# Find work from Vector?

• November 22nd 2010, 08:08 AM
MrCryptoPrime
Find work from Vector?
Question: Find the work done in moving a particle from P=(0http://webwork2.math.utah.edu/webwor...144/char3B.png0) to Q=(4http://webwork2.math.utah.edu/webwor...144/char3B.png7) if the magnitude and direction of the force are given by v=http://webwork2.math.utah.edu/webwor...144/char3C.png1http://webwork2.math.utah.edu/webwor...144/char3B.png4http://webwork2.math.utah.edu/webwor...144/char3E.png.

Converted to standard form: PQ = <4,7>
Length of force vector: ||v|| = sqrt(17)
Took arctan(4/1) to find direction: 75.96 (degrees)
u = sqrt(17)[cos(75.96), sin(75.96)]

This whole vector physics application thing is still really confusing to me. Could someone show me how to solve the rest of this problem and try to explain the generalities behind these sorts of applications to make it easier to solve others and understand them better? Thanks!
• November 22nd 2010, 08:18 AM
Unknown008
The work done is defined as the product of force applied and the distance moved in the direction of the force.

Make a sketch and you will realise that the displacement is not in the same direction as the force applied.

You'll have to resolve the force in a component parallel to the displacement.

The angle the displacement does with the x axis is 60.26 degrees nd that of the force is 75.96 degrees as you got.

The difference is 15.71 degrees (taking into consideration all the digits in the decimal).

You'll have to resolve the force.

The force that produced the displacement is given by FcosA

Where F is the magnitude of the applied force and A the angle with the displacement.

So, we get the force as $\sqrt{17} cos(15.71) = 3.97\ units$

The distance is given by the magnitude of the vetor <4, 7>

You have the force and distance, you can find the work now. (Smile)
• November 22nd 2010, 08:21 AM
skeeter
Quote:

Originally Posted by MrCryptoPrime
Question: Find the work done in moving a particle from P=(0http://webwork2.math.utah.edu/webwor...144/char3B.png0) to Q=(4http://webwork2.math.utah.edu/webwor...144/char3B.png7) if the magnitude and direction of the force are given by v=http://webwork2.math.utah.edu/webwor...144/char3C.png1http://webwork2.math.utah.edu/webwor...144/char3B.png4http://webwork2.math.utah.edu/webwor...144/char3E.png.

Converted to standard form: PQ = <4,7>
Length of force vector: ||v|| = sqrt(17)
Took arctan(4/1) to find direction: 75.96 (degrees)
u = sqrt(17)[cos(75.96), sin(75.96)]

This whole vector physics application thing is still really confusing to me. Could someone show me how to solve the rest of this problem and try to explain the generalities behind these sorts of applications to make it easier to solve others and understand them better? Thanks!

work is the scalar (dot) product of force and displacement ...

$(i + 4j) \cdot (4i + 7j) = 4 + 28 = 32$

work is a scalar quantity.
• November 22nd 2010, 08:30 AM
MrCryptoPrime
Still a bit uneasy about what exactly is meant by force and displacement, but thank you for all your input. This should get me through for now and I am sure if I keep working at it I will eventually understand! :) Of course, I have the naive tendency to need to understand every component of everything which is impossible because everything can be explained at an infinitely smaller or larger scale. Anyhow, thanks you two!