Work done on lifting/falling things - Solved numerical | Work & Energy | Physics | Khan Academy
TLDRThe video script explains the concept of work done by gravity and a person. It first calculates the positive work done by gravity on a 5 kg dumbbell falling 10 meters, using the formula force (mass times gravity) times displacement. The result is 500 joules. Then, it discusses a woman doing negative work as she lowers a 20 kg barbell 0.2 meters, applying a force equal to its weight to counteract gravity, resulting in -40 joules of work. The script emphasizes the directionality of force and displacement in determining whether work is positive or negative.
Takeaways
- 📚 The script discusses the concept of calculating work done by gravity when objects are dropped or lifted.
- 🔢 The first problem involves a 5 kg dumbbell dropped from a height of 10 meters, with gravity (g) at 10 m/s².
- 📈 The work done by gravity is calculated using the formula: force (F) multiplied by displacement (d).
- 💡 The force of gravity on an object is found by multiplying its mass (m) by the acceleration due to gravity (g).
- 📉 The direction of work done is positive when the force and displacement are in the same direction, negative when opposite.
- 📐 For the dumbbell, the work done by gravity is positive because both force and displacement are downwards.
- 🧮 The calculation for the dumbbell's work done is 5 kg * 10 m/s² * 10 m, resulting in 500 joules.
- 🏋️♀️ The second problem involves a woman lowering a 20 kg barbell rod through a distance of 0.2 meters.
- ⚖️ The force exerted by the woman on the barbell is equal to the weight of the barbell (mg) to maintain a constant speed.
- 📉 The work done by the woman is negative because her force (upwards) is opposite to the displacement (downwards).
- 🧮 The calculation for the woman's work done is 20 kg * 10 m/s² * 0.2 m, resulting in -40 joules, indicating negative work.
Q & A
What is the formula to calculate the work done by a force?
-The formula to calculate the work done by a force is the force multiplied by the displacement of the object in the direction of the force.
What is the force of gravity acting on an object?
-The force of gravity acting on an object is calculated by multiplying the mass of the object (m) by the acceleration due to gravity (g), which is expressed as F = m * g.
In the first problem, why is the work done by gravity considered positive?
-The work done by gravity is considered positive when the force of gravity and the displacement of the object are in the same direction, which is the case when the dumbbell is falling downward.
What would be the work done by gravity if the dumbbell was thrown upwards?
-If the dumbbell was thrown upwards, the work done by gravity would be negative because the force of gravity is downward while the displacement is upward, opposite directions.
How is the work done by the woman on the barbell calculated in the second problem?
-The work done by the woman on the barbell is calculated by multiplying the force she applies (which is equal to the weight of the barbell, mg) by the displacement (h), and since the force is upward while displacement is downward, the work is negative.
Why does the woman need to apply a force equal to the weight of the barbell while lowering it?
-The woman needs to apply a force equal to the weight of the barbell to balance the force of gravity and maintain a constant speed (no acceleration) while lowering it.
What is the unit of work done in the context of this script?
-The unit of work done is the newton meter, which is also known as a joule.
What is the significance of the direction of force and displacement in determining the sign of work done?
-The direction of force and displacement determines whether the work done is positive or negative. If they are in the same direction, the work is positive; if they are in opposite directions, the work is negative.
How does the woman manage to lower the barbell with a constant speed?
-The woman manages to lower the barbell with a constant speed by applying a force equal to the weight of the barbell, ensuring that there is no net force causing acceleration.
Why is the work done by the woman on the barbell considered negative in the second problem?
-The work done by the woman is considered negative because her force is applied upwards while the displacement of the barbell is downwards, indicating opposite directions.
Outlines
🏋️ Work Done by Gravity on a Falling Dumbbell
The script begins by addressing the calculation of work done by gravity when an object is dropped or lifted. The first problem involves a 5-kilogram dumbbell falling from a height of 10 meters. The gravitational force (g) is given as 10 m/s². The work done by gravity is calculated using the formula: work = force × displacement. The force of gravity is determined by the mass of the dumbbell (5 kg) multiplied by the acceleration due to gravity (10 m/s²), resulting in a force of 50 kg*m/s². The displacement is the height from which the dumbbell falls, which is 10 meters. Multiplying these values gives a work done of 500 kg*m²/s², which is equivalent to 500 joules. The work is positive because the force and displacement are in the same direction, indicating that gravity is doing positive work on the dumbbell as it falls.
🏋️♀️ Work Done by a Woman Lowering a Barbell
The second problem in the script involves a woman who slowly lowers a 20-kilogram barbell rod through a distance of 0.2 meters. The task is to find the work done by the woman on the barbell. The woman is exerting a force to counteract the weight of the barbell, which is mg (mass times gravitational acceleration). Since the barbell is moving at a constant speed, the force she applies is equal and opposite to the gravitational force, which is 20 kg * 10 m/s² = 200 N. The displacement is 0.2 meters, and the work done is calculated as force times displacement. However, since the woman is pushing the barbell downwards against gravity, the work done by her is negative, indicating that it requires effort to lower the barbell. The calculation results in -40 N*m, or -40 joules, reflecting the negative work done by the woman as she overcomes gravity to lower the barbell.
Mindmap
Keywords
💡Work Done
💡Dumbbell
💡Gravity
💡Displacement
💡Gravitational Force
💡Mass
💡Acceleration Due to Gravity (g)
💡Barbell
💡Positive and Negative Work
💡Newton
💡Joule
Highlights
Calculating work done by gravity on a falling object involves force of gravity multiplied by displacement.
Work done by a force is positive when force and displacement are in the same direction.
Force of gravity on an object is calculated as mass times gravitational acceleration (g).
In the case of a dumbbell falling, gravity does positive work as force and displacement are in the same direction.
The work done by gravity on a 5 kg dumbbell falling 10 meters is 500 joules.
When an object is lifted, gravity does negative work if the force of gravity and displacement are in opposite directions.
To calculate work done by a person on an object, consider the force exerted by the person and the displacement of the object.
When an object moves at a constant speed, the net force acting on it is zero, implying balanced forces.
The force exerted by a person to lower an object at a constant speed is equal to the weight of the object.
The direction of the force and displacement determines whether work done is positive or negative.
In the case of lowering a 20 kg barbell, the woman does negative work as her force is upwards while displacement is downwards.
The work done by the woman on the barbell is calculated to be -40 joules.
Understanding the direction of forces and displacement is crucial for determining the sign of work done.
The concept of work done is applicable to both lifting and lowering objects, with different signs depending on the direction of forces.
The video demonstrates the calculation of work done in two scenarios: a falling dumbbell and a lowered barbell.
The video provides a step-by-step guide to calculating work done, emphasizing the importance of force and displacement directions.
The video encourages viewers to pause and attempt calculations themselves to reinforce learning.
The video concludes by summarizing the key points about work done by gravity and the force exerted by a person.
Transcripts
Browse More Related Video
Work and Kinetic Energy - Physics
Work Done By a Force - Incline Planes & Dot Product Formula - Physics
Calculating gravitational potential energy | Modeling energy | High school physics | Khan Academy
How to Calculate Work Done | Physics | Work = Force x Distance
Work and Energy : Definition of Work in Physics
Work done by gravity (path independent)| Work & Energy | Physics | Khan Academy
5.0 / 5 (0 votes)
Thanks for rating: