Work Through a Displacement At An Angle

AI Thread Summary
To find the work done by a force acting at an angle, the equation W = F * cos(θ) * d is used, where θ is the angle between the force and the direction of displacement. In this case, a 65 N force at 170° and a displacement of 2.2 m at 30° require calculating the effective distance in the direction of the force. The correct approach involves determining the dot product of the force and displacement vectors rather than simply multiplying angles. The realization that work is a scalar quantity simplifies the calculation. Ultimately, the correct method leads to an accurate solution for the work done.
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Homework Statement



Find the work done when a force of 65 N acting at an angle of 170° from the x-axis is applied to an object that moves through a displacement of 2.2 m at an angle of 30°.

Homework Equations



W = Fcos\Thetad

where d is the distance moved in the direction of the force.

The Attempt at a Solution



I know I am slipping on my distance. The distance the object is traveling in the direction of the force is 2.2 m multiplied by the difference in the angles
W = ( 65 N ) * cos( 170° ) * ( 2.2 m ) * cos( 150° )

Obviously this is wrong, I don't understand how to find the distance part of the equation.
 
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Nevermind, I completely forgot that work is a scalar quantity and that obviously means it results from a dot product. I solved it...

I just found the vectors of the force and direction, and found their dot product.
 

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