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negation
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Homework Statement
I'm trying to bridge F =ma to m/2(dv^{2}/dx). It was shown in the course book I have but there's a huge disconnection in the steps.
negation said:Homework Statement
I'm trying to bridge F =ma to m/2(dv^{2}/dx). It was shown in the course book I have but there's a huge disconnection in the steps.
The Attempt at a Solution
F =ma = m.(dv/dt) = m(dv/dx . dx/dt) = mv(dv/dx). Where do I take it from here?
dauto said:Multiply both sides of your equation by dx to get
F dx = mv dv
Integrate both side, what do you get?
rude man said:Formally differentiate d/dx(v^2). What do you get?
Newton's Second Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the heavier the object, the more force is needed to accelerate it.
In physics, Work is defined as the product of force and displacement, where the force acts in the same direction as the displacement. It is a measure of the energy transferred to or from an object by an external force.
According to Newton's Second Law, the net force acting on an object is directly proportional to its acceleration. This means that if a force is applied to an object, it will accelerate and therefore, do work. The work done by a force is equal to the force multiplied by the displacement of the object in the direction of the force.
The formula for calculating Work is W = F * d * cosθ, where W is the work done, F is the force applied, d is the displacement of the object, and θ is the angle between the force and displacement vectors. This formula is derived from the dot product of force and displacement vectors.
Understanding the connection between these two principles helps scientists accurately predict and analyze the motion of objects. It allows them to calculate the amount of force needed to move an object a certain distance, or the distance an object will travel when a certain force is applied. This knowledge is crucial in fields such as mechanics, engineering, and physics.