## 9 (e) F=ma

The Second Law of MotionSuppose you are baby-sitting two children who love wagon rides. Their favorite part is when you accelerate quickly. When you get tired and sit in the wagon, one of the children pulls you. He soon finds he cannot accelerate the wagon nearly as fast as you can. How is the wagon’s acceleration related to the force pulling it? How is the acceleration related to the wagon’s mass?

According to Newton’s second law of motion, acceleration depends on the object’s mass and on the net force acting on the object. This relationship can be written as an equation.

f=ma

Acceleration is measured in meters per second per second (m/s2), and mass is measured in kilograms (kg). According to Newton’s second law, then, force is measured in kilograms times meters per second per second (kg·m/s2). The short form for this unit of force is the newton (N). Recall that a newton is the SI unit of force. You can think of 1 newton as the force required to give a 1-kg mass an acceleration of 1 m/s2.

Changes in Force and Mass

How can you increase the acceleration of the wagon? Look again at the equation. One way to increase acceleration is by changing the force. If the mass is constant, acceleration and force change in the same way. So to increase the acceleration of the wagon, you can increase the force used to pull it.

Another way to increase acceleration is to change the mass. According to the equation, acceleration and mass change in opposite ways. If the force is constant, an increase in mass causes a decrease in acceleration. The opposite is also true: A decrease in mass causes an increase in acceleration with a constant force. To increase the acceleration of the wagon, you can decrease its mass. So, instead of you, the children should ride in the wagon.

What are two ways to increase the acceleration of an object?