Shortcut Methods

Numerical on Potential and Potential energy:

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: $W = 5 N \times 20 m = 100 J$ Therefore, the work done on the particle is 100 J.

Potential Energy (Spring):

$P E = (1 / 2) k x^{2}$ 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). $P E = (1 / 2) \times 100 N/m \times (0.1 m)^{2} = 0.5 J$ Therefore, the potential energy stored in the spring is 0.5 J.

Potential Energy (Gravitational):

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

Gravitational Potential Energy:

$P E = m g h$

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

Kinetic Energy:

$K E = 1 / 2 m v^{2}$ 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: $K E = (1 / 2) \times 10 kg \times (10 m/s)^{2} = 500 J$

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

Shortcut Methods

Numerical on Potential and Potential energy:

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Shortcut Methods

Numerical on Potential and Potential energy:

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

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