The second law of motion explains the relationship between force, mass, and acceleration.

The relationship of force to mass and acceleration can be expressed mathematically using the following equation:

Force = mass X acceleration or *F = ma*

The law states that the acceleration of an object depends on the mass of the object and the amount of force applied. Newton's second law of motion is also called the law of force and acceleration.

If we use the same formula for force to solve for acceleration, we can use the following formula:

*acceleration* = force over mass
*force*
*mass*
or *a* = F over m
*F*
*m*

The second law has two parts. Let's break it down and look at each part.

Look at the two carts below. Which one will require the smallest amount of force to push?

You would only have to exert a small force on the empty cart to accelerate it. However, when the cart is full, the same amount of force will not accelerate the cart as much as before.

In the diagram below, three carts with different masses are shown. The red arrows indicate the force applied to the cart, and the green arrows show the resulting acceleration. The size of the force applied to all three carts is the same.

How does the acceleration change in each figure? Click on the green acceleration button to see the answer.

Use your notes to summarize the relationship between the mass and acceleration of an object when the same size force is applied.

Interactive popup. Assistance may be required. If the same amount of force is applied, an object's acceleration decreases as its mass increases.The carts below have boxes with the same mass on them. If we apply different amounts of force, which one will have the greater acceleration? Click on the green acceleration button to see the answer.

Use your notes to summarize the relationship between force and acceleration of objects that have the same mass.

Interactive popup. Assistance may be required. The acceleration of objects (with the same mass) will increase as force increases.