A 650-kg roller coaster car starts from rest at the top of the first hill at height 26m and rolls down the frictionless track and passes through second hill at height 16m, third hill at height 9m and reach end of ride.
Calculate the gravitational potential energy at the top of first, second, and third hills and at the end of the ride.
Calculate the kinetic energy at the top of first, second, and third hills and at the end of the ride.
Calculate the speed of the car at the top of first, second, and third hills and at the end of the ride.
Sample solution
Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell.
In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.
God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.
Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.
To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.
References
Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.
Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.
Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.
Sample Answer
Sample Answer
Essay: The Physics of Roller Coaster Energy
Roller coasters are thrilling amusement park rides that rely on the principles of physics to create an exhilarating experience for riders. One key concept that comes into play is the transformation of energy as a roller coaster car moves along its track. In this essay, we will explore the gravitational potential energy, kinetic energy, and speed of a roller coaster car at different points along its journey.
Thesis Statement
The roller coaster car’s energy changes as it moves along the track, with gravitational potential energy converting to kinetic energy and vice versa, showcasing the fundamental principles of physics in action.
Gravitational Potential Energy Calculation
The gravitational potential energy (GPE) of an object is given by the formula:
[ GPE = m \times g \times h ]
where:
( m = 650 , \text{kg} ) (mass of the roller coaster car),
( g = 9.8 , \text{m/s}^2 ) (acceleration due to gravity),
( h ) is the height above the reference point.
At the Top of the First Hill (26m)
[ GPE_{1} = 650 \times 9.8 \times 26 = 165,620 , \text{J} ]
At the Second Hill (16m)
[ GPE_{2} = 650 \times 9.8 \times 16 = 101,440 , \text{J} ]
At the Third Hill (9m)
[ GPE_{3} = 650 \times 9.8 \times 9 = 56,970 , \text{J} ]
At the End of the Ride (Ground Level)
At ground level, the height is 0, so the GPE will be zero.
Kinetic Energy Calculation
The kinetic energy (KE) of an object is given by the formula:
[ KE = \frac{1}{2} \times m \times v^2 ]
where:
( v ) is the velocity of the object.
At the Top of the First Hill
Since the car starts from rest, its initial KE is zero.
At the Second Hill
To calculate KE at the second hill, we need to find the speed of the car at that point.
[ GPE_{1} = KE_{2} + GPE_{2} ]
[ 165,620 = \frac{1}{2} \times 650 \times v^2 + 101,440 ]
[ v = 14.7 , \text{m/s} ]
[ KE_{2} = \frac{1}{2} \times 650 \times (14.7)^2 = 73,040.25 , \text{J} ]
At the Third Hill
To find KE at the third hill, we repeat the process:
[ GPE_{2} = KE_{3} + GPE_{3} ]
[ 101,440 = \frac{1}{2} \times 650 \times v^2 + 56,970 ]
[ v = 10.9 , \text{m/s} ]
[ KE_{3} = \frac{1}{2} \times 650 \times (10.9)^2 = 39,597.25 , \text{J} ]
At the End of the Ride
At ground level, all GPE is converted to KE.
[ KE_{\text{End}} = GPE_{3} = 56,970 , \text{J} ]
Conclusion
In conclusion, as the roller coaster car moves along its track, it experiences changes in gravitational potential energy and kinetic energy. These energy transformations are fundamental in creating the thrilling and dynamic experience that roller coasters provide for riders. Physics plays a crucial role in understanding and designing these exhilarating rides.
