Exploring Newtons 2nd Law of motion

How does the mass of a ball affect the distance it will travel ?
Exploring Newtons 2nd Law of motion.

Background Research
How does changing the mass of an object effect how far it will travel ?
This question can be answered by Newtons 2nd law of motion; Force equals mass multiplied acceleration (F= ma). This law states that a force on an object will cause it to accelerate in the direction of the force. The greater the force exerted on the object, the greater the acceleration. But how does mass effect this ?
To find out, an experiment will be put into place where the force will be applied by rolling balls of different masses down a ramp.
The distance an object travels once in motion depends on the force initially applied to it as well as any counteracting forces, such as friction or air resistance.
The greater the mass of the ball rolling down the ramp, the farther it should travel when the force begins the same.
An example of how this relates to real life is the scenario of two people at a water park. If a man with a large mass and a man with a smaller mass race down a water slide, the slider with the larger mass will reach the bottom first and travel further. Present, is the frictional resistance on the slide as well as air resistance on the body of the slider. Both these resistances will slow down the sliders.
The total acceleration is equal to the force of gravity minus the force of air resistance and divided by the mass.
The force of air resistance is the same for both sliders, however the force due to gravity is equal to mass times acceleration due to gravity. This means the slider with greater mass will travel at a larger total acceleration, hence traveling a longer distance in most cases.
As discovered later on through the experiment, solid balls travelled further than balls that were hollow. This is because the closer the mass is to the axis of rotation, the easier to add angular velocity to the object. Hence, this increases the speed. This can be related to real life in the form of a figure skater. When spinning, they often bring their limbs closer to their body to assist in the escalation of their speed.
In this experiment, the force will be applied by rolling balls of different masses down a ramp. The distance travelled by the ball on the flat surface will then be measured and recorded. This information will be used to verify Newtons 2nd Law of motion.
Sources:
Stack exchange inc. 2014. Why is the moment of inertia for a hollow sphere higher than a uniform sphere? http://physics.stackexchange.com/questions/100444/why-is-the-momentof-inertia-for-a-hollow-sphere-higher-than-a-uniform-sphere (accessed
University of Virginia physics department. 2003. Newton 's 2nd Law of Motion! A Physical
Science Activity. http://galileo.phys.virginia.edu/outreach/8thGradeSOL/Newtons2Frm.htm
(accessed

Aim
The aim of this experiment is to investigate which ball travels the furthest in consideration of each balls mass.

Hypothesis
The water filled toy ball will travel the furthest, having the largest mass.

Materials and Equipment
Timber ramp - approximately 80 degree angle
Measuring tape
Kitchen scales
Soft play toy ball*
Golf ball*
Tennis ball*
Water filled toy ball*
* When carrying out your own experiment you may different balls as long as they vary in mass. Variables
Independent- The mass of the ball is the only thing to be changed.
Dependent- The distance that each ball travels is what is being measured.
Controlled- Variables that must remain the same include the starting point and the slope of the ramp. As well as the force applied to the ball and the surface that the ball rolls on.

Method
1. Weigh each of the four balls using a kitchen scale and record results.
2. Set up the timber ramp on a flat surface and have the slope of the ramp on an 80 degree angle.
3. Take one of the four balls and place it on the top of the ramp. Release the ball from your hand and allow it to roll down the ramp.
4. Wait for the ball to stop rolling and use the measuring tape to measure the distance from where the ball first met the flat surface, to its current location.
5. Repeat this 10 times in order to receive results with a higher accuracy. Add all the results together and divide by 10 to find the average distance.
6. Repeat steps 3-5 with the other three balls.
7. Record the data in a table. Place the data of the average distances in a column graph to clearly see the differences in results and compare.

Risk assessment
By using timber in this experiment, a safety risk includes receiving a splinter. A precaution is to sand the timber before it is put in use. Another safety measure includes wearing gloves whilst doing the experiment which will prevent the timber from coming in contact with your skin. If a splinter is apprehended, it can be removed by using a pair of sterilized tweezers. Another hazard is the injury that may occur if a ball with large mass or a rigid surface falls and strikes your foot. A preventative measure is to wear a pair of protective shoes whilst conducting the experiment.

Results
Distance travelled by each ball over 5 trials (distance in metres)
Type of ball Mass (g)

Trial 1
(m)

Trial 2
(m)

Trial 3
(m)

Trial 4
(m)

Trial 5
(m)

Soft play toy ball

6

2.36

1.84

0.98

3.35

2.14

Golfball

26

15.01

12.88

10.37

29.7

8.42

Tennis ball 53

4.56

4.61

1.97

3.57

4.87

Water filled Toy ball 50.3

41.95

13.15

34.86

39.84

168

Average distance travelled
Type of ball

Mass (g)

Average distance travelled (m)

Soft play toy ball

6

2.2

Golfball

46

15.2

Tennis ball

53

3.9

Water filled Toy ball

168

36

Average Distance Travelled (m)

40

30

20

10

0 soft play ball

golf ball

tennis ball

water filled ball

Types of Balls soft play ball

golf ball

tennis ball

water filled ball

Discussion
The results of the experiment conducted clearly supports the hypothesis.
However there is a flaw. Generally, the larger the mass of the ball, the further it travelled.
Yet the golfball managed to travel on average 5 times the distance of the tennis ball even though its mass is 7g less. I suspect this may possibly occur as the golf ball is tightly compacted where as the tennis ball is hollow. The tennis ball has a larger inertia than the golf ball due to it this. The closer the mass to the axis of rotation, the easier to add angular velocity to the body of the ball. The potential energy of a sphere is converted into translational energy and rotational energy. Objects with large moments of inertia require lots of rotational energy for a given angular velocity. Therefore they have more rotational energy at a given linear "speed". If more energy goes into rotation, less will go into translation, and it will roll more slowly. This has happened to the tennis ball.
Unfortunately, it has been constant wet weather and due to the lack of space available indoors, the experiment had to be carried outside. Although it wasnʼt raining at the time of the experiment, the floors were waterlogged. Even though all the balls still travelled on the same ground surface, they were still affected differently due to the materials they are constructed of. Majority of the balls were not influenced too much, with their results still matching the hypothesis. However as mentioned previously, the tennis ball was affected and this is another predicted reason why. The felt like material absorbs more water than the three other rubber balls do. This could have possibly increased the friction, slowing it down. The distance one ball travelled also varied quite a lot at times through the trials. This is due to air resistance as the wind grew stronger and weakened through the period of the experiment. The water filled ball was altered the most, as it travelled 63% less distance on this trial than the average. The order of which ball travelled furthest still remained intact, which demonstrates how they were all affected by the air resistance as seen in the results table for trial 3.
To be more successful next time, the experiment should be conducted on a sunny day with minimal wind. If the available space is large enough, the experiment may even be done indoors. Another aspect to think about is to have all solid balls, rather than some hollow and some not. Lastly, it would the validity of the experiment would be increased if all the balls had the same surface, being made of the same materials. This would mean that the only thing that could affect the distance is the mass, size and air resistance.

Conclusion
In conclusion, the experiment supported the hypothesis. The water filled ball was the largest in mass, and travelled the furthest.
The purpose of the experiment was to understand and verify Newtonʼs 2nd Law of Motion which states that the force of an object is measured by mass multiplied by acceleration.
The distance an object travels once in motion depends on the force initially applied to it as well as friction or air resistance. In this experiment the beginning force was kept constant, being applied by rolling the balls down a ramp. Due to this, it is the counteracting forces mainly affecting the distance, which is the mass. This has been demonstrated successfully. Bibliography
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(accessed 25 Aug. 2014)

Reddit inc. 2014. Why does a hollow cylinder roll down a slope faster than a full cylinder? http://www.reddit.com/r/askscience/comments/1rd6yw/ why_does_a_hollow_cylinder_roll_down_a_slope/ (accessed 26 Aug. 2014)

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