A roller coaster (425 kg) moves from A (5.00 m above the ground) to B (28.0 m above the ground). Two nonconservative forces are present: friction does -2.00 104 J of work on the car, and a chain mechanism does +3.00 104 J of work to help the car up a long climb. What is the change in the car's kinetic energy, ÄKE = KEf - KE0, from A to B?
Ah, roller coasters, the perfect combination of thrills and physics! Let's calculate the change in the car's kinetic energy, shall we?
Now, change in kinetic energy (ΔKE) can be calculated by subtracting the initial kinetic energy (KE0) from the final kinetic energy (KEf). So, we need to determine the car's initial and final kinetic energy.
Since no horizontal forces are mentioned, we can safely assume that the change in kinetic energy is solely due to the change in gravitational potential energy.
The work done by friction (-2.00 × 10^4 J) and the chain mechanism (+3.00 × 10^4 J) will solely affect the gravitational potential energy, not the kinetic energy.
So, let's calculate the change in potential energy (ΔPE) from A to B first:
ΔPE = m * g * Δh
Where:
m = mass of the roller coaster = 425 kg
g = acceleration due to gravity (approx. 9.81 m/s^2)
Δh = change in height = final height (28.0 m) - initial height (5.00 m)
ΔPE = 425 kg * 9.81 m/s^2 * (28.0 m - 5.00 m)
Now, since ΔPE is equal to -ΔKE (due to conservation of energy), we can write:
ΔKE = - ΔPE = - (425 kg * 9.81 m/s^2 * (28.0 m - 5.00 m))
So, plug in the numbers and let's calculate:
ΔKE = - (425 kg * 9.81 m/s^2 * (28.0 m - 5.00 m))
After doing the math, the change in kinetic energy (ΔKE) from A to B should be a positive value since the work done by the chain mechanism is greater than the work done by friction.
But hey, don't take my calculations too seriously, I'm just a clown bot after all.