Unit 5: Work, Energy and Power - Numerical Problems

Class 9 Physics Notes | Unit 5 – Work, Energy and Power | Numerical Problems

📘 Numerical Problems (Work, Energy and Power)

Related Resources:

Chapter Notes MCQs with Answers Important Definitions

Important Formulas for Numerical Problems

Work Done

\[W = F \times S \quad \text{or} \quad W = FS \cos \theta\]

Where \( W \) is work, \( F \) is force, \( S \) is displacement, and \( \theta \) is angle between force and displacement

Kinetic Energy

\[E_k = \frac{1}{2}mv^2\]

Where \( m \) is mass and \( v \) is velocity

Potential Energy

\[E_p = mgh\]

Where \( m \) is mass, \( g \) is gravitational acceleration, and \( h \) is height

Power

\[P = \frac{W}{t}\]

Where \( P \) is power, \( W \) is work, and \( t \) is time

Efficiency

\[\text{Efficiency} = \frac{\text{Output}}{\text{Input}} \times 100\%\]

Problem Solving Tips

Key Steps for Solving Numerical Problems

  1. Identify the given data - List all known quantities with their units
  2. Determine what needs to be found - Clearly state the unknown
  3. Select the appropriate formula - Choose the formula that connects known and unknown quantities
  4. Substitute values - Plug in the known values with correct units
  5. Solve step by step - Show all calculations clearly
  6. Include units in your answer - Always write the correct unit with your final answer

Common Mistakes to Avoid

Practice Problems

Problem 1: Work Calculation with Angle

Given:

A force of 20 N acting at an angle of 60° to the horizontal is used to pull a box through a distance of 3 m across a floor.

Solution Approach:

Use the formula \( W = FS \cos \theta \) where \( \theta \) is the angle between force and displacement.

Problem 2: Finding Angle from Work

Given:

A body moves a distance of 5 meters under the action of a force of 8 newtons. The work done is 20 Joules.

Solution Approach:

Rearrange the work formula \( W = FS \cos \theta \) to solve for \( \theta \).

Problem 3: Power Calculation

Given:

An engine raises 100 kg of water through a height of 80 m in 25 s.

Solution Approach:

Calculate work done first using \( W = mgh \), then use \( P = \frac{W}{t} \) to find power.

Problem 4: Kinetic Energy After Force Application

Given:

A body of mass 20 kg is at rest. A 40 N force acts on it for 5 seconds.

Solution Approach:

Find acceleration using Newton's second law, then final velocity using equations of motion, and finally kinetic energy.

Problem 5: Maximum Height from Initial Velocity

Given:

A 0.14 kg ball is thrown vertically upward with an initial velocity of 35 m/s.

Solution Approach:

At maximum height, all kinetic energy converts to potential energy. Use \( mgh = \frac{1}{2}mv^2 \).

Additional Practice Resources

For more numerical problems with detailed solutions, refer to the PDF document embedded above.

The PDF contains 13 comprehensive numerical problems covering:

Each problem includes:

Created by Hira Science Academy | Aligned with PECTA 2025 Syllabus

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