The Relationship Between Mass And Acceleration

Mass is a property of matter equal to the measure of an object’s resistance to changes in either the speed or direction of its motion. The mass of an object is not dependent on gravity and therefore is different from but proportional to its weight.

Speed is the time rate of change of position of a body without regard to direction. Linear speed is commonly measured in such units as meters per second, miles per hour, or feet per second. Velocity represents speed but according to the bodies direction. We can calculate from a distance time graph with dy/dx.  

Acceleration describes the time rate the velocity is changing at. The relationship between acceleration and velocity is like the relationship between velocity and displacement. Acceleration is a vector quantity. For uniform velocity, a = 0. If ‘a’ is a non-zero constant, the object is said to be uniformly accelerated. The average acceleration of an object is defined as:

Average acceleration = change in velocity / time taken

In my investigation, I will aim to find the relationship between mass and acceleration.

Method

I will do this be setting up an apparatus which will measure the rate of acceleration. First, I will set up a height of 15cm and length of 227cm ramp. At this height, I do not have to apply a force to the trolley to accelerate the trolley because it will be able to slide down due to the force of gravity. This way, the force of gravity can be kept constant. Then, I will use a ticker machine and ticker tape to measure the rate of acceleration. I will stick the ticker tape into a trolley of 850g and let it fall. Each 10 mark on the ticker tape represents 0.2 seconds so I will cut the ticker tape in strips of 10 marks. By plotting the strips onto a graph, it would tell us the speed in which the trolley travelled. From this, we can calculate the acceleration of the trolley:

Acceleration = final velocity – initial velocity =   D v        

                                       Time                             t

I used a ticker machine to calculate the rate of acceleration because it would show the rate in which acceleration changes. If we just timed how long it takes for the trolley to reach the end of the trolley, it would only give us the average acceleration. It would not be possible to measure the change in acceleration.

I chose 15cm height ramp because from our preliminary results we found the marks on the ticker tape appeared most clearly at this height. Previously, the height of the ramp was 43cm and it was too high of the marks to appear clearly and because of this, my results weren’t as accurate.

The average angle of the ramp was 3.87 ÌŠ. I chose this angle because I found from preliminary results that if the angle is too high, the marks on the ticker tape would not print accurately. Before, the average angle was 10.7 ÌŠ and we found it difficult to read the ticker tape.

I clamped the ramp in place because this way, the height of the ramp is less prone to change so it acceleration will only be affected by the mass of the trolley. This will make our results more accurate.

I added 400g of mass each time because from preliminary tests, I found that the ranges of the results were too close to each other to see a correlation when we added 100g each time. So to make the results more clear to see if mass affects acceleration, I decided to add more weights. This way, there would be a greater difference in the results and it would be clearer to distinguish a correlation.

I chose a trolley of 850g because the trolley was light weight and the wheels were fairly smooth. Because it was light weight it would be easier to add mass on and be less affected by friction. Because the wheels were smooth, the frictional force would be less. This will make our results more accurate.

To keep my investigation fair, I will only change one factor- the trolley’s mass. I will keep everything else the same such as the height of the ramp and the ramp itself because these factors would affect the results if they’re are not kept the same.

Prediction

I predict that the mass of the trolley will not affect the rate of acceleration. This is because according to Galileo’s laws of motion, all bodies accelerate at the same rate regardless of their size or mass. For example, the fact that a feather falls slower than a steel ball is due to amount of air resistance that a feather experiences (a lot) versus a steel ball (very little).

Also according to Newton’s second law, the acceleration and gravitational force of a body is directly proportional to each other. He adds to Galileo’s law of motion by saying everything falls at the rate of 9.8m/s.

He calculates this by:

(F=force, m=mass of Earth (), a=acceleration, r=radius of Earth, G=gravitational constant (6.7-10‾ᶥᶥ Nm²/kg²), g=gravitational force)

If F=ma and F=gm

ma=gm

So you can cancel m to get a=g

Factors which affects the rate of acceleration:

Friction would affect the rate of acceleration because it increases the reluctant force by griping on the wheels and increasing the time it takes for the wheels to turn. Sometimes this can be good because it makes cars easier to manoeuvre. To show that friction affects the acceleration, we could carry out the same experiment, but instead of changing the mass, we would add different materials to the ramp. This would show us how surface area affects acceleration.

The gradient in which the body is travelling would also affect the acceleration because some of the force would go into the other direction instead of going down so it experiences more drag. This would increase the time it takes for the body to fall. We can show this in our experiment by increasing the angle of the ramp instead of mass.

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The shape of the body will also affect its acceleration because the more wide it is the more air resistance/ drag it will have. Air resistance slows down an object because it opposes a force in the opposite direct to gravity, so the force of gravity is less. We can show this by changing the size of the surface area of the trolley but keeping mass the same.

Results

Average Acceleration

From the graph, we can see that generally, as the mass increases, so does the acceleration. There’s a steep liner gradient from 850g-1650g, and acceleration increased by 4.82ms‾². Even though the actual results shows a decrease in acceleration between 1650g-2100 by 0.53 ms‾², the line of best fit tells us it is actually increasing. Overall, acceleration increased by 0.2m/s‾² every 100g that was added.

Average Speed

The average speed shows as the mass increased, so does its speed. There is a liner gradient between 850g-1250, and the speed increased by 1.7cm/s. From 250g-2050g, the speed decreases by 0.75cm/s². However, from 2050g-2450g, the speed increases again by 0.66cm/s². Overall, although it decreases, the line of best fit shows that it increases greatly from 850g-1250, then the line starts levelling out from 1250g-1450g.

Accuracy Rating

The accuracy rating generally shows that as the mass increases, the level of accuracy also increases. This graph shows the higher the number of accuracy, the lower the level of accuracy. There is a huge fall in the number of accuracy rating between 850g-2050. It went from 38.67 to 29, a difference of 9.67. From 850g-2050g, the number of accuracy kept decreasing and overall, it decreased by 14.3. However, from 2050g-2450g, it increased by 2.

This may be because as mass increases, the bigger the friction is on the wheels. The larger the friction the better the wheels can grip on the surface so travels more accurately and is less likely to skid. This tells us, the results of acceleration and speed for 850g is very likely to be an outlier because the level of accuracy is very low.

Comparison:

When we compare the results of the average acceleration to its speed, we can see it’s directly proportional because as the acceleration increased, so did the speed. This is because acceleration shows how speed changes.

When we compare the level of accuracy to the acceleration and speed, it tells us the results for 850g is very likely to be anomalie and possibly 1250g as well. If that were true, the graphs would show that there is no connection an object’s mass to its acceleration. This would prove Galileo’s law of motion and Newton’s second law that the rate of acceleration is constant and is not affected by size or mass.

However, our experiment does prove their theories are correct because our experiment shows that the less resultant forces oppose to gravity (more friction in this case), the faster the body accelerates and does not depend on its mass.

Evaluation

I believe my experiment went fairly well because I felt I could justify the reasons why I obtained these results and although I have some anomalies, most of the results were fairly accurate.

However, there were some flaws in my experiment such as:

I found it hard to set off the trolley at the position on the ramp each time because it was not marked clearly.

I did not wipe/grease the ramp after each experiment, doing this would have make the friction of the ramp more consistent

When I plotted the strips of ticker tape on the graph, I did not line them accurately on the squares. This made some of my results inaccurate.

Improvements

To improve my experiment, I would have made the height of the ramp lower because it would experience more friction for the wheels to grip on. I would have also used trolleys with different masses but the same density. This way, drag/air resistance be more likely to be the same so there would only be one factor affecting the results. This would make out results more accurate.

To obtained accurate results, we can perform this experiment in a vacuum. This is because in a vacuum, you would not experience any resultant force as you do in Earth so you could accurately calculate acceleration. However, we can only experience a vacuum in space.

In earth, to decrease resultant forces, we can carry out this experiment in:

Under water

High altitude

Air tight conditions