# Example: Newton 1

## Understanding the situation

Newton's 1st law plays out in different ways for different situations. Let's consider how the forces balance (or don't) on these different cases.

## Presenting a sample problem

Draw free-body diagrams and identify the forces acting on the following objects:

1. A piano being pushed but remaining at rest sitting on the floor
2. A piano being pushed along the floor at a constant velocity
3. A goat sliding on ice on a level puddle
4. Stopping a speeding express train.

## Solving this problem

To begin with each problem we should consider a system schema: What are the objects we need to consider and what are their interactions? For each, we have the object of interest, the earth pulling it down (by gravity), the earth touching it (contact force), and, in the case of the pushed piano, someone pushing it.

Here's what the free-body diagrams look like for each case.

1. The person pushing the piano is not pushing hard enough to get it moving. Since it's velocity is not changing, the forces on it must be balanced — the up forces balancing the down forces and the left forces balancing the right forces. The free-body diagram is shown at the right. The friction force balances the person's push. To get it moving, the pusher would have to push harder than the maximum friction.

2. If the person pushing has gotten the piano started and wants to keep it moving at a constant velocity, the person has to push with a force EQUAL to the force of friction, so the forces balance and the velocity doesn't change.

3. Balancing the forces on a moving object restores the situation equivalent to an object moving on a frictionless surface. If the goat is sliding on the ice and the ice has negligible friction, no force is needed to keep it going. It has a velocity and there is nothing acting in a horizontal direction to change that.

4. If you want to slow down a massive train moving to the right, you need a force acting to the left. When the train locks its wheels using its brakes (fixing the wheels so they can't turn), the wheels slide along the rails provided maximal friction pointing back to the left and slowing the train down.

Joe Redish 9/21/14

Article 519