Differences for calculating work required to move a book vertically and horizontally?

Question

I'm a bit confused about the difference in calculating work done in vertical and horizontal directions.

WorkDone = Force x DistanceMoved. For forces in a vertical direction the WorkDone is equal to the gravitational potential energy gained. So, the work done lifting a 2kg book through 1.5m is (about) 30 J.

Some books will ask questions of the form: how much work is required to move a 2kg across a 1.5m table? If the book has a weight of (about) 20 N then the answer we arrive at is 30 J.

But intuitively, it is (normally) easier to move things across than it is up - the answers shouldn't be equal.

So am I right in saying that the weight of the book isn't, on its own, important for calculating work done moving the book across the table? And that, in addition, for example, we would need things like surface area, friction per unit of surface area? In other words, it is the force required to move the book rather than weight of the book that is important?

Answer 1

Yes......folks get confused between work and *effort*.

You can hold a book by your hand with your outstretched arm until it burns so bad you no longer have contr5ol over holding it and you drop it. You expend a lot of effort and energy, but...you do no *work*.

Laypeople confuse the utilitarian term 'work' with something that requires action or movement, but the term is a scientific one.

It is, as you pointed out strictly a (cause-and-effect) term used to gain insight into put a number on the movement of some object:

You apply some amount of force.....the object moves some distance....work was done. How much? The product of the applied force multiplied by the distance moved.

This removes the necessity of taking friction into account, and mass and so on. You can push on a skid loaded with automobile parts all day and never move it. You can push as hard as you can and never move it. You can push with 2, 3, maybe 4 people and never move it. That doesn't count for how much 'work' gets done tho.

On the other hand you can use a crane to lift an Easter basket. The same amount of work is done if the crane lifts it 2 feet, or if YOU lift it 2 feet!

The term sort of equalizes things, and that's good because what good is a definition of somehting that is dependent on who does the lifting, wher ethe lifting is done, how fast, how slow, and so on. The word done is the same, AS LONG AS the force applied is the same and the distance moved is the same. That is a useful metric with which to work and measure against.

Does this help you at all?



Whew.....that was a lot of work. ;)

Answer 2

I don’t agree with the following statements in your question.

“Some books will ask questions of the form: how much work is required to move a 2kg across a 1.5m table? If the book has a weight of (about) 20 N then the answer we arrive at is 30 J.”

If you move a book of 2kg across a 1.5 m table, the work is not 30 J.

As you have stated in your later part of the question it depends upon the force you have applied and not upon the weight of the book.

Suppose you apply a force of 2 N the work done is 2 x 1.5 = 3 J

If you apply a force of 6N then the work done is 6 x 1.5 = 9 J and so on.

We can’t calculate the work done in these cases with out knowing the force which we applied on it.

But in the case of vertical displacement we know that the force needed to lift it up is a minimum force equal to the weight of the body.

If the body is lifted up with out acquiring a velocity then the work done = weight x height.

Answer 3

You're right - the "force" portion of the equation refers to whether the book is moved against gravity (ie: moved vertically), or against friction (ie: against the table).

So depending on the actual mass of the book, and the friction coefficient between the book and the surface of the table, the two "work" values can differ.

Answer 4

Ask your teacher. It is a sincere friendly advise. It will increase your confidence level. As these type of questions come to minds of your kind of guys which is quite good! Asking the teacher helps to gain more insight and find out more interesting ideas. More over it needs a quite bit of explanation. For example the friction per surface area you have stated is not right as " friction is independent of area of contact". So feel free to clarify "concepts" from your teacher.