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# Newton's Laws of Motion: Effect of Masses on Acceleration

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## 1. Introduction

### 1.1 Background Information:

Newton’s second law of motion states that the acceleration of an object depends on two variables: the net force acting on the object and mass. The acceleration of an object is dependent directly upon the net force acting on the object, and inversely to the mass of the object. Acceleration is the total rate at which an object changes its velocity. However net force is the vector total of forces acting on a particle or body. Mass is inertia or resistance to change of motion. It is a property that determines the body's acceleration under the given force.

Equations for Mass and Acceleration:

• Mass​=force ÷ acceleration (m=F/a).
• Acceleration: ​The formula for acceleration is below:
• Newton’s second law equation: ​In equation form, Newton's second law of motion is a = F net m. This is often written in the more familiar form: F​net​ = ma.

A real-world example of where Newton’s second law of motion applies is ​riding a bicycle which is a good example of this law of motion at work. Your bicycle is the mass. The leg muscles pushing on the pedals of your bicycle is the force. Another example is if you use the same force to push a truck and push a car. The car will have a greater acceleration than the truck because the car has less mass. On the other hand, mass is very crucial to study because it helps with the study of chemical reactions which is an important component in science. If scientists are able to know the quantities of reactants for a certain reaction, then it will be easier to predict how much amounts of that product need to be made.

Newton’s second law of motion is important because it shows us the relationships between forces and motion. It also allows you to find the acceleration of an object. This is incredibly useful information for scientists, engineers and inventors which will help them in their jobs.

### 1.2 Research Question/ Problem/Aim :

How does the different masses (100g and 500g) affect the overall acceleration of the trolley, does it accelerate faster or slower?

### 1.3 Hypothesis:

The heavier the mass on the trolly the more time it will take to accelerate. However the less mass on the trolly the faster it will accelerate because when the force acting upon the object is increased, the acceleration of that object is increased. As the mass of an object is increased, the acceleration of that object is decreased. This is based on Newton’s second law of motion. In this experiment however, the 100g mass will accelerate faster than the 500g mass because it’s lighter.

### 1.4 Variables:

#### Variables:

Independent variable: The masses used in the trials:

• 100g
• 500g

Each mass was used in the trials along with 3 repeats

Dependent variable: The final change in acceleration in both of the different trials.

Control Variables:

Why is it controlled: Method to control:

The force applied(0.1):

It’s important that throughout the whole experiment the same force is applied to provide a fair test and accurate results.

Pulling the cart at a constant speed will help give accurate results, instead of speeding up then suddenly slowing down.

The distance marked (total distance was 2 meters): These were all measurements It’s important that the distance between all the points are properly marked to make sure that not only our results are reliable but to make the other tests fair.

By using the meter stick you can accurately find the points that need to be marked with tape. This way your data can be accurate.

## 2. Procedure

### 2.1 Materials:

#### Materials

Materials: Measurements: Quantity:

• Stopwatch or phone - 1
• String - 1
• mass block 1 100g 1
• mass block 2 500g 1
• Spring scale - 1
• Marker - 1
• Roll of tape - 1
• Cart/trolly n/a 1
• Meter stick 1 meter 2
• Measuring scale n/a 1

### 2.2 Diagrams and Photographs of the experiment:

Image 1:​ A image f the cart where the masses were placed during each repeat

Image 2:​ Image of the setup for the experiment

### 2.3 Method

1. Gather all the materials
2. Get a cart and then place a 100g mass block on top of the cart
3. Weigh the mass of the cart and record it in Trial 1
4. Attach the spring scale to the cart
5. Place the cart with the spring scale attached to it at the beginning of the track
6. Then place the meter stick on the table and mark with your tape the different spots the cart will pass (the marks it will pass is: 0.25m, 0.50m, 0.75m, 1.0m, 1.25m, 1.50m, 1.75m, 2.0m)
7. Every time the cart passes one of the marks press lap on your phone
8. The cart will be pulled until the last mark which is 2.0m
9. Record the force used to pull your cart (This should be the same for all carts and trials as well as if you do any repeats)
10. The data you collected from the experiment will be recorded on the table you were given at the beginning of this experiment
11. Repeat this procedure again with the cart and the 500g mass block to be able to interpret the data

### 2.4 Safety Precautions

1. Make sure that your experiment is being conducted inside of a lab
2. No one should have any kind of food or drink inside the lab
3. For girls, make sure your hair is tied up to avoid it getting caught on anything
4. Also, make sure when whoever in your group is pulling the cart, everyone who is timing should take a step back so that when the person pulling the cart moves no one gets in their way and results in them being injured.
5. Don’t conduct the experiment in a area that will harm the environment or any living organism
6. Don’t eat or drink anything during the experiment or in the lab at any time.

## 3. Results

### 3.1 Raw Data: (​Table 1: ​Shows the different trials and repeats for both the 100g and 500g)

Trial 1:(100g)

Mass: 611.5g

Force: 0.1

Distance Traveled (seconds)

0.25m 0.50m 0.75m 1.0m 1.25m 1.50m 1.75m 2.0

Repeat 1: 1.17 2.16 2.9 3.79 4.31 5.65 6.13 6.8

Repeat 2: 1.91 2.7 3.44 4.2 5 5.77 6.33 6.97

Repeat 3: 1.79 2.79 3.68 4.41 5.07 5.82 6.75 7.39

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Trial 2:(500g)

Mass: 1,024.2g

Force: 0.1

0.25m 0.50m 0.75m 1.0m 1.25m 1.50m 1.75m 2.0

Repeat 1: 1.80 3.13 4.23 5.08 5.85 6.65 7.4 7.96

Repeat 2: 1.56 2.8 3.92 5.97 7.03 7.64 8.27 8.86

Repeat 3: 1.68 3.08 4.5 5.03 5.91 6.57 7.43 8.93

Table 2: Averages for both trials (100g and 500g) (seconds)

0.25m 0.50m 0.75m 1.0m 1.25m 1.50m 1.75m 2.0m

Trial 1: 1.62 2.55 3.34 4.13 4.79 5.75 6.40 7.05

Trial 2: 1.68 3.02 4.10 5.36 6.26 6.95 7.70 8.58

Table for Acceleration of each trial

Trial 1 Trial 2

a= F/m

a= 0.10/0.6115

a= 0.16N/kg

a= F/m

a= 0.10/1.0242

a= 0.10N/kg

Graph 1:

Graph 2:

## 4. Discussion

### 4.1 Conclusion

​In conclusion, Newton’s second law of motion is related to force, acceleration and mass. We can conclude from the experiment that when the mass increased, the force needed to accelerate or move the car increased as well. From the experiment, we also can conclude F to m and a are directly proportional while m to a is indirectly proportional. We can confirm this claim by using the acceleration formula (A = f/m) for each trial because the force that applied was constant. We can also conclude that when any object's mass is increased, the force required to accelerate will decrease.

### 4.2 Evaluation

My hypothesis was supported because I had stated that the less mass the trolly carried the faster it will accelerate because as the force acting on the object is increased, the acceleration of the object is also increased. As the mass of an object is increased, the acceleration of that object is decreased. This the experiment proves that the 100g mass block accelerated faster than the 500g mass block mainly because 100g is lighter than 500 which is why it took a minimum amount of time for the trolley to get to the end of the track with 100g block.

### 4.3 Evaluating the method

Our method was sufficient because we didn’t do the experiment on the floor as this would have slowed down the cart because the floor was bumpy. We decided to do it on the table because it was a smooth surface and would allow the trolley to move with ease. Another thing we did was we had repeats for the trials, this was to ensure our data was reliable which is why we took a while to finish conducting our experiment. We also had more than one person timing; we had 3 people doing it. We did this so if someone didn’t time correctly we had spare times to write in our data, if both of the timings were completely different from each other we would do the whole thing again because that means an error took place. However most of the time when we ran the trials and repeats everyone got the same times.

One thing to improve in our method for next time is to make sure our measurements are accurate because we had to restart 2 times because we didn’t measure properly, however the first 2 runs were tests to make sure everything was working so it didn’t affect our data.

### 4.4 Improvements

One of the biggest improvements for this experiment is the way the timing was carried out. Although we did 3 repeats which gave us an average after we completed the experiment. In some of the columns they times were off by at least 2 or 3 seconds, which affected our overall average. Although it wasn’t a very big deal, our results aren’t considered accurate. This is because the way we timed the trolly in one of our repeats was incorrect. Another improvement we can make is the fact that when the experiment was taking place we were all clustered next to the person pulling the trolly with the spring scale. This not only was dangerous but also affected the results because someone was blocking their way, which is what lead to us having to do several practices before actually collecting data and filling our tables.

### 4.5 Final conclusion

The less mass an object carries the faster it will accelerate, however, if an object is carrying a heavy mass the acceleration will be much slower.

## 5. Bibliography

1. “Force, Mass & Acceleration: Newton's Second Law of Motion.” ​LiveScience​, Purch, www.livescience.com/46560-newton-second-law.html.
2. schema Follow. “Newton's Laws of Motion with Real-Life Examples.” ​LinkedIn SlideShare​, 26 Apr. 2014, www.slideshare.net/icheema/newtons-laws-of-motion-with-real-life-examples.
3. Jha, Alok. “What Is Newton's Second Law of Motion?” ​The Guardian​, Guardian News and Media, 11 May 2014, www.theguardian.com/science/2014/may/11/what-is-newtons-second-law-of-motion.
4. “Newton's Laws of Motion.” ​NASA​, NASA, www.grc.nasa.gov/www/k-12/airplane/newton.html.
5. “Newton's Second Law of Motion.” ​NASA​, NASA, www.grc.nasa.gov/WWW/k-12/airplane/newton2.html.
6. “Newton's Second Law of Motion.” ​The Physics Classroom​, www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law.
7. Admin. “Newton's Second Law Of Motion - Application, Examples & Momentum.” ​BYJUS​, Byju's, 23 Jan. 2020, byjus.com/physics/newtons-second-law-of-motion-and-momentum/.
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Newton’s Laws of Motion: Effect of Masses on Acceleration. (2022, September 27). Edubirdie. Retrieved February 26, 2024, from https://edubirdie.com/examples/newtons-laws-of-motion-effect-of-masses-on-acceleration/
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