**1. What is work done by a constant force?**

**Answer:** Work done by a constant force is defined as the product of the force and the displacement in the direction of the force. Mathematically,

where F is the force, d is the displacement, and θ is the angle between the force and the displacement.

**2. How is work done by a variable force calculated?**

**Answer:** Work done by a variable force is calculated by integrating the force over the displacement. Mathematically,

where **F** is the force vector and ** ds** is the differential displacement vector.

**3. What is kinetic energy?**

**Answer:** Kinetic energy is the energy possessed by an object due to its motion. It is given by the formula

where m is the mass of the object and v is its velocity.

**4. Define potential energy.**

**Answer:** Potential energy is the energy possessed by an object due to its position or configuration. Common types include gravitational potential energy U=mgh and elastic potential energy

where m is mass, g is acceleration due to gravity, h is height, k is the spring constant, and x is the displacement from equilibrium.

**5. Explain the work-energy theorem.**

**Answer:** The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. Mathematically,

**6. What is power?**

**Answer:** Power is the rate at which work is done or energy is transferred. It is given by

where W is work and t is time. The unit of power is the watt (W).

**7. Describe the potential energy of a spring.**

**Answer:** The potential energy stored in a compressed or stretched spring is given by

, where k is the spring constant and x is the displacement from the spring’s equilibrium position.

**8. What is the conservation of mechanical energy?**

**Answer:** The conservation of mechanical energy states that in the absence of non-conservative forces (like friction), the total mechanical energy (sum of kinetic and potential energies) of a system remains constant.

**9. Differentiate between conservative and non-conservative forces.**

**Answer:** Conservative forces, such as gravity and spring force, do not dissipate mechanical energy and have associated potential energies. Non-conservative forces, like friction and air resistance, convert mechanical energy into other forms (e.g., heat) and do not have associated potential energies.

**10. What is motion in a vertical circle?**

**Answer:** Motion in a vertical circle involves an object moving along a circular path in a vertical plane, where gravitational force affects the object’s motion. It requires sufficient centripetal force to maintain the motion, which varies with the position in the circle.

**11. Explain elastic collisions in one dimension.**

**Answer:** In an elastic collision, both momentum and kinetic energy are conserved. For two objects colliding in one dimension, the relative speed of approach before the collision equals the relative speed of separation after the collision.

**12. Explain inelastic collisions in one dimension.**

**Answer:** In an inelastic collision, momentum is conserved, but kinetic energy is not. Some of the kinetic energy is converted into other forms of energy, such as heat or deformation. In a perfectly inelastic collision, the colliding objects stick together and move with a common velocity after impact.

**13. Describe elastic collisions in two dimensions.**

**Answer:** In two-dimensional elastic collisions, both momentum and kinetic energy are conserved. The collisions are analyzed by resolving the velocities into components along mutually perpendicular axes and applying conservation laws to each axis separately.

**14. Describe inelastic collisions in two dimensions.**

**Answer:** In two-dimensional inelastic collisions, momentum is conserved in both dimensions, but kinetic energy is not. The analysis involves resolving velocities into components and using conservation of momentum for each direction while accounting for the loss of kinetic energy.

**15. What is the significance of the spring constant (k) in the context of potential energy?**

**Answer:** The spring constant kkk determines the stiffness of the spring. A larger kkk means a stiffer spring that requires more force to compress or stretch by a given amount. It directly influences the potential energy stored in the spring.

**16. How is the work done by gravity calculated?**

**Answer:** The work done by gravity is calculated as

, where m is the mass of the object, g is the acceleration due to gravity, and h is the vertical displacement of the object.

**17. What is the relation between work and energy?**

**Answer:** Work is the process of energy transfer. When work is done on an object, energy is transferred to or from the object, changing its kinetic or potential energy.

**18. Define the unit of power and give an example.**

**Answer:** The unit of power is the watt (W), which is equivalent to one joule per second (J/s). An example is a 60-watt light bulb, which consumes 60 joules of energy per second.

**19. What is mechanical energy?**

**Answer:** Mechanical energy is the sum of kinetic and potential energy in a system. It represents the energy associated with the motion and position of an object.

**20. Explain the concept of work done by a spring force.**

**Answer:** The work done by a spring force when it is compressed or stretched is given by

, where k is the spring constant, x_{i }is the initial displacement, and x_{f} is the final displacement. This represents the change in the spring’s potential energy.