Numerical on Potential and Potential energy:

1. Work Done:

$$W= F \times d$$ where

• W = work done (in joules)
• F = force applied (in newtons)
• d = displacement (in meters)

In this case, the force is 5 N and the displacement is 20 m, so the work done is: $$W= 5 \text{ N} \times 20 \text{ m} = 100 \text{ J}$$ Therefore, the work done on the particle is 100 J.

2. Potential Energy (Spring):

$$PE = (1/2) kx^2$$ where,

• PE = potential energy (in joules)
• k = spring constant (in newtons per meter)
• x = displacement from the relaxed position (in meters)

Here, k= 100 N/m, and x= 0.1 m (10 cm). $$PE = (1/2) \times 100 \text{ N/m} \times (0.1 \text{ m})^2 = 0.5 \text{ J}$$ Therefore, the potential energy stored in the spring is 0.5 J.

3. Potential Energy (Gravitational):

$$PE = mgh$$ where

• PE = potential energy (in joules)
• m = mass (in kilograms)
• g = acceleration due to gravity (9.8 m/s²)
• h = height (in meters)

Here, m is 5 kg, g= 9.8 m/s² and h is 10 m: $$PE = 5\text{ kg}\times 9.8 \text{ m/s}^2 \times 10 \text{ m} = 490 \text{ J}$$ Therefore, the potential energy gained by the block is 490 J.

4. Gravitational Potential Energy:

$$PE = mgh$$

Here, m= 20 kg, g= 9.8 m/s² and h= 10 m. $$PE = 20 \text{ kg} \times 9.8 \text{ m/s}^2 \times 10\text{ m} = 1960 \text{ J}$$ Therefore, the gravitational potential energy of the object is 1960 J.

5. Kinetic Energy:

$$KE= 1/2 mv^2$$ where

• KE = kinetic energy (in joules)
• m = mass (in kilograms)
• v = velocity (in meters per second).

Here, m= 10 kg and v= 10 m/s: $$KE= (1/2) \times 10\text{ kg} \times (10\text{ m/s})^2 = 500\text{ J}$$

Therefore, the kinetic energy of the block is 500 J.