# Example: Applying Newton's 2nd law - simple case

## Understanding the situation

Here's an example of a typical problem in which one might use Newton's 2nd law to analyze the forces on an object. What's critical is the creation of diagrams that represent how we are modeling the system: the system schema and the free-body diagram.

## Presenting a sample problem

You are holding your physics book against the wall by pressing on it as shown in the figure at the right. You are pressing hard enough so that the book doesn’t move.

(a) Draw system schema that will help you analyze the motion of the book.

(b) Draw a free-body diagram for the book. For each force identify the kind of force, what object is causing it, and what object is feeling it.

(c) What relations are there among the forces in your diagram? That is, which forces or sums of forces have to be equal? How do you know?

(d) If you press slightly less hard, you discover the book starts to slide downward and after a moment or so it is moving slowly but at a constant velocity. While it is sliding down at a constant speed, what forces have changed in your diagram compared to when it was stationary? Are any of the balances you determined in (c) now invalid? Explain.

## Solving this problem

(a) Your System Schema should include the book, everything that's touching it (hand, wall), and everything that is acting on it through a non-touching force (earth). Since we are only going to be focusing on the book, other items (arm) and other connections are not required. The connections are contact forces (normal and friction – c) and weight (g).

(b) The book is touched by two objects – the hand and the wall – and it has contact forces with each of them. The contact forces involve both normal forces and friction forces. The wall and the hand push the book and the weight of the book tries to pull the book down, but friction forces from the hand and the wall prevent it. The only non-touching force on the book is the force of gravity from the earth pulling it down.

(c) Since the book is stationary, it is not accelerating and the net force on it must be zero. Therefore, both the horizontal and vertical forces have to sum to be equal to zero.

(d) The book is moving at a constant speed so the net force must still be zero by N2. The balances we determined in (c) must therefore still hold. But it says that you are pressing slightly less hard so all of the contact forces will be reduced. You are pressing less hard so the wall is pressing back less hard as well (since it balances your force). Since the frictions are balancing the weight again, they must be the same. (This is possible because we now have sliding instead of static friction.)

Joe Redish 8/14/15

Article 364