Newton's Second Law

Have you ever crashed your toy cars together and noticed that one of the cars remained in its position while the other car was launched in the opposite direction? This is an application of Newton's Second Law of Motion. The force an object possesses equals its mass, multiplied by the acceleration of the object. If one object has a larger mass and it is accelerated at the same rate as another object with a smaller mass, the object with the larger mass will produce more force than the smaller object.

Several toys use this principle to entertain us as we play with them. When you fire a ball in a pinball machine, for instance, the force generated by the spring is great enough to overcome the inertia of the projectile and accelerate the ball up the track to enter the game area. Other toys that fire projectiles, launch flying objects, or accelerate objects to perform actions also take advantage of Newton's second law. Many simple machines that are components of toys also follow this principle. Levers, pulleys and wheel and axles all make up components of toys that allow forces to be transferred in different directions making toys move as they do.

This can also be demonstrated easily with a baseball and a baseball bat. The ball has a relatively small mass compared to the bat, but when the pitcher throws the ball it is accelerated to high a degree. The bat has a much larger mass than the ball, but is accelerated at a slower rate. Based on Newton's second law, the difference in mass causes the bat to have more force than the ball even though it is accelerated less. This sends the ball in the opposite direction of the swing of the bat resulting in a hit.

Force

This can be demonstrated mathematically by the following formula:

F = m x a

F = Force (N)

m = mass (kg)

a = Acceleration (m/s²)

The force of an object is determined by an object's mass and how much it is accelerated. The ball in our example is small in mass but is accelerating at a high rate. The bat has a higher mass but is accelerating at a slower rate. We can examine this in the following scenario:

Example 1: A baseball with a mass of 0.1 kg is accelerating at 40 m/s². What force would be generated by the ball?

F = ma

F= (0.1 kg)( 40 m/s²)

F= 4 N

Example 2: If the bat has a mass of 0.57 kg and is swung with an acceleration of 9.2 m/s² what is the force generated by the bat.

F= ma

F = (0.57)(9.2m/s)

F = 5.2 N

As you can see, the bat generates more force than the baseball, which causes the ball to move in the opposite direction. This is only part of the story; we also have to take into account the momentum of the ball and the bat.

Momentum

Momentum is also an application of Newton's second law. Momentum is the product of an object's mass and its velocity. You can think of momentum as a way to express how difficult it is to stop a moving object. When objects have a large mass, they do not have to be moving very fast in order to carry a lot of momentum. This does not mean that small objects cannot carry a lot of momentum, but they will have to be travelling at a high velocity to obtain the same momentum. This is easier to understand if we look at this mathematically.

p = m x v

p= momentum (kg • m/s)

m = mass (kg)

v= velocity (m/s)

As you can see if you increase the mass or the velocity of an object the momentum will increase. Let's take two toy cars as an example: There is a toy that allows the users to crash hot wheel cars together on a track called the Criss Cross Crash. The users were able to accelerate two cars and create a head on collision by depressing a spring and releasing the energy to the car. Let's use this example to demonstrate momentum.

Example 1: If a 0.25 kg car is traveling at 4 m/s and a .5 kg car is travelling at 4 m/s which car will have the greater momentum? Which car will survive the crash the best?

Let's look at the first car:

p = m x v

p = (0.25 kg)(4 m/s)

p = 1 kg • m/s

Example 2: Now let's look at the second car:

p = m x v

p = (0.5kg)(4m/s)

p = 2 kg • m/s

As you can see from the calculations, the second car has the greater momentum and therefore would fare better in the crash.

Using Newton's second law we can describe the forces generated by an object. We can calculate the amount of force generated by an accelerating object and we can determine the amount of momentum that an object possesses at a given velocity. In this section we looked at forces that are working independently when in reality forces always exist in pairs. In the next section we will look at Newton's third law of motion and examine the nature of forces in real world applications.

[CC BY 4.0] UNLESS OTHERWISE NOTED | IMAGES: LICENSED AND USED ACCORDING TO TERMS OF SUBSCRIPTION