacement is perpendicular to the force, no work is done by that force.
How does the acceleration of the ball compare when it falls straight down versus when it slides down at an angle?
-The ball accelerates more quickly when it falls straight down compared to when it slides down at an angle. This is because the effect of gravity is reduced when the motion is not directly in line with the force of gravity.
What happens to the effect of a force when the angle between the force and the motion increases?
-As the angle between the force and the motion increases, the effect of the force starts to reduce. When the angle is 90 degrees, the force has no effect in that direction, and no work is done by the force in the direction of the displacement.
Why does the ball not move when you try to slide it horizontally due to gravity?
-The ball does not move horizontally because gravity is acting vertically downward, and there is no component of gravitational force in the horizontal direction to cause motion.
What is the work done by gravity when a ball is displaced horizontally on a perfectly horizontal slide?
-The work done by gravity is zero when the ball is displaced horizontally because the displacement is perpendicular to the direction of the gravitational force.
How does the work done by gravity relate to the path taken by the ball when it falls from a height?
-The work done by gravity does not depend on the path taken by the ball. Regardless of whether the ball falls straight down, slides down, or follows a curvy path, the work done by gravity is the same and is calculated as the product of the gravitational force and the vertical height (h) through which the ball falls.
What is the conclusion about the work done by gravity when considering the ball moving on a staircase-like path?
-The conclusion is that even if the ball moves on a staircase-like path, the total work done by gravity is the same as if it fell straight down. This is because only the vertical displacements contribute to the work done by gravity, and their sum equals the total height (h) of the fall.
What is the practical implication of understanding that work done by gravity is independent of the path taken?
-The practical implication is that when calculating the work done by gravity on an object falling from a certain height, you can simplify the calculation by focusing only on the vertical height covered, without needing to consider the complexity of the path taken.
Outlines
📚 Understanding Work Done by Gravity
This paragraph introduces the concept of work done by gravity and how it can be calculated. The instructor discusses two scenarios: one where a ball is dropped from a height and another where it rolls down a slide. The key point is to understand that the work done by gravity depends on the force (gravitational in this case) and the displacement in the direction of the force. The paragraph emphasizes that even if the path of motion is different, the work done by gravity remains the same as long as the initial and final heights are identical. This is because the force of gravity is always vertical, and only vertical displacements contribute to the work done by gravity.
🔄 Effects of Force in Different Directions
The second paragraph explores the effects of a force when applied in different directions. Using the analogy of pushing a mop, the instructor explains that a force can have an effect on the motion of an object even when applied at an angle. However, the effect of the force diminishes as the angle between the force and the direction of motion increases. The paragraph establishes that when the force and motion are perpendicular to each other, the effect of the force is zero, meaning no work is done by the force in the perpendicular direction. This principle is then applied to the concept of work done by gravity, reinforcing that the work done by gravity is independent of the path taken and depends solely on the vertical displacement.
🛤️ Work Done by Gravity: Path Independence
In this paragraph, the concept of work done by gravity is further elaborated by discussing the path independence of gravitational work. The instructor uses the metaphor of a ball moving down a staircase of varying sizes to illustrate that regardless of the complexity of the path (be it stairs, a slide, or a curvy path), the work done by gravity remains constant. This is because only the vertical displacement (the change in height) matters when calculating the work done by gravity. The paragraph concludes with the understanding that the work done by gravity is solely dependent on the initial and final heights, not the path taken between them, which is a fundamental principle in physics.
Mindmap
Keywords
💡Work
💡Gravitational Force
💡Displacement
💡Acceleration
💡Path Independence
💡Force and Motion
💡Angle
💡Staircase Analogy
💡Perpendicular
💡Effect of Gravity
💡Horizontal Motion
Highlights
The question posed is which case of two scenarios involves more work done by gravity - a ball falling straight down or rolling down a slide.
Work done is calculated as the force acting on a body multiplied by the displacement of that body.
In both scenarios, the gravitational force (mg) acting on the balls is the same.
Displacement in the first case is simply the height (h) from which the ball falls.
In the second case, the displacement (s) is greater than the height as the ball rolls down the slide.
The work done by gravity is not necessarily more when the displacement is larger, because the angle between force and displacement must be considered.
When force and displacement are not in the same direction, work done must be calculated considering the directional component of the displacement.
Gravity can make objects accelerate in other directions, not just downward.
The ball accelerates more quickly in the first case, indicating a greater effect of gravity.
In the third case where the object is intended to slide horizontally, gravity has no effect as the force and motion are perpendicular.
Forces have maximum effect when in line with motion and the effect reduces as the angle between them increases.
When the angle between force and motion is 90 degrees, the force has zero effect and therefore zero work is done.
The work done by gravity on a ball falling from a height is independent of the path taken and depends only on the vertical displacement (height).
The work done by gravity can be thought of as the force acting on the body times the height it covers from one point to another.
The concept of work done can be extended to any force, not just gravity, and the principles discussed apply similarly.
In summary, the work done by gravity on an object falling from a certain height is the same regardless of the path taken.
The video provides a clear understanding of how to calculate work done when the force and displacement are not aligned.
Practical examples and thought experiments help to illustrate the concepts of work done and the effects of forces in different directions.
Transcripts
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