Physics, 29.02.2020 01:39 jamarengle2

A cutting tool under microprocessor control has several forces acting on it. One force is F⃗ =−αxy2j^, a force in the negative y-direction whose magnitude depends on the position of the tool. The constant is α = 3.00 N/m3 . Consider the displacement of the tool from the origin to the point x= 2.85 m , y= 2.85 m .a. Calculate the work done on the tool by F⃗ if this displacement is along the straight line y=x that connects these two points.

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Answer from: kimsouther2

The work done is 49.48 J.

The tool is acted upon by a force F = $-axy^{2} j$

a = 3.00 $\frac{N}{m^{3} }$

Now the tool is displaced along the straight line y = x

Then the force F follows by the line:

F = $-ay^{3} j$ , putting x = y so that it satisfies the given straight line equation y = x

So we need only y-coordinate to calculate the work done W.

$W=\int\limits {F} \, ds$ , here ds is the displacement element.

$W=\int\limits^{2.85}_0 {-ay^{3} } \, dy =-3*[y^{4}/4 ]^{2.85}_0$

W = -3 × $[(2.85)^{4}/4 ]$

W = -49.48 J

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Answer from: 2021CanadyRaniya

Explanation:

Given that

F=-αxy²j

α=3N/m³

Displacement from x=2.85 to y=2.85

Since, y=x

Then dy=dx

ds=dx i + dy j

a. Work done

W=∫ F.ds from (0,0) to (2.85,2.85)

W=∫(-αxy²j).(dx i + dy j) (0,0)—(2.85,2.85)

Note, i.i=j.j=1 i.j=j.i=0

W=∫-αxy²dy from (0,0)—(2.85,2.85)

W=-α∫xy²dy from (0,0)—(2.85,2.85)

x=y

W=-α∫y³dy from (0,0)—(2.85,2.85)

W=-αy⁴/4. from (0,0)—(2.85,2.85)

W=-3[(2.85)⁴/4-0]

W=-49.48J

The work done on the tool by the force is -49.48J

Answer from: Quest

Ineed the problem dude

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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A cutting tool under microprocessor control has several forces acting on it. One force is F⃗ =−αxy2j...

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