Class 11 >> Physics >> work-energy-and-power >> kinetic-and-potential-energies >> calculate-energy-stored-in-spring
Skip to Practice

calculate-energy-stored-in-spring

🚀 The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In the context of mechanical energy, we consider two forms: kinetic energy (energy of motion) and potential energy (stored energy due to position). The energy stored in a spring, known as elastic potential energy, can be calculated using Hooke's Law, which states that the force exerted by a spring is proportional to its displacement from the equilibrium position. The formula for the energy stored in a spring is given by: \( E = \frac{1}{2} k x^2 \), where \( E \) is the elastic potential energy, \( k \) is the spring constant, and \( x \) is the displacement from the equilibrium position.

Theory Explanation

Understanding Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. It is given by the formula: \( KE = \frac{1}{2} mv^2 \), where \( m \) is the mass of the object and \( v \) is its velocity.

\[ KE = \frac{1}{2} mv^2 \]
Understanding Potential Energy

Potential energy is the energy stored in an object due to its position or configuration. For gravitational potential energy, the formula is: \( PE = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the height above a reference point.

\[ PE = mgh \]
Calculating Energy Stored in a Spring

The energy stored in a spring when it is compressed or stretched is given by the formula: \( E = \frac{1}{2} k x^2 \), where \( k \) is the spring constant and \( x \) is the displacement from the equilibrium position. This formula derives from the work done on the spring as it is compressed or stretched.

\[ E = \frac{1}{2} k x^2 \]

Key Points

  • 🎯 Kinetic energy depends on the mass and velocity of an object.
  • 🎯 Potential energy depends on the position of an object in a gravitational field or its configuration in a spring.
  • 🎯 The work done on an object results in a change in its kinetic energy.
  • 🎯 The energy stored in a spring is proportional to the square of its displacement.
  • 🎯 Understanding the relationship between work, energy, and power is crucial in physics.

🛠 Simulation is being generated. Please check back in a few moments.

Examples:💡

Example 1: Calculate the energy stored in a spring with a spring constant of 200 N/m that is compressed by 0.5 m.

Solution:

Step 1: Identify the spring constant (k) and the displacement (x). Here, k = 200 N/m and x = 0.5 m.

\[ k = 200 \text{ N/m}, \ x = 0.5 \text{ m} \]

Step 2: Use the formula for elastic potential energy: \( E = \frac{1}{2} k x^2 \).

\[ E = \frac{1}{2} (200) (0.5)^2 \]

Step 3: Calculate the energy: \( E = \frac{1}{2} (200) (0.25) = 25 \text{ J} \).

\[ E = 25 \text{ J} \]

Example 2: A 5 kg object is moving at a speed of 10 m/s. Calculate its kinetic energy.

Solution:

Step 1: Identify the mass (m) and velocity (v). Here, m = 5 kg and v = 10 m/s.

\[ m = 5 \text{ kg}, \ v = 10 \text{ m/s} \]

Step 2: Use the formula for kinetic energy: \( KE = \frac{1}{2} mv^2 \).

\[ KE = \frac{1}{2} (5) (10)^2 \]

Step 3: Calculate the kinetic energy: \( KE = \frac{1}{2} (5) (100) = 250 \text{ J} \).

\[ KE = 250 \text{ J} \]

Common Mistakes

  • Mistake: Confusing kinetic energy with potential energy.

    Correction: Remember that kinetic energy is related to motion, while potential energy is related to position or configuration.

  • Mistake: Incorrectly applying the formula for energy stored in a spring by not squaring the displacement.

    Correction: Always ensure to square the displacement (x) in the formula \( E = \frac{1}{2} k x^2 \).

← Back Start Practice