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AP Physics 2: Exam Prep27 chapters | 158 lessons | 13 flashcard sets

Instructor:
*Betsy Chesnutt*

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

You can use Newton's second law of motion to predict the motion of an object that is acted on by several forces. In this physics lab, learn how to do this and get some practice applying the second law to some real life situations.

Imagine that you are about to jump out of an airplane flying 10,000 feet above the ground. Should you take a parachute? Of course! With a parachute, you will fall more slowly and therefore be much less likely to be injured or killed when you hit the ground.

The rate at which you fall depends on the forces that act on you. There are two main forces that act on any falling object. The Earth exerts a gravitational force downward, causing you to speed up. The air also exerts an upward force on you as you pass through it, which tends to slow you down. While the force of gravity is constant and only depends on your weight, the upward air resistance force depends on many things, including how fast you're moving and your size and shape. A parachute greatly increases this force, causing you to fall more slowly.

Isaac Newton explained the relationship between force and motion in his famous three law of motion. Newton's **second law of motion** says that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. You can use it to predict the motion of an object. The **net force** is the vector sum of all the forces that act on the object.

Since you might not have an airplane and parachute available, in this lab we will try to use Newton's second law to understand and predict the falling motion of two familiar objects, a ball and a plastic cup.

To begin, find a smooth ball, like a baseball or a tennis ball, and a plastic cup. Use a balance or scale to find the mass (in kg) of both objects. You also need a stopwatch, a long string, and a ruler or meter stick to measure distances. You will need to recruit a helper as well!

Next, find a relatively high place from which to drop the objects. A second story window or balcony would be great, but you can also simply stand on a table or chair.

Before dropping anything, you need to measure the distance that the object will fall. Be sure to drop from the exact same height each time. To measure the height, you can drop a string from your hand all the way to the ground, then measure the length of the string (in meters) using a ruler or meter stick.

Since the ball is smooth and round, the air will not exert much force on it while it is falling. Therefore, gravity is the primary force that is determining the motion of the ball. This is similar to what would happen to you when you first jumped out of the plane and didn't deploy your parachute. To predict the motion of the ball, start with a free body diagram, like the one shown below, that shows all the forces acting on the ball.

The force of gravity acting on the ball is equal to its mass (*m*) multiplied by the gravitational acceleration (*g* = 9.8 m/s2). For example, if your ball has a mass of 0.1 kg, then the force of gravity acting on it will be 0.98 N.

Because no other forces act on the ball while it is falling, the net force on the ball is just equal to the force of gravity, and we can use Newton's Second Law to determine that the acceleration of the ball is -9.8 m/s2. This acceleration is negative because the net force is directed downward and the ball is speeding up in a downward direction.

Knowing this acceleration, you can calculate how long it will take the ball to fall using some basic kinematics. Let's assume that the ball falls a distance of -10 m and has an initial velocity of zero. Although your ball should also start with an initial velocity of zero, it probably won't fall exactly 10 m, so make sure that you use your actual measurements when making calculations!

This is the distance equation. Since the initial velocity is zero that term drops out. We only need to have the distance and acceleration to find the time that the object falls.

Now that you have predicted how long it will take the ball to hit the ground, try it and see how accurate your prediction was! Have your assistant hold the stopwatch and time the exact time from the moment the ball leaves your hand until the moment when it hits the ground. Because this may be difficult to measure accurately, you will want to do it several times and find an average time.

So, was your prediction correct? Probably your time was a little longer than what we predicted. Why do you think this happened?

Remember that we assumed that there was NO air resistance force acting on the ball, but in reality, there may have been a small force from the air that caused the ball to accelerate a little bit less than it would if there were really no other forces.

It's a little more complicated to predict the motion of the cup, right? Because of the shape and mass of the cup, the force of the air acting on it will be pretty large. Since we don't know exactly what this force will be, why don't you first measure the time it takes the cup to fall and then use this information to calculate the average air resistance force acting on the cup?

Drop the cup several times from the same height from which you dropped the ball and measure the time it takes to fall each time. From that information, determine the acceleration of the cup. Remember that this acceleration should be LESS THAN 9.8 m/s2.

For example, let's assume that the cup has the same mass as the ball, and is dropped from 10 m again, and falls for 2.3 s. Remember, in your calculations, use the measurements that you made in your experiment! We'll use the same distance equation, but this time we will find acceleration.

Now, draw a free body diagram of the cup as it falls. There should be TWO forces acting on the cup. You can use the free body diagram to write out an equation for Newton's Second Law to find the force that the air must exert on the cup.

From this, you can see that the air exerted an average upward force of 0.6 N while the cup was falling. Now you try it and find the force on your cup!

Newton's **second law of motion** says that the acceleration of any object is directly proportional to the **net force** acting on it and inversely proportional to its mass. In this lab, we were able to use the second law to predict the motion of falling objects.

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AP Physics 2: Exam Prep27 chapters | 158 lessons | 13 flashcard sets

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