## Newton's Second Law in Two Dimensions

### Newton's Second Law in Two Dimensions: Example

There isn't any new physics looking at Newton's Second Law in more dimensions. All we have to work with is our working definition:

The **vector sum** of the forces on **one object** is equal to the mass of **that one object** times the acceleration of **that one object**.

We should put it to good use. The approach used in one dimension is still appropriate.

- Determine a single object.
- Find all forces on that one object.
- Find vector sum of all the forces (use free-body diagram).
- Set equal to the mass of that one object times the acceleration of that one object (also a vector).
- Extract scalar relationships that can connect what you know with what you want to find.

### Newton's Second Law in Two Dimensions: on an Incline

Here is another example of Newton's Second Law. I show an approach to dealing with incline problems.

### Newton's Second Law in Two Dimensions: Hanging Mass

For this example, we look at a mass being hung by a series of ropes. I show another trick in dealing with Newton's Second Law problems, where the object is a vertex of ropes.

### Exercises

*Do Now!* Do these exercises immediately.

*Not Now!* Do these after you start to forget the topic, say in a week.

*More!* More exercises if you want. Maybe review before a test.

### Required Problems

### Solution

1. A 750 kg mass is hanging from two cables, one is set 75 degrees from the horizontal and the other is set 60 degrees. What are the tensions in the cables?

### Solution

2. Using Newton's second law, derive the acceleration of an object sliding down a frictionless surface set an angle q above the horizontal.

### Solution

3. You think a pulley gives you leverage? Your car is stuck and there is a tree 100 m behind you. Instead of using a pulley, you attach a cable between the car and the tree and then pull on the cable in the middle the perpendicular direction with a 10,000 N tension force, T. If the cable is taught at a 2 degree angle (see figure), what is the force pulling on the car?