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14 May 202303:16

TLDRThe video script demonstrates a physics problem-solving process for calculating work done by a force. Given a force of 15N at a 45-degree angle to the horizontal and a displacement of 49 meters, the script uses trigonometry to find the horizontal component of force, which is 10.61N. It then applies the work formula (work = force x displacement x cos(angle)) to determine the work done as 520.89 Joules. The script also explains how to convert this work into kilo calories, resulting in 0.1244 kilo calories. The explanation is aimed at helping viewers understand the concept of work in physics and encourages them to ask more questions.

Takeaways

  • 🔍 The problem involves calculating the work done by a force in physics.
  • 📏 Given information includes a force of 15N, an angle of 45 degrees with the horizontal, and a distance of 49 meters.
  • 📐 The formula for work done by a force is work = force x displacement x cos(angle).
  • 📉 The force is not in the direction of displacement, so its horizontal component must be found using trigonometry.
  • 📈 Horizontal component of force = force x cos(angle), which equals 10.61N for the given 45-degree angle.
  • 🔧 The work done by the force is calculated using the horizontal component and the displacement.
  • 🔢 The work done is 520.89 Joules, calculated as 10.61N x 49m x cos(0 degrees).
  • ⚖️ The angle between the horizontal direction and displacement is zero, simplifying the calculation.
  • 🔗 To convert Joules to kilo calories (KCAL), divide the work in Joules by 4184.
  • 🔄 The work done is equivalent to 0.1244 kilo calories after conversion.
  • 🤔 The script encourages asking more physics questions for further assistance.

Q & A

  • What is the given force in the physics problem?

    -The given force in the problem is 15 Newtons (15n).

  • What is the angle between the force and the horizontal?

    -The angle between the force and the horizontal is 45 degrees.

  • What is the distance over which the force is applied?

    -The distance over which the force is applied is 49 meters.

  • What is the formula for work done by a force?

    -The formula for work done by a force is work equals force times displacement times the cosine of the angle between the force and the displacement.

  • How can you find the component of force in the direction of displacement?

    -You can find the component of force in the direction of displacement by using trigonometry to calculate the horizontal component of the force, which is equal to the force times the cosine of the angle.

  • What is the horizontal component of the force in the given problem?

    -The horizontal component of the force in the given problem is 10.61 Newtons (10.61n).

  • What is the work done by the force in moving the object horizontally over a distance of 49 meters?

    -The work done by the force in moving the object horizontally over a distance of 49 meters is 520.89 Joules (520.89 J).

  • How is the angle between the horizontal direction and displacement in the problem?

    -The angle between the horizontal direction and displacement in the problem is zero degrees since the force is acting horizontally.

  • What is the conversion factor from Joules to KiloCalories?

    -The conversion factor from Joules to KiloCalories is 1 KiloCalorie equals 4184 Joules.

  • How many KiloCalories is the work done by the force equivalent to?

    -The work done by the force is equivalent to 0.1244 KiloCalories.

  • What is the significance of the cosine function in calculating work?

    -The cosine function is significant in calculating work as it accounts for the directionality of the force relative to the displacement. It ensures that only the component of the force in the direction of the displacement contributes to the work done.

  • What would be the work done if the force was acting at a different angle?

    -The work done would be different if the force was acting at a different angle. The work is maximized when the force is in the same direction as the displacement (cosine of 0 degrees) and minimized or zero when the force is perpendicular to the displacement (cosine of 90 degrees).

Outlines

00:00

🔍 Calculating Work Done by a Force

This paragraph discusses a physics problem involving the calculation of work done by a force. Given information includes a force of 15 Newtons (N) applied at a 45-degree angle to the horizontal, and a displacement of 49 meters. The formula for work done, W = F * d * cos(θ), is introduced, where θ is the angle between the force and displacement. Since the force is not in the direction of displacement, the horizontal component of the force is calculated using trigonometry: horizontal component = F * cos(45°) = 15N * cos(45°) = 10.61N. The work done by the force is then calculated by considering the horizontal component acting over the displacement with an angle of 0° between them, resulting in W = 10.61N * 49m * cos(0°) = 520.89 Joules (J). The paragraph also explains how to convert Joules to kilo calories (kcal), with the conversion factor 1 kcal = 4184 J. The final work in kcal is found by dividing 520.89 J by 4184, yielding 0.1244 kcal. The explanation concludes with an invitation for further questions and a closing note.

Mindmap

Keywords

💡Work

In physics, 'work' is the measure of energy transfer that occurs when an object is moved over a distance by applying a force in the direction of the object's displacement. It is a scalar quantity and is calculated using the formula: work = force × displacement × cos(angle). In the context of the video, work is calculated to determine the amount of energy required to move an object horizontally over a distance of 49 meters with a force of 15N at an angle of 45 degrees to the horizontal.

💡Force

Force is a vector quantity that describes the interaction between two objects, causing a change in the motion of an object. It is measured in newtons (N). In the script, a force of 15N is given, which is the magnitude of the push or pull acting on an object. The force is crucial in calculating the work done on the object as it moves through space.

💡Displacement

Displacement refers to the change in position of an object. It is a vector quantity that points from the initial to the final position and is independent of the path taken. In the video, the displacement is given as 49 meters, which is the straight-line distance over which the work is done by the force.

💡Angle

The angle in this context is the measure of the space between two lines or planes that intersect, and it is crucial in determining the component of the force that contributes to the work done. The script mentions an angle of 45 degrees between the force and the horizontal, which is used to find the horizontal component of the force that does the work.

💡Component of Force

A component of force is a part of a vector quantity that acts in a specific direction. In the video, the horizontal component of the force is calculated using trigonometry to find how much of the total force contributes to the work done in the direction of displacement.

💡Trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. In the script, trigonometry is used to calculate the horizontal component of the force by applying the cosine of the angle (45 degrees) to the total force, resulting in a component of 10.61N.

💡Cosine

Cosine is a trigonometric function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. In the video, cosine is used in the formula to find the horizontal component of the force (cos 45 degrees) and to calculate the work done, where the angle between the force and displacement is 0 degrees.

💡Joule

The joule (J) is the SI unit of energy, work, or amount of heat. It is defined as the work done when a force of one newton moves an object through a distance of one meter in the direction of the force. In the script, the work done is calculated to be 520.89 joules.

💡Kilogram Calorie (KCAL)

A kilogram calorie (kcal), also known as a food calorie, is a unit of energy equivalent to the energy expended by the body to metabolize one kilogram of water when it is raised by 1 degree Celsius. In the video, the work done in joules is converted to kcal to provide an alternative measure of energy, with 1 kcal equaling 4184 joules.

💡Conversion

Conversion in this context refers to the process of changing one unit of measurement to another. The script demonstrates the conversion of work from joules to kcal, which is done by dividing the work in joules by 4184 to obtain the equivalent energy in kcal.

Highlights

A physics problem is being solved step by step.

Given information includes a force of 15N at a 45-degree angle to the horizontal and a distance of 49 meters.

The objective is to find the work done by the force.

The formula for work done is force x displacement x cos(angle).

The force is not in the direction of displacement, so the horizontal component of force is needed.

Horizontal component of force is calculated using trigonometry: force x cos(angle).

The horizontal component of force is 10.61N.

Work is then calculated using the horizontal force, displacement, and a 0-degree angle.

The calculated work done is 520.89 Joules.

The work done is equivalent to horizontally moving the object over 49 meters.

Conversion of work from Joules to kilo calories is discussed.

One kilo calorie equals 4184 Joules.

The work of 520.89 Joules is converted to 0.1244 kilo calories.

The work done by the force is equivalent to 0.1244 kilo calories.

The solution to the physics problem is presented clearly and concisely.

The video provides a step-by-step guide to solving the physics problem.

The final answer is presented with an invitation for further questions.

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