What work is done by a force (in newtons) F = 3.1xi + 3.1j, with x in meters, that moves a particle from a position r1 = 2.1i + 2.5j to r2 = - -4.9i -3.9j?

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* Physics/Math - bobpursley, Thursday, March 1, 2007 at 6:27am

Work is the dot product of Force and displacement.

Change in displacement is r2 minus r1. I will be happy to critique your work on this.

Rememeber dot product is a scalar, the sum of i component times i component plus j component times j component etc.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
Here is what I did:

W1=integral of Fxdx = integral (3.1x)dx
= 1.55x^2 evaluated at x2=-4.9 and x1=2.1.
= [(1.55(-4.9)^2)-(1.55(2.1)^2)]
= 30.38 J
W2=integral of Fydy = integral (3.1)dy
= 3.1[(-3.9)-(2.5)]
= -19.84 J
Wnet = W1+W2
Wnet = 30.38-19.84
Wnet = 11 J

Is this correct???

The procedure you set up is correct. I don't have a calculator here, so I didn't check math.

What is wrong with my thinking here???

I got the right answer...stupid careless error on my behalf.

The only thing I see "wrong" is the 11 J is a rounded number.

To calculate the work done by a force, you need to find the dot product of the force and the displacement. Here's how you can do it step by step:

1. Find the displacement vector between the initial position r1 and the final position r2. You can do this by subtracting r1 from r2:

Δr = r2 - r1 = (-4.9i - 3.9j) - (2.1i + 2.5j)
= -6.8i - 6.4j

2. Calculate the dot product of the force F and the displacement vector Δr. The dot product is calculated by multiplying the corresponding components of the two vectors and then summing them up:

F · Δr = (3.1xi + 3.1j) · (-6.8i - 6.4j)
= (3.1x)(-6.8) + (3.1)(-6.4)
= -21.08x - 19.84

3. Integrate the dot product expression over the range of x from the initial position x1 to the final position x2:

Work = ∫[x1, x2] (F · Δr) dx
= ∫[2.1, -4.9] (-21.08x - 19.84) dx
= [-10.54x^2 - 19.84x] | [2.1, -4.9]
= [-10.54(-4.9)^2 - 19.84(-4.9)] - [-10.54(2.1)^2 - 19.84(2.1)]
= [115.37 - 38.98] - [-48.43 - 8.33]
= 153.35 J

So, the work done by the force is 153.35 Joules.

It appears that there was an error in your calculation, resulting in the incorrect answer of 11 J. Please double-check your integration and arithmetic steps to identify the error.