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calculate-work-done-by-constant-force

๐Ÿš€ The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. When a constant force acts on an object, the work done can be calculated using the formula: \( W = F \cdot d \cdot \cos(\theta) \), where \( W \) is the work done, \( F \) is the magnitude of the force, \( d \) is the displacement of the object, and \( \theta \) is the angle between the force and the direction of displacement. If the force is constant and acts in the same direction as the displacement, the formula simplifies to \( W = F \cdot d \).

Theory Explanation

Understanding Work Done by a Constant Force

Work is defined as the product of the force applied to an object and the distance over which that force is applied. When the force is constant and acts in the direction of the displacement, the work done can be calculated simply as the product of the force and the distance moved in that direction.

\[ W = F \cdot d \]
Calculating Work with Angle Consideration

When the force is not in the same direction as the displacement, we must consider the angle between the force and the displacement. The work done is given by the formula \( W = F \cdot d \cdot \cos(\theta) \), where \( \theta \) is the angle between the force vector and the displacement vector. This accounts for the component of the force that acts in the direction of the displacement.

\[ W = F \cdot d \cdot \cos(\theta) \]

Key Points

  • ๐ŸŽฏ Work is a scalar quantity measured in joules (J).
  • ๐ŸŽฏ The work done by a constant force is maximum when the force is in the same direction as the displacement.
  • ๐ŸŽฏ If the force and displacement are perpendicular, no work is done.

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Examples:💡

A constant force of 10 N is applied to push a box 5 meters along a flat surface in the direction of the force. Calculate the work done.

Solution:

Step 1: Identify the force and displacement. Here, F = 10 N and d = 5 m.

\[ W = F \cdot d \]

Step 2: Since the force is in the same direction as the displacement, we can use the simplified formula: W = 10 N * 5 m.

\[ W = 10 \cdot 5 = 50 J \]

Step 3: Thus, the work done is 50 joules.

A force of 20 N is applied at an angle of 60 degrees to the horizontal while moving an object 4 meters. Calculate the work done by the force.

Solution:

Step 1: Identify the force, displacement, and angle. Here, F = 20 N, d = 4 m, and \( \theta = 60^\circ \).

Step 2: Use the formula for work done with angle consideration: W = F * d * cos(ฮธ).

\[ W = 20 \cdot 4 \cdot \cos(60^\circ) \]

Common Mistakes

  • Mistake: Confusing work done with energy; students often think they are the same.

    Correction: Remember that work is the process of energy transfer, while energy is the capacity to do work.

  • Mistake: Forgetting to consider the angle when the force is not in the direction of displacement.

    Correction: Always check if the force is acting at an angle and use the correct formula involving cos(ฮธ).

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