What is the dot product formula for constant force work?

In summary, the physics work formula for a vector is the product of the force and displacement, which can also be expressed as a scalar product of the two vectors. This formula is W=Fs\cos(\theta).
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cbarker1
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What is the physics work formula for a vector?
 
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Re: Constant Work formula

The work $W$ done by an agent exerting a constant force is the product of component of the force in the direction of the displacement and the magnitude of the displacement of the force:

\(\displaystyle W=Fs\cos(\theta)\)

It is sometimes convenient to express this equation in terms of a scalar product of the two vectors $\textbf{F}$ and $\textbf{s}$. We write this scalar product $\textbf{F}\cdot\textbf{s}$. Because of the dot symbol, the scalar product is often called the dot product. Thus we can express the equation above as a scalar product:

\(\displaystyle W=\textbf{F}\cdot\textbf{s}=Fs\cos(\theta)\)
 

FAQ: What is the dot product formula for constant force work?

What is the formula for calculating work done by a constant force?

The formula for calculating work done by a constant force is Work = Force x Distance, where Work is measured in joules (J), Force is measured in newtons (N), and Distance is measured in meters (m).

How is the constant force work formula derived?

The constant force work formula is derived from the fundamental principle of work, which states that work is equal to the force applied multiplied by the distance over which the force is applied. This can be mathematically represented as W = F x d. When the force is constant, this formula simplifies to W = F x d.

What is the significance of using a constant force in the work formula?

Using a constant force in the work formula allows us to accurately calculate the work done on an object, as the force remains constant throughout the entire distance. This simplifies the calculation and provides a more accurate result compared to when the force is not constant.

Can the constant force work formula be used for non-constant forces?

No, the constant force work formula can only be used for situations where the force applied remains constant throughout the entire distance. If the force varies, the work done must be calculated using the more general formula W = ∫F(x) dx, where F(x) represents the varying force and dx represents the infinitesimal distance.

In what situations can the constant force work formula be applied?

The constant force work formula can be applied in various situations, such as lifting an object with a constant force, pushing or pulling an object with a constant force, or when an object is moving at a constant velocity due to a constant force acting on it. It can also be used for calculating the work done by a spring with a constant force constant.

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