# Predicting the Motion of an Object: Physics Lab

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.

## How Fast Will You Fall?

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.

## Newton's Second Law

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.

## Getting Started

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.

## Part 1: Dropping a Ball

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.

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