Q A rollercoaster of mass 400 kg is stationary at the highest point on the track. It then drops to the lowest point through a vertical distance of 24 m.
Calculate:
a) the potential energy of the car at the top of the ride.
b) the speed of the car at its lowest point, ignoring air resistance.
My answer for (a) is 94176 N, and for (b) is 21.7 m/s
Appreciate if someone could check these answers if correct. If wrong, can they point me in the right direction.
TIA
You used g=9.81 m/s^2, which is fine. Both of your answers are correct.
Thanks for taking the time.
You're welcome! I'm glad to hear that your answers are correct. It seems like you have a good understanding of the concept of potential energy and kinetic energy in this scenario.
Just to provide a bit more explanation, let's go through the steps to get the answers:
a) To find the potential energy at the top of the ride, you can use the formula: potential energy = mass * acceleration due to gravity * height.
In this case, the mass of the rollercoaster is 400 kg, and the height is given as 24 m. The acceleration due to gravity, g, is 9.81 m/s^2.
So, the potential energy = 400 kg * 9.81 m/s^2 * 24 m = 94176 J.
b) To calculate the speed of the car at its lowest point, you can make use of the conservation of energy principle, which states that the total energy of a system is conserved.
At the top of the ride, the rollercoaster only has potential energy. As it drops down to the lowest point, all of the potential energy is converted into kinetic energy.
So, the potential energy at the top = kinetic energy at the bottom.
You already calculated the potential energy at the top as 94176 J.
Now, to find the kinetic energy at the bottom, you can use the formula: kinetic energy = 0.5 * mass * velocity^2.
Since the potential energy is completely converted into kinetic energy, we can equate the two equations:
Potential energy at the top = Kinetic energy at the bottom
94176 J = 0.5 * 400 kg * velocity^2
Solving for velocity, we get:
velocity^2 = (2 * 94176 J) / 400 kg
velocity^2 = 470.88 J / kg
velocity = sqrt(470.88 J / kg)
velocity ≈ 21.7 m/s.
So, the speed of the car at its lowest point, ignoring air resistance, is approximately 21.7 m/s.
Keep up the good work! If you have any more questions, feel free to ask.