Relating Velocity, Acceleration, and Force to Newton's First Law of Motion

 Question 

So why exactly does an object come to a stop or start moving? How can we tell if an object will continue to move forever?

Objective

By completing this objective you will be able to explain the following:

Shown a tire rolling across a platform and coming to a stop the student will identify the force(s) affecting the tire and explain how those force(s) cause the tire to slow down by accelerating the tire in a direction opposite to the direction of its velocity and thus changing the tire’s state of motion complying with Newton’s first law of motion.

Review of Velocity, Acceleration, and Force

Before we get into that though we should first review some concepts on velocity, acceleration, and force. You should recall that a velocity measures an object's change in position over time, and acceleration measures an object's change in velocity. For example, if while driving you accelerate a car from 50 mph to 60 mph you've essentially changed the car's velocity.

You should also remember that to cause an acceleration a force needs to be applied to an object. For example, if you were to put a coin on your desk and push it, when would the velocity of the coin change the quickest? When you push the coin with a small force or a large force? Take a minute and try it for yourself!

What you should have noticed is that the larger the force the more quickly the coin changes velocity (it moves faster).

Galileo's Inclined Planes

Let's take a few minutes to go over the contributions of Galileo Galilei by reviewing how his work with inclined planes helped to develop the concept behind Newton's first law of motion.

Galileo noted that a ball, rolling down an inclined plane would begin to speed up while a ball rolling up an inclined plane would begin to slow down.

Figure 2

Galileo also noted that the smoother the surface the ball was rolling on the longer it would take the ball to come to a stop. This observation prompted Galileo to hypothesize that if a ball was rolling along a horizontal plane, the ball would keep rolling forever it there was no outside forces affecting the ball's motion.

Figure 3

As you may have noticed this is very similar to what we previously discussed about acceleration and velocity, only here we take it one step further and say that it is a force that causes the ball to come to slow down and come to a stop. But what force(s) do you think are at work here, causing the ball to slow down whether on an inclined plane or a horizontal plane? Take a minute to think about it!

On an inclined plane at least three forces are at work. The force of gravity, which acts vertically, causes the ball to speed up when moving down the inclined plane and causes the ball to slow down while it is moving up the inclined plane. The friction force between the ball and the plane as well as the air resistance between between the ball and the air in the environment cause the ball to slow down as it moves. On the horizontal plane only the force due to friction and air resistance are at work.

Galileo went on to confirm his hypothesis by doing the following experiment. Before watching the video, how do you think Galileo would have confirmed his earlier hypothesis using inclined planes? Take a minute to think about what you might do to confirm or deny Galileo's hypothesis.

From this experiment Galileo combined his ideas and concluded that if there were no forces acting on a moving object, then the object would continue to travel forever without losing any speed. This turns out to be a fundamental property that all objects share, that is, objects tend to resist changes in their motion. We call this property of objects to resist changes in their motion inertia. It should be noted that Newton's first law of motion is often called the law of inertia.

Example Problems

Try your hand at the following questions to test your understanding of the concepts we've covered so far. Solutions are given below.

1). If a tire rolling across a floor comes to a stop, what forces caused the tire to come to a stop?

2). How are velocity, acceleration, and force related to the motion of the tire in the above problem?

3). Identify an example of inertia. Why is this an example of inertia?

Solutions

1). As the tire rolls across the floor the friction force between the floor and the tire and the air resistance between the tire and the air surrounding the tire would cause the tire to slow down.

2). Suppose the velocity of the tire was to the right. The force from friction, F_f, and air resistance, F_R, would be acting towards the left, which means that the acceleration of the tire would be in the opposite direction to the tire's motion, causing the tire to slow down.

Figure 4

3). Suppose you are standing in a bus and not holding on to anything. If the bus started to accelerate abruptly you might fall towards the back of the bus. This is because you are standing still which is what your body wants to keep doing. When the bus accelerates your body wants to stay in the same position. Thus you will feel like you are moving backwards as the bus moves forwards.

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