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define-kinetic-energy

๐Ÿš€ The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Kinetic energy is the energy that an object possesses due to its motion, and it is defined as the work needed to accelerate an object from rest to its current velocity. The formula for kinetic energy (KE) is given by KE = 1/2 mvยฒ, where m is the mass of the object and v is its velocity. The work-energy theorem connects the concepts of work and energy, showing that the work done on an object results in a change in its kinetic energy.

Theory Explanation

Understanding Kinetic Energy

Kinetic energy is the energy of an object in motion. It depends on the mass of the object and the square of its velocity. The faster an object moves, the more kinetic energy it has. This energy can be calculated using the formula KE = 1/2 mvยฒ, where m is the mass and v is the velocity of the object.

\[ KE = \frac{1}{2} mv^2 \]
Work-Energy Theorem

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. If an object is acted upon by a net force, the work done by that force will result in a change in the object's kinetic energy. Mathematically, this can be expressed as W = ฮ”KE = KE_final - KE_initial.

\[ W = \Delta KE = KE_{final} - KE_{initial} \]

Key Points

  • ๐ŸŽฏ Kinetic energy is directly proportional to the mass of the object and the square of its velocity.
  • ๐ŸŽฏ The work-energy theorem connects work done to changes in kinetic energy.
  • ๐ŸŽฏ Kinetic energy can never be negative; it is always zero or positive.

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Examples:💡

A car of mass 1000 kg is moving with a velocity of 20 m/s. Calculate its kinetic energy.

Solution:

Step 1: Identify the mass (m) and velocity (v) of the car. Here, m = 1000 kg and v = 20 m/s.

Step 2: Use the kinetic energy formula: KE = 1/2 mvยฒ.

\[ KE = \frac{1}{2} \times 1000 \times (20)^2 \]

Step 3: Calculate the kinetic energy: KE = 1/2 \times 1000 \times 400 = 200000 J.

\[ KE = 200000 J \]

A cyclist accelerates from rest to a speed of 10 m/s. If the mass of the cyclist and the bicycle is 75 kg, find the work done by the cyclist to reach this speed.

Solution:

Step 1: Calculate the initial kinetic energy (KE_initial) when the cyclist is at rest: KE_initial = 0 J.

\[ KE_{initial} = 0 J \]

Step 2: Calculate the final kinetic energy (KE_final) using the formula: KE_final = 1/2 mvยฒ = 1/2 \times 75 \times (10)^2.

\[ KE_{final} = \frac{1}{2} \times 75 \times 100 = 3750 J \]

Step 3: The work done (W) is equal to the change in kinetic energy: W = KE_final - KE_initial = 3750 - 0 = 3750 J.

\[ W = 3750 J \]

Common Mistakes

  • Mistake: Confusing kinetic energy with potential energy; students may think they are the same.

    Correction: Remember that kinetic energy is energy of motion, while potential energy is stored energy based on position.

  • Mistake: Forgetting to square the velocity in the kinetic energy formula.

    Correction: Always double-check the formula KE = 1/2 mvยฒ to ensure that the velocity is squared.

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