Is the 680J mentioned in this problem a red herring?

[walking]

Am I right in thinking the 680J thing is a red herring? Even using the author's method of "same work required in either case" (ie =mgh in both cases) we still end up cancelling h and getting $$F=\frac{mg\sin \theta}{\cos \phi}\ge mg\sin \theta=320$$ etc. I.e. no need for 680J. Maybe I am wrong?

 

[kuruman]

What is angle $\phi$ in your expression?

 

[haruspex]

What is angle $\phi$ in your expression?

Seems a reasonable guess that it's the angle the applied force makes to the slope.
So, yes, the 680J is a scarlet kipper.

 

[kuruman]

Seems a reasonable guess that it's the angle the applied force makes to the slope.
So, yes, the 680J is a scarlet kipper.

There is no such angle mentioned in the statement of the problem. To me it looks like a Clupea harengus rubrum introduced by OP. Also, under the assumption that the worker pushes with a force parallel to the incline, the 680 J is needed to find the sine of the angle of the incline a.k.a. the inverse of the mechanical advantage of the incline.

 

[haruspex]

There is no such angle mentioned in the statement of the problem.

There does not need to be.
We are aked for the minimum force. That would include minimising wrt the angle of application. That is what the inequality is doing in post #1.

the 680 J is needed to find the sine of the angle of the incline

We are not given any distances, so I fail to see how the work done can be relevant.

 

[add314]

the 680 J is needed to find the sine

but can it be done by just simply projecting forces on axis (if you build it parallelly to the incline surface). Thus we assume that force imparted by worker is parallel to incline and the gravitational force projection to axis equals to $$m g sin\alpha$$(since no force of friction given), and the alpha is an angle of incline. Therefore $$mgsin\alpha = F$$ Next we get the angle.

 

[rsk]

The 680J allows you to work out the vertical height the box has to be lifted.

Then, since the ramp is frictionless and therefore the only work done is against gravity, 680J is also the work done by moving the box that way so you can work out the distance moved along the ramp. As someone said above you can think about projection of forces, but it's just as easy to say 320N x distance = 680J.

Then your height and the length of the ramp allow you to find the angle.
Edited to add - However, since this is really about ratio and proportion, as @haruspex says above you can do it more simply by using just the ratio of the forces

so instead of sinθ = x1/x2, we'd have sinθ = F2/F1

 

[haruspex]

The 680J allows you to work out the vertical height the box has to be lifted.

It's still irrelevant to the question asked. You could change the 680J to any other value and still get the same answer for the force.

 

[rsk]

It's still irrelevant to the question asked. You could change the 680J to any other value and still get the same answer for the force.

You could, yes. But in any class of students you will have some who instantly spot a mathematical short cut and some who only see that having tried it first with numbers and thinking about the physics.

Since both give the same answer, and since the work was given in the question, there will be no penalty for using it. In the end, the best method is the one which aids the understanding of the individual student.

 

[kuruman]

It's still irrelevant to the question asked. You could change the 680J to any other value and still get the same answer for the force.

Yes. I tried to salvage the 680 J but it's unsalvageable.

 

[haruspex]

You could, yes. But in any class of students you will have some who instantly spot a mathematical short cut and some who only see that having tried it first with numbers and thinking about the physics.

Since both give the same answer, and since the work was given in the question, there will be no penalty for using it. In the end, the best method is the one which aids the understanding of the individual student.

I take a very different view.
It is right and proper that question setters should salt the questions with extraneous information. It's not done often enough. Figuring out what's relevant is all part of gaining a proper understanding, and better reflects the real world.
The penalty for the inefficient approach is time lost in the exam. Full credit to @walking for avoiding the trap here.

 

[rsk]

I take a very different view.
It is right and proper that question setters should salt the questions with extraneous information. It's not done often enough. Figuring out what's relevant is all part of gaining a proper understanding, and better reflects the real world.
The penalty for the inefficient approach is time lost in the exam. Full credit to @walking for avoiding the trap here.

In my experience, figuring out what's necessary often comes as a consequence of using what isn't and hence discovering that it isn't necessary. Indeed, problem sets are often created with that in mind and some students will better understand why the work is unnecessary once they have used it a few times.