力和加速度

Newton's second law describes the relationship between force and acceleration and this relationship is one of the most fundamental concepts that apply to many areas of physics and engineering.

F equals ma is the mathematical expression of Newton's second law. This illustrates that greater force is required to move an object of a larger mass. It also demonstrates that for a given force acceleration is inversely proportional to mass. That is, with the same applied force smaller masses accelerate more than larger masses

Here we will demonstrate an experiment that validates Newton's second law by applying forces of different magnitudes to a glider on a nearly frictionless air track

Before going into the details of how to run the experiment, let's study the concepts and laws that contribute to the data analysis and interpretation.

The set-up consists of an air track, a glider, a photogate timer at a known distance d from the starting point, a pulley, and a string running from the glider over the pulley.

If one attaches a weight to the other end of the string and releases it, the weight will apply a force on the glider causing it to accelerate. This force is given by Newton's second law. At the same time, the force on the weight will be due to gravitational acceleration minus the tension force in the string connecting the falling weight to the glider. This tension force is the mass of the weight times the acceleration of the glider.

By equating the force on the glider with the force on the weight, one can derive the formula to theoretically calculate glider's acceleration.

The experimental way to calculate the glider's acceleration is with the help of the photogate timer. This gives us the time taken by the glider to travel distance d from the starting point. Using this information, one can calculate the glider's speed and then, with the help this kinematics formula, one can calculate the magnitude of experimental acceleration.

Now that we understand the principles, let's see how to actually conduct this experiment in a physics lab

As mentioned before, this experiment uses a glider connected by a line passing over a pulley to a weight. The glider slides along an air track, which creates a cushion of air to reduce friction to negligible levels.

As the weight falls, the pulley redirects the tension in the line to pull the glider, which has a 10 cm long flag on top. A photogate at a known distance from the starting point records the amount of time it takes for the flag to pass through it

The glider's final velocity is the length of the flag divided by the time to pass through the photogate. With the glider's final velocity and the distance traveled, it is possible to calculate acceleration.

Set up the experiment by placing the photogate timer at the 100 cm mark on the air track and the glider at the 190 cm mark. The glider has a mass of 200 grams. Hold the glider so it does not move and add weights to the end of the string so the total hanging mass is also 10 grams

Once the weights are in place, release the glider, record its velocity for five runs and calculate the average. Use the mass of the glider and the hanging weight to calculate the experimental and theoretical accelerations then record the results.

Now add four more weights to the glider, doubling its mass to 400 grams. Place the glider at the 190 cm mark to repeat the experiment. Release the glider and record its velocity for five runs. Again, calculate and record the average velocity and the experimental and theoretical accelerations.

For the last set of tests, remove the weights from the glider so it has its original mass of 200 grams. Then, add weights to the hanging mass until it has a new mass of 20 grams. Repeat the experiment for another five runs.

Finally, add more weights to the hanging mass until it is 50 grams and repeat the experiment for five more runs.

Recall, the theoretical acceleration of the glider is equal to the acceleration due to gravity g multiplied by the ratio of the mass of the falling weight and the mass of the weight and glider together. As the theoretical values on this table show, acceleration decreases as the mass of the glider increases.

Conversely, acceleration increases as the mass of the falling weight increases, due to the greater force. Note that the accelerations predicted by this equation can have a maximum value of g, which is 9.8 meters per second squared.

Next, let's see how to calculate the experimental acceleration. For example, the first test used a 200-gram glider and a 10-gram weight. The average speed after traveling 100 centimeters was 0.93 meters per second. Using the kinematics equation discussed before, the experimental acceleration comes out to be 0.43 meters per second squared. This same calculation, applied to the other tests, produces the results shown on this table.

The differences between experimental and theoretical accelerations may have several causes, including limitations in measurement accuracy, the very small but not completely negligible friction on the air track, and the air pocket beneath the glider, which may add to or subtract from the force of tension along the string.

Forces are present in almost all phenomena in the universe. Brought down to Earth, forces affect all aspects of daily life.

Striking the head may cause trauma and impair cognitive functions. A study of sports related concussions used special hockey helmets fitted with three-axis accelerometers to measure acceleration during impact.

Data were sent by telemetry to laptop computers, which recorded the measurements for later analysis. Knowing the accelerations and the mass of the head, it was possible to use Newton's second law, F=ma, to calculate the impact forces on the brain.

Civil engineers building footbridges are interested in studying the effect of force induced by foot load on these structures. In this study, the researchers placed sensors on a footbridge that measured vibrations induced by the pedestrians. The structural response was then measured in terms of vertical acceleration, which is an important parameter in studying the stability of these structures

You've just watched JoVE's introduction to force and acceleration. You should now understand the principles and protocol behind the lab experiment that validates Newton's second law of motion. As always, thanks for watching!