## SAT Physics Subject Test

**Chapter 3 ****Newton’s Laws**

**THE SECOND LAW**

Newton’s second law predicts what will happen when a force *does* act on an object: The object’s velocity will change and it will accelerate. More precisely, it says that its acceleration, **a**, will be directly proportional to the magnitude of the total—or *net*—force (**F**_{net}) and inversely proportional to the object’s mass, *m*.

**F**_{net} = *m***a**

This is the most important equation in mechanics!

The mass of an object is directly related to its weight: The heavier an object is, the more mass it has. Two identical boxes, one empty and one full, have different masses. The box that’s full has the greater mass, because it contains more stuff; more stuff means more mass. Mass is measured in**kilograms (kg)**. (Note: An object whose mass is 1 kg weighs about 2.2 pounds on the surface of the Earth, though, as will be discussed later, mass and weight are not the same thing and should not be confused with each other.) It takes twice as much force to produce the same acceleration of a 2 kg object than of a 1 kg object. **Mass** measures an object’s inertia—its resistance to acceleration.

**The Skinny on the Second Law**

This law defines force. The second law relates the acceleration an object of a certain mass experiences when a force is applied to it. The larger the force on the object, the larger its acceleration. It’s like the difference between pulling a wagon filled with heavy packages alone and having a friend help you pull. The wagon pulled by your joint force has a greater acceleration.

F_{net} is the sum of all the forces acting on an object. Beware, there can be forces acting on an object without causing a net acceleration. This happens when the forces cancel each other out—that is F_{net} = 0 N.

Forces are represented by vectors; they have magnitude and direction. If several different forces act on an object simultaneously, then the net force, **F**_{net}, is the vector sum of all these forces. (The phrase *resultant force* is also used to mean *net force*.)

Since **F**_{net} = *m***a**, and *m* is a *positive* scalar, the direction of **a** always matches the direction of **F**_{net}. Finally, since *F* = *ma*, the units for *F* equal the units of *m* times the units of *a*.

**Force vs. Motion**

Remember that an object

does not have to move in

the direction of the net

force, in the same way

that an object doesn’t

have to move in the

direction of acceleration.

[F] = [m][a]

= kg·m/s^{2}

A force of 1 kg·m/s^{2} is renamed 1 **newton** (abbreviated N). A medium-size apple weighs about 1 N.

The relationship between the direction of net force and velocity is the same as the relationship between acceleration and velocity. Forward forces speed up objects, backward forces slow down objects, and forces perpendicular to the velocity are responsible for turning.

1. What net force is required to maintain a 5,000 kg object moving at a constant velocity of magnitude 7,500 m/s?

Here’s How to Crack It

The first law says that any object will continue in its state of motion unless a force acts on it. Therefore, no net force is required to maintain a 5,000 kg object moving at a constant velocity of magnitude 7,500 m/s. Here’s another way to look at it: Constant velocity means **a** = 0, so the equation **F**_{net} = *m***a** immediately gives **F**_{net} = 0.

2. How much force is required to cause an object of mass 2 kg to have an acceleration of 4 m/s^{2} ?

Here’s How to Crack It

According to the second law, **F**_{net} = *m***a** = (2 kg)(4 m/s^{2}) = 8 N.

3. An object feels two forces: one of magnitude 8 N pulling to the left and one of magnitude 20 N pulling to the right. If the object’s mass is 4 kg, what is its acceleration?

Here’s How to Crack It

Forces are represented by vectors and can be added and subtracted. Therefore, an 8 N force to the left added to a 20 N force to the right yields a net force of 20 –8 = 12 N to the right. Then Newton’s second law gives **a** = **F**_{net}/*m* = (12 N to the right)/(4 kg) = 3 m/s^{2} to the right.