This was on my exam. I wasn't sure how to solve it.

[PhysicsKid0123]

Homework Statement

I tried to solve for the force vectors but I had no clue how to do it? I tried plenty of times after the exam and still haven't found the components. Help?

Homework Equations

F\bullet\Deltar

The Attempt at a Solution

 

[TSny]

Can you express $\vec{F} \cdot \Delta\vec{r}$ in terms of the magnitude of the force, the magnitude of the displacement, and the angle between the force and the displacement?

In this problem, what is the angle between the force and the displacement?

 

[PhysicsKid0123]

Yes, but I don't see how you can find the angle between them. You need a given angle or the force vector?

 

[TSny]

The particle starts from rest. The force is constant in magnitude and direction. So, how does the direction of the force relate to the direction of the displacement?

 

[PhysicsKid0123]

They relate by the dot product of the force vector and position vector. Vector F dot Vector r = abs F * cos()* abs r. Or by components, vector F dot vector r = Fx*rx + Fy*ry...

 

[TSny]

OK. So $W = Frcosθ$.

You should be able to get the magnitude of the force from this equation. You just need to know what to use for r and θ.
Once you get $F$ you should be able to express the force vector $\vec{F}$ in component form.

 

[Superman1271]

When you push something at rest, what direction does it move with respect to the force you applied?

 

[PhysicsKid0123]

I don't see how you can find the angle to begin with.. For r I'd simply use sqrt(20).

 

[TSny]

If an object is at rest when a force is applied in the x direction, which way does the object move?

 

[Chestermiller]

According to the problem statement, the force and displacement are going to be pointing in the same direction. So the angle between them is zero. First calculate the magnitude of the force necessary to cause 24 J of work when the particle travels sqrt(20) meters. Then determine the equation for a unit vector in the same direction as r. This will be the unit vector in the direction as F also.

Chet