# Newton's Laws of Motion Lab Question

• Elkay
In summary, the conversation discusses a lab where the acceleration of two masses connected by a string and hanging on a pulley was calculated. The data showed that as the masses became closer in value, the percent difference between the experimental and theoretical accelerations increased. This was due to factors such as the inertia of the pulley and friction, which were not accounted for in the theoretical calculations. However, if the masses were significantly different, these factors were negligible and the values were closer to the theoretical value. The conversation ends with a request for clarification on why this happens.

#### Elkay

I performed a lab where I had to find the acceleration of two masses that were connected by a string and hanging on a pulley. The equation used was:

After performing the calculations I got the following data:

Looking at my data, I noticed that as M1 and M2 became closer in mass, the percent difference between the experimental acceleration and the theoretical acceleration became larger and larger. I don't quite understand why that would happen. My lab instructor tried to explain it to me, but I didn't get it. So I'm hoping that someone here could help. Thank you.

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hmm...

it would seem that as m1 and m2 approach the same value then the acceleration of the system will get closer to 0

since the forces on both sides of the pulley would be balanced

that's fine, but you're not actually setting the masses exactly equal, and so you should have some acceleration, the theoretical one you calculated

however...when you are actually measuring this in a real world setting and the acceleration is getting quite small, well then the other factors start to play a larger role

the other factors being: the inertia of the pulley, the friction between the pulley and the string, and the friction of the bearing in the pulley, and I suppose if you were taking incredibly accurate measurements (perhaps the strain that the masses cause in the string, and the air resistance and...blah blah, lol)

in doing the theoretical calculations, you did not take these factors into account...but as you see from the values in the actual experiment, they are there

however, if the difference between m1 and m2 is quite large, then these factors are basically negligible and that's why your values for the greater differences between the masses are closer to the theoretical value

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I would first like to commend you on your well-designed experiment and accurate data collection. Your results clearly show a relationship between the masses and the acceleration, as predicted by Newton's Second Law of Motion (F=ma).

The increase in percent difference between the experimental and theoretical accelerations as the masses become closer in value is likely due to experimental error. In this case, the error could be caused by the string not being perfectly taut, the pulley not being completely frictionless, or human error in measuring the masses or timing the motion. As the masses become more similar, even small errors can have a larger impact on the results.

To minimize these errors, it is important to carefully control and measure all variables in the experiment. Additionally, repeating the experiment multiple times and taking an average of the results can help to reduce the impact of any individual errors.

Overall, your experiment and results demonstrate the fundamental principles of Newton's Laws of Motion and the importance of careful experimental design and data analysis in scientific research. Keep up the good work!

## 1. What is Newton's first law of motion?

Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest and an object in motion will continue in motion with a constant velocity unless acted upon by an external force.

## 2. How does Newton's second law of motion relate force, mass, and acceleration?

Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that the more force applied to an object, the greater the acceleration will be, and the more mass an object has, the less it will accelerate.

## 3. What is the formula for calculating force using Newton's second law of motion?

The formula for calculating force is F = ma, where F represents force in Newtons, m represents mass in kilograms, and a represents acceleration in meters per second squared.

## 4. How does Newton's third law of motion explain action and reaction forces?

Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that when an object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

## 5. How can Newton's laws of motion be applied in everyday life?

Newton's laws of motion can be applied in everyday life in numerous ways, such as understanding the movement of objects in sports, predicting how a car will accelerate and decelerate, and even explaining the motion of planets in our solar system. These laws are also used in engineering and design to create structures and machines that function properly and safely.