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What is the Mathematical Definition of Work Done by Forces in Physics?

What is Work Done by Forces?

In physics, "work" is a term we use to explain what happens when a force pushes or pulls something and makes it move.

To put it simply, we can think about work this way:

Work Done (WW) = Force (FF) x Distance (dd) x Cosine of the Angle (θ\theta)

Here’s what those terms mean:

  • WW: This represents the work done. We measure it in joules (J).
  • FF: This is the strength of the force that is pushing or pulling the object. We measure it in newtons (N).
  • dd: This is how far the object moves in the direction of the force. We measure it in meters (m).
  • θ\theta: This is the angle between the direction of the force and the direction the object is moving.

Important Points to Remember:

  • Work happens only when the object moves in the same direction that the force is applied.

  • If the angle (θ\theta) is 0 degrees, it means the force is pushing directly in the direction of the movement. So all of the force contributes to the work, and the formula becomes W=FdW = F \cdot d.

  • If the angle (θ\theta) is 90 degrees, the force is pushing sideways and not helping the object move. In this case, no work is done, meaning W=0W = 0.

Understanding how work is done is really important because it helps us look at how energy moves around in different systems.

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What is the Mathematical Definition of Work Done by Forces in Physics?

What is Work Done by Forces?

In physics, "work" is a term we use to explain what happens when a force pushes or pulls something and makes it move.

To put it simply, we can think about work this way:

Work Done (WW) = Force (FF) x Distance (dd) x Cosine of the Angle (θ\theta)

Here’s what those terms mean:

  • WW: This represents the work done. We measure it in joules (J).
  • FF: This is the strength of the force that is pushing or pulling the object. We measure it in newtons (N).
  • dd: This is how far the object moves in the direction of the force. We measure it in meters (m).
  • θ\theta: This is the angle between the direction of the force and the direction the object is moving.

Important Points to Remember:

  • Work happens only when the object moves in the same direction that the force is applied.

  • If the angle (θ\theta) is 0 degrees, it means the force is pushing directly in the direction of the movement. So all of the force contributes to the work, and the formula becomes W=FdW = F \cdot d.

  • If the angle (θ\theta) is 90 degrees, the force is pushing sideways and not helping the object move. In this case, no work is done, meaning W=0W = 0.

Understanding how work is done is really important because it helps us look at how energy moves around in different systems.

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