The definition of acceleration allows us to find the results for the questions about the relationship between force and energy:
Newton's second law gives a relationship between force, mass and acceleration of bodies.
F = ma
Where F is the force, m is the mass, and a is the acceleration.
From kinematics the acceleration is defined by
a =[tex]\frac{dv}{dt}[/tex]
If we use the chain rule.
[tex]a = \frac{dv}{dx} \frac{dx}{dt}[/tex]
[tex]a= v \frac{dv}{dx}[/tex]
We substitute
F = [tex]\frac{dv}{dx}[/tex]
∫ F dx = m ∫ v dv
∫ F dx = ½ m v²
The term on the right is kinetic energy, therefore force and kinetic energy are related, but it is easier to use energy because it is a scalar since force is a vector quantity, it has three components.
Work is defined by the dot product of force times distance.
W = ∫ F . d x
If we assume a system moving at constant speed, the upward force is equal to the weight of the body.
F= W= mg
Let's substitute.
W = m g h
The term is potential energy, therefore potential energy is equal to work and is directly related to the applied force.
In general, the concepts of energy are used when we want the result at a specific point and Newton's second law is used when we want the result at all points.
In conclusion using the definition of acceleration in kinematics we can find the results for the questions the relationship of force and energy are:
Learn more gives force and energy here: brainly.in/question/4177014
