How to find the work done by forces on an inclined plane. Work done by friction and a pulling force.

Zero Wait Tutoring
3 Nov 202307:04
EducationalLearning
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TLDRIn the video, a 250 kg box is pulled up a 30° ramp using a 2,000 Newton force at an 18° angle to the incline. The problem involves calculating the work done by friction and the pulling force over a 12 m displacement. The solution includes splitting forces into components, analyzing the free body diagram, and applying the work formula with the given coefficient of friction (μ = 3). The work of friction is found to be 5,413 Joules, while the work done by the pulling force is 22,825.3 Joules.

Takeaways
  • 📏 The problem involves a 250 kg box being pulled up a ramp at a 30° angle to the horizontal.
  • 📐 The pulling force (FP) is applied at an 18° angle to the ramp and has a magnitude of 2,000 Newtons.
  • 📚 The force components are calculated using trigonometric functions: FPx = FP * cos(beta) and FPy = FP * sin(beta), where beta = 18°.
  • 🧲 Gravity's components are also calculated: mg * cos(theta) and mg * sin(theta), with theta = 30°.
  • 🚫 The box experiences a normal force (FN) perpendicular to the ramp and a frictional force (FF) opposing the motion.
  • 🔢 The coefficient of friction (mu) is given as 3, which is used to calculate the frictional force.
  • 🛣️ The box is moved a distance of 12 meters up the ramp (Delta X = 12 m).
  • 🔨 Work done by friction (WF) is calculated using the formula WF = mu * (mg * cos(theta) - FP * sin(beta)) * Delta X.
  • 🔧 Work done by the pulling force (WP) is calculated as WP = FP * Delta X * cos(beta).
  • 🔢 The numerical values for the work done by friction and the pulling force are calculated to be 5,413 Joules and 22,825.3 Joules, respectively.
  • 📝 The script concludes with the final answer for the work done by the pulling force, which is 22,825.3 Joules.
Q & A

  • What is the mass of the box being pulled up the ramp?

    -The mass of the box is 250 kg.

  • What is the angle of the ramp with respect to the ground?

    -The ramp makes a 30° angle with the ground, denoted as Theta.

  • What is the magnitude of the pulling force applied to the box?

    -The pulling force, FP, is 2000 Newtons.

  • What is the angle between the pulling force and the ramp?

    -The pulling force makes an 18° angle with the ramp, denoted as beta.

  • How is the force of pulling decomposed into its components?

    -The force of pulling is decomposed into FP cosine of beta (parallel to the ramp) and FP sine of beta (perpendicular to the ramp).

  • What are the two components of the gravitational force acting on the box?

    -The gravitational force is split into mg cosine of theta (parallel to the ramp) and mg sine of theta (perpendicular to the ramp).

  • What is the normal force acting on the box?

    -The normal force, FN, is perpendicular to the ramp and is equal to the sum of the gravitational force component perpendicular to the ramp and the pulling force component perpendicular to the ramp.

  • What is the coefficient of friction between the box and the ramp?

    -The coefficient of friction, mu, is 3.

  • What is the distance the box is moved up the ramp?

    -The box is moved 12 meters up the ramp, denoted as Delta X.

  • How is the work done by friction calculated?

    -The work done by friction is calculated as the product of the friction force (mu times the normal force), the displacement (Delta X), and the cosine of the angle between them (-1, since they are in opposite directions).

  • What is the final answer for the work done by the pulling force?

    -The work done by the pulling force is 22,825.3 Joules, calculated as the product of the magnitude of the pulling force, the magnitude of the displacement, and the cosine of the angle between them.

Outlines
00:00
🔍 Force Analysis on an Inclined Plane

The first paragraph introduces a physics problem involving a 250 kg box being pulled up a 30° ramp with a force of 2,000 Newtons at an 18° angle to the incline. The force and gravity are decomposed into their respective components along the ramp. The normal force, friction force, and the coefficient of friction (μ = 3) are also considered. The problem requires calculating the work done by friction and the pulling force over a 12 m displacement up the ramp. The work of friction is determined by analyzing forces in the Y direction, leading to the equation WF = μ(mg cos(θ) - FP sin(β)) * ΔX, using the force components and displacement. The angle between the friction force and displacement is 180°, resulting in negative work due to the opposing direction.

05:00
📚 Calculation of Work Done by Friction and Pulling Force

The second paragraph focuses on calculating the work done by both friction and the pulling force. The work done by friction is computed using the formula WF = μ * (mg cos(θ) - FP sin(β)) * |ΔX| * cos(180°), which simplifies to WF = -3 * 250 * 9.8 * cos(30°) + 2,000 * sin(18°) * 12, yielding a result of -5,413 Joules. The work done by the pulling force is easier to calculate, using the formula WP = FP * ΔX * cos(β), resulting in WP = 2,000 * 12 * cos(18°), which equals 22,825.3 Joules. The summary concludes with the final answer for the work done by the pulling force.

Mindmap
Keywords
💡Ramp
A ramp is a sloping surface that allows for the movement of objects from a lower level to a higher one. In the video's context, the ramp is inclined at a 30-degree angle to the ground, serving as the pathway for the 250 kg box to be pulled upwards. The ramp's angle is crucial in calculating the forces acting on the box and is a central element in the problem-solving process.
💡Force
Force is a push or pull upon an object resulting from its interaction with another object. In the script, the force is applied to pull the box up the ramp at an 18-degree angle. The force is broken down into its components (FP cosine of beta and FP sine of beta) to understand its effect in the horizontal and vertical directions, which is essential for analyzing the work done and the motion of the box.
💡Component
In physics, a component refers to a part of a vector quantity that is aligned with a particular axis. The script discusses the components of the pulling force and gravity, which are essential for the free body diagram and for calculating the net force acting on the box in both the x and y directions.
💡Free Body Diagram
A free body diagram is a graphical representation of all the forces acting on an object. In the video, the free body diagram includes gravity, the pulling force, normal force, and friction force. It helps visualize and calculate the net forces and the box's acceleration in the context of the inclined ramp.
💡Normal Force
The normal force is the force exerted by a surface that supports the weight of an object resting on it, acting perpendicular to the surface. In the script, the normal force (FN) is identified as the force that prevents the box from sinking into the ramp, and it is calculated in relation to the other forces acting on the box.
💡Friction
Friction is the force that resists the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. The script mentions the coefficient of friction (mu) as 3, which is used to calculate the friction force (FF) that opposes the motion of the box up the ramp.
💡Coefficient of Friction
The coefficient of friction (mu) is a scalar value that represents the ratio of the force of friction between two bodies to the force pressing them together. In the video, a coefficient of friction of 3 is given, which is used in the formula for calculating the friction force opposing the box's movement up the ramp.
💡Displacement
Displacement is the change in position of an object. In the script, the displacement (Delta X) is the distance the box is moved up the ramp, which is 12 meters. It is a key variable in calculating the work done by the pulling force and by friction.
💡Work
Work in physics is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. The script calculates the work done by the pulling force and by friction, which requires understanding the force components and the displacement of the box.
💡Cosine
The cosine function relates the angle of a right triangle to the ratio of the lengths of its adjacent side to its hypotenuse. In the script, cosine is used to find the horizontal and vertical components of forces and to calculate the angles between the forces and the displacement, which is necessary for determining the work done.
💡Newton
A Newton is the SI unit of force. It is defined as the force required to accelerate a one-kilogram mass by one meter per second squared. In the video, the pulling force is given as 2,000 Newtons, which is a key value in determining the work done and the components of the force acting on the box.
Highlights

A 250 kg box is pulled up a 30° ramp using a 2,000 Newton force at an 18° angle to the incline.

The force applied (FP) is decomposed into its X and Y components using trigonometric functions.

Gravity is also decomposed into components along and perpendicular to the ramp.

A normal force (FN) is introduced, acting perpendicular to the ramp's surface.

Friction force (FF) is considered, opposing the box's motion up the ramp.

The coefficient of friction (μ) is given as 3, affecting the calculation of friction force.

The box is moved a distance of 12 meters up the ramp (ΔX).

Work done by friction and the pulling force is calculated using the formula work = force * displacement.

The work of friction is determined by the forces in the Y direction and the angle between them.

Friction force is calculated using μ times the normal force.

The work of friction is negative, indicating energy dissipation.

The work done by the pulling force is calculated considering the angle of the force relative to displacement.

The final work done by the pulling force is found to be 22,825.3 Joules.

The problem demonstrates the application of trigonometry and Newtonian mechanics in calculating work.

The solution involves understanding the components of forces and their impact on work done.

The problem highlights the importance of considering both the magnitude and direction of forces in physical calculations.

The final answer provides a clear example of how to calculate work done by different forces in a mechanical system.

Transcripts

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Physics ProblemForce AnalysisRamp InclineFriction WorkBox PullingGravity ComponentsNormal ForceCoefficient of FrictionDisplacementWork Calculation