In physics, work done is defined as the product of force applied to an object and its displacement. Work is a scalar quantity and is typically measured in the unit of Joules (J).

The formula for calculating work is:

W = F x d

where W is the work done, F is the force applied, and d is the distance over which the force is applied.

Work is a measure of the energy transferred to or from an object. When work is done on an object, energy is transferred to the object and the object’s kinetic energy or potential energy increases. When work is done by an object, energy is transferred from the object and the object’s kinetic energy or potential energy decreases.

For example, if you lift a box off the ground and place it on a shelf, you are doing work on the box because you are applying a force (your lifting force) over a distance (the height of the shelf). This work increases the gravitational potential energy of the box.

Here we are providing numerical problems based on work and energy for class 9 science. Answers are also provided so that students can check their answers after solving the numerical problems.

## Problems Based on Work and Energy for Class 9 Science

Q.1. A box is lifted to a height of 10 meters by a force of 50 N. How much gravitational potential energy does the box have at this height?

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Answer: 500 JoulesQ.2. A box with a mass of 5 kg is moving at a velocity of 10 m/s and collides with a stationary box. After the collision, the first box is at rest and the second box has a velocity of 5 m/s. What is the change in kinetic energy of the system?

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Answer: -250 JoulesQ.3. A box with a mass of 5 kg is moving at a velocity of 10 m/s. What is its kinetic energy?

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Answer: 250 JoulesQ.4. A box with a mass of 5 kg is lifted to a height of 10 meters. How much work is required to lift the box?

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Answer: 500 JoulesQ.5. A 50 N force is applied to a box to move it a distance of 10 meters. How much work is done on the box?

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Answer: 500 Joules## How to approach and solve problems.

To solve problems on work and energy, it is important to have a good understanding of the definitions and formulas related to these concepts, as well as the physical principles that govern them. Some key points to consider include:

- The formula for calculating work is W = F x S where W is the work done, F is the force applied, and d is the distance over which the force is applied.
- Energy is the ability to do work or cause change, and can take many forms, including kinetic energy (the energy of motion), potential energy (stored energy), and mechanical energy (the sum of kinetic and potential energy).
- The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. This means that the total amount of energy in a closed system remains constant, even if the energy is converted from one form to another.
- When solving problems on work and energy, it is often helpful to draw a diagram to represent the problem, identify all of the forces acting on an object, and determine the direction and magnitude of these forces. It is also important to clearly define your variables and choose a coordinate system that is appropriate for the problem.
- To solve problems on work and energy, you may need to use a variety of formulas, including the formula for work (W = F x S), the formula for kinetic energy (KE = (1/2) mv
^{2}), and the formula for gravitational potential energy (PE = mgh). It is important to use the correct formula for the type of energy and situation being considered.