Physics Acceleration

Scientific question: How does the incline of a slope influence the acceleration of a cart when it travels down a wooden plank?

Introduction:

What is an incline plane? Commonly referred to as a ramp or a slope, an incline plane is an even surface that is titled at an angle. An object placed on the tilted surface will often slide down the surface, accelerating because of an unbalanced force. The rate at which an object travels down the slope is dependent upon how tilted the slope is; the greater the tilt of the plane, the faster the rate which an object will slide down. Thus, if a physics cart is released on at a steep slope, the acceleration of the cart is expected to roll down the slope at a faster rate. As shown in figure 1, when a cart is released on an inclined plane, there’s always two to four forces acting upon the cart – the force of gravity (acts in a downward direction), the normal force (the support force exerted upon the object that is in contact with another stable object), the force of movement (the force from the wheels-moment of an object) and the force of friction (the force exerted by a surface as an object moves across). According to Isaac Newton’s law of Universal Gravitation, objects near the surface of the earth accelerate at a rate of 9.8m/s/s towards the ground.

The purpose of this investigation was to determine the relationship between the angle of inclination and the acceleration of a physics cart. This was done to determine whether if the physics cart had increased or decreased in acceleration when an incline plane was increased by the addition of bricks. This investigation could relate to the real world as there are many inclinations in roads, which is essentially, this whole investigation except in a miniature concept of the real world, with the ramp being the road inclination and the cart being the cars/vehicles on the road.

This investigation could relate to the Johnstown incline plane located in Johnstown where there are many floods (refer to figure 2.0). This incline plane was constructed as a ‘lifesaver’. When the flood waters flooded through the Conemaugh and Stonycreek Valleys on March 17, 1936 and July 20, 1977, the incline carried men, women, children and vehicles to safety and help. It is one of the longest and steepest hoists in the world and one of the few transportation systems of its kind still in existence.

The Johnstown incline composes of two sets of tracks implanted in the side of the hill on which two cars run simultaneously one from the bottom to the top and the other from the top to the bottom. The cars are 15 feet and 6 inches wide 33 feet and 11 inches long, and weigh 92 tons each. Each car can hold up to fifteen tons, and are hauled by strong steel cables which are controlled by a 400 horsepower electric motor. The cables, three on each track, are two inches in diameter, 1,130 feet long, and are safety tested to 335,000 pounds (167 tons). The track is 867.1 feet long and the top is 1,693.5 feet above sea level. In order to provide safety to the population of the towns, an experiment consisting of the relationship between the acceleration of an object and the incline could help developers with the angle of the hill and ensure the motion of the car when it is travelling simultaneously from the bottom of the hill to the top and vice versa.

Newton’s second law of motion states that the behaviour of objects for which all existing forces are not balanced and the acceleration of an object is dependent on two variables – the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and Aim
To determine how the incline of a slope affects the acceleration of an object.

Hypothesis
It is hypothesized that as the height of the incline plane is increased, the acceleration of the cart will also increase. This is accordingly stated in Newton’s second law of motion testifying that as the force of an object is increased by unbalanced existing forces including the force of gravity, normal force, force of movement and the force of friction, the acceleration of the object would also increase. It is also hypothesized that the acceleration of the object will always remain less than the acceleration due to gravity of 9.8m/s/s due to air resistance and other frictional forces according to Isaac Newton’s law of Universal Gravitation.
Variables table
Dependent Variable
Independent Variable
Controlled Variable

Acceleration of Cart (m/s)

Height of slope (incline)
Type of Vehicle – Cart

Length of Ramp

Ticker Timer

Type of Ramp – Timber Ramp

Power pack

Materials
1x Ticker Timer
12x Ticker tape (1.5m long each)
1x Vehicle – physics cart
1x Wooden plank (124cm x 24xm x 1cm)
1x Ruler (at least 15cm)
1x Voltmeter
1x Scissors
1x Calculator
1x Pencil and eraser
1x Laptop
3x Paper clip
1x Power pack
3x Bricks (height: 8cm)
2x Electrical wires

Method:
Experimental set up:
1. A brick was placed onto the table and the end of a wooden plank was placed on top of it to create slope.
2. The ticker timer was placed on top of the ramp and it was connected with 2 electrical wires that were also connected to a power pack.
3. The power pack was attached to a powerpoint and the powerpoint was switched on.
4. Thirteen strips of ticker timer tape was measured and cut out.
5. A ticker timer tape was attached to the ticker time and then it was connected to the cart using sticky tape.
6. The cart was placed on the top of the ramp and held in position ready to be released.

Experimental testing:
7. The voltmeter was switched and the ticker timer and the cart were released at the same time.
8. The timer was turned off and the tape was disconnected from the cart carefully.
9. The tape was laid out on a table.
10. Steps 1-11 were repeated with different amounts of brick and a new ticker tape for the other eleven trials.

Calculating the data: 13. The tape was divided into five spaces by drawing a line on every fifth dot. 14. The final velocity was calculated by measuring the final five dots using a ruler. 15. The time was calculated by adding all of the spaces up and multiplying it by 0.1 (the time of each space). 16. The initial velocity was calculated by measuring the first dot (0). 17. The measurements calculated were used in the formula to determine the acceleration of the tape. 18. The acceleration was recorded and steps 13-17 were repeated to calculate the acceleration of all the tapes. 19. The accelerations were recorded into a table and a graph was made accordingly.

Results:
Figure 3.0 – Table – acceleration

Acceleration (m/s/s) Inclination
Trial 1
Trial 2
Trial 3
Average
1
8cm (1 brick)
0.45
0.45
0.39
0.43
2
16cm (2 bricks)
0.96
0.97
0.93
0.95
3
24cm (3 bricks)
1.75
1.72
1.43
1.63

Figure 4.0 – Line graph – average acceleration:

Figure 5.0 – Area graph three dimensional – average acceleration:

Figure 6.0 – Bar graph – average acceleration:

Discussion:
The purpose of this investigation was to explore the relationship and theory behind a cart’s acceleration through different incline planes with addition of bricks. An experiment as such; based around is a miniature concept of the real world through the connections of roadwork activity including cars/vehicles on the road and up a hill like the Johnstown incline plane. According to Newton’s second law of motion, as the force acting upon an object is increased, the acceleration of the object is also increased. Similar to the experiment, it was hypothesised that as the incline of the slope was increased, the acceleration would too also.

The results supported the hypothesis and theory showing that each time a brick was added to increase the inclination, the acceleration of the cart increased. This is evident in the results above (refer to figure 4.0) showing that the inclination of 8cm ramp made the cart travel at an average acceleration of 0.43 m/s/s while the inclination of a 24cm ramp made the cart travel at a higher speed with an acceleration of 1.63m/s/s. The results shown in the graphs (refer to figure 5.0, 6.0 and 7.0) is evident to prove that the acceleration increased every time the slope was raised.

There are four forces acted upon an object accelerating to the ground. The four forces are the force of gravity, the normal force, the force of movement and the force of friction. When the four forces are increased by a higher slope, this results in the object accelerating at a higher speed. This theory was supported in the final results proving that the cart accelerated faster when the incline was increased. The results also supported Isaac Newton’s law of Universal Gravitation as the cart rolling down the inclined plane on all trials have an acceleration less than the acceleration due to gravity of 9.8ms/s.

Many factors affected the final results. The ticker tape might have been measured inaccurately resulting in different lengths of ticker tape. This could’ve affected the overall measurement of the final velocity on the ticker tapes resulting in an inaccurate calculation of the acceleration. Another factor that could’ve affected the results was the variety of materials. As the experiment was performed over the course of two lessons, this meant that different materials like carts, ticker timers, electricity wires and planks were used. The different variety of materials used may have affected the performance of the experiment (positively or negative) resulting upon inaccurate data. The final factor that may have affected the results was the inaccurate measurements of the dots on the ticker tape. The ticker tapes were measured by all the members in the group which meant that there were different rulers used. This affects the final calculation of the acceleration of the cart resulting in unreliable and inaccurate results.

If this experiment were to be conducted again, different strategies would be used to in order maintain reliable and accurate results. Repetition would be a strong concept used to measure the length of the ticker tape. By measuring the ticker tape more than once, this ensures that the tape is measured really accurately resulting in the same length of tape throughout the whole experiment. If the experiment had to be conducted over more than one lesson, a box should be provided to place all the materials used and labelled so it can be used again the in the next trials. This means the same materials will be used throughout the course of the trials maintaining the same performance in all the tests. Another strategy that would be changed is to only allow one person to measure the ticker tape. This will result in the same ruler being used throughout the measurements and this will stop any inaccuracy. Following all of new strategies would mean that the results would more likely be more successful and accurate.

Bibliography:
Board of Regents of the University of Wisconsin System .(2009). Scientific Reports (WWW) . http://writing.wisc.edu/Handbook/SciRep_Abstract.html (accessed August 2013)
The Physics Classroom .(2013). Newtons Second Law (WWW). http://www.physicsclassroom.com/class/newtlaws/u2l3a.cfm (accessed August 2013)
Michaels Computing.(Unknown Date). Johnston Incline (WWW). http://www.johnstownpa.com/History/hist17.html (accessed August 2013)

Bibliography: Board of Regents of the University of Wisconsin System .(2009). Scientific Reports (WWW) . http://writing.wisc.edu/Handbook/SciRep_Abstract.html (accessed August 2013) The Physics Classroom .(2013). Newtons Second Law (WWW). http://www.physicsclassroom.com/class/newtlaws/u2l3a.cfm (accessed August 2013) Michaels Computing.(Unknown Date). Johnston Incline (WWW). http://www.johnstownpa.com/History/hist17.html (accessed August 2013)