On a farm, you are pushing on a stubborn pig with a constant horizontal force with magnitude 30.0 N and direction 37.0° counterclockwise from the +x-axis. How much work does this f... On a farm, you are pushing on a stubborn pig with a constant horizontal force with magnitude 30.0 N and direction 37.0° counterclockwise from the +x-axis. How much work does this force do during a displacement of the pig that is: s = -(2.00 m)i + (4.00 m)j? Show that the work done by this force can be calculated in two ways as given by the equation W = F * s * cos(θ) = F_x * x + F_y.
Understand the Problem
The question is asking how to calculate the work done by a constant horizontal force on a stubborn pig during a specified displacement. It involves using the formula for work done and indicates that this can be done in two different ways, depending on the components of the force and the direction of the displacement.
Answer
The work done is \( W = F \cdot d \).
Answer for screen readers
The work done is given by the formula ( W = F \cdot d ), where ( F ) is the constant force applied in the direction of the displacement and ( d ) is the displacement.
Steps to Solve
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Identify the formula for work done The formula for work done ($W$) by a force ($F$) acting on an object over a displacement ($d$) is given by: $$ W = F \cdot d \cdot \cos(\theta) $$ where $\theta$ is the angle between the force and the displacement direction.
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Determine the force and angle If the force is horizontal and the displacement is also horizontal, then $\theta = 0^{\circ}$. Consequently, $\cos(0^{\circ}) = 1$.
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Substitute known values into the formula To find the work done, substitute the values of the force and the displacement. For example, if the force is $F$ newtons and the displacement is $d$ meters, then: $$ W = F \cdot d \cdot 1 $$ or simply: $$ W = F \cdot d $$
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Calculate the final work done Multiply the force by the displacement to find the total work done by the force on the pig: $$ W = F \cdot d $$
The work done is given by the formula ( W = F \cdot d ), where ( F ) is the constant force applied in the direction of the displacement and ( d ) is the displacement.
More Information
Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force. In this scenario, if the force is applied effectively in the same direction as the movement, the work done can be maximized.
Tips
- Confusing the angle: Ensure that you correctly identify the angle between the force vector and the direction of displacement.
- Forgetting to use the cosine function when the force and displacement are not in the same direction. Always check the angle involved.
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