A roller coaster is at the top of a 98.2 m hill and has a mass of 1831.0 kg. It is traveling at a velocity of 23.7 m/s. What is the coaster car's TOTAL energy?
I took the eg=1/2mv^2 and plugged in (1831)(9.8)(98.2) and got 1762081.16
I then took the ek= 1/2mv^2 and plugged in 1/2(1831.0)(9.8)(23.7)^2 and got 5039426.51 and then added the 2 values to get a total of 6801507.671
am i right?
The numbers are correct, but the words are not. The first thing you did was mgh, not 1/2 m v^2
So yes, it is mgh+1/2 mv^2
I didn't check calc work.
No. Eg is not (1/2) mV^2. What you say you plugged in, M g H, is correct however.
Your ek should not include a gravity term.
ok so i see what i did wrong and got a value of 2276308.355 J
To calculate the total energy of the roller coaster car, you need to consider both potential energy (PE) and kinetic energy (KE). The potential energy is related to the height of the coaster, and the kinetic energy is related to its velocity.
The formula for potential energy is PE = mgh, where m is the mass of the car (1831.0 kg), g is the acceleration due to gravity (typically, 9.8 m/s²), and h is the height of the hill (98.2 m). Plugging in these values, you correctly calculated the potential energy (PE) to be 1762081.16 J.
The formula for kinetic energy is KE = 1/2mv², where v is the velocity of the car (23.7 m/s). Plugging in the values, you correctly calculated the kinetic energy (KE) to be 5039426.51 J.
To find the total energy, simply add the potential energy and the kinetic energy together. So, adding 1762081.16 J and 5039426.51 J, you correctly found the total energy to be 6801507.67 J.
Therefore, your calculation is correct, and the roller coaster car's total energy is indeed 6801507.67 J.