a 4,500 kg roller coaster starts from the top of a 45 m hill with a velocity of 3m/s. The car travels to the bottom through a loop and continues up the next hill. The end of the roller coaster has a level surface that is 4m off the ground. Assume that there is no friction on the roller coaster ride and energy is conserved. How much potential energy will the roller coaster have when it is traveling at 14m/s?
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i guess im just not sure where to start
initial PE+initial KE=finalPE+finalKE
you know initial h, and v, so the left side can be calculated.
the right side, you know final KE, solve for PE
i keep getting the incorrect answer.
To find the potential energy of the roller coaster when it is traveling at 14 m/s, we need to consider the conservation of energy principle. According to this principle, the total mechanical energy of an object remains constant as long as there is no friction or external work done on the object.
The mechanical energy consists of two components: kinetic energy (KE) and potential energy (PE). Kinetic energy is the energy of motion, while potential energy is the energy associated with an object's position or height above a reference point.
Initially, at the top of the 45 m hill, the roller coaster has gravitational potential energy due to its height. This can be calculated using the formula:
PE = mgh
Where:
PE is the potential energy (in joules),
m is the mass of the roller coaster (in kilograms),
g is the acceleration due to gravity (approximately 9.8 m/s²),
and h is the height of the hill (in meters).
Given:
m = 4,500 kg
g = 9.8 m/s²
h = 45 m
Using the above values, we can calculate the initial potential energy:
PE_initial = 4,500 kg * 9.8 m/s² * 45 m
= 1,960,200 Joules (rounded to the nearest joule)
When the roller coaster is traveling at 14 m/s on the level surface at the end, all of the initial potential energy is converted into kinetic energy.
The equation for kinetic energy is:
KE = 0.5 * m * v²
Where:
KE is the kinetic energy (in joules),
m is the mass of the roller coaster (in kilograms),
and v is the velocity of the roller coaster (in meters per second).
Given:
m = 4,500 kg
v = 14 m/s
Using the above values, we can calculate the kinetic energy:
KE_final = 0.5 * 4,500 kg * (14 m/s)²
= 1,323,000 Joules (rounded to the nearest joule)
Therefore, when the roller coaster is traveling at 14 m/s, its potential energy is completely converted into kinetic energy. The final total mechanical energy (E_final) is equal to the kinetic energy (KE_final):
E_final = KE_final
= 1,323,000 Joules (rounded to the nearest joule)