Calculate Work of Vector Force in XY Plane

In summary, a particle undergoes a displacement of (1.57, 3.21) m while a constant force of (5.81, 3.93) N acts on it. To calculate the work done by the force, we use the formula W = F * D * cos(theta), where theta is the angle between the force and the displacement vectors. The magnitude of the resultant displacement and force vectors can be found using the Pythagorean theorem. Finally, the work done can be calculated using the dot product of the unit vectors.
  • #1
Idividebyzero
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1. A particle moving in the xy plane undergoesa displacement ~s = (sxˆı + sy ˆ|), with sx =
1.57 m, sy = 3.21 m, while a constant force F=(Fxˆı+Fyˆ|),withFx=5.81N,Fy=3.93 N, acts on the particle.
Calculate the the work done by vector F.
.




2.W=FDcos(theta)
inverse tangent



3. first found the magnitude of the resultant vector for the displacement via the theorum of pathagoreas. Using the same method i found the magnitude of the force resultant. Used inverse tangent times y over x for the angle. with those values i pluged into W=F*Dcos(theta). answer was incorrect. Okay, thought about it some more, the only work done through the applied force is on the X axis using just the x vectors calculated the work, that is also incorrect.
 
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  • #2
never mind i had a brain fart forgot unit vector dot products...lmao
 

1. What is the formula for calculating the work of a vector force in the XY plane?

The formula for calculating the work of a vector force in the XY plane is W = F * d * cos(θ), where W is the work, F is the magnitude of the force, d is the displacement, and θ is the angle between the force and the displacement.

2. What is the unit of measurement for work in the XY plane?

The unit of measurement for work in the XY plane is joules (J). This unit is equivalent to Newton-meters (N*m).

3. Can the work of a vector force be negative in the XY plane?

Yes, the work of a vector force can be negative in the XY plane. This occurs when the angle between the force and the displacement is greater than 90 degrees, meaning the force is working against the displacement.

4. How does the direction of the force affect the work in the XY plane?

The direction of the force does not affect the work in the XY plane, as long as the force and displacement are in the same plane. The angle between the force and displacement is what determines the work done.

5. Can you calculate the work of a vector force if the force is not constant in the XY plane?

Yes, you can still calculate the work of a vector force if the force is not constant in the XY plane. This can be done by breaking down the force into smaller components and calculating the work for each component separately, then adding them together to get the total work done.

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