A roller-coaster car with a mass of 550 kg starts at rest from a point 46 m above the ground. At point B, it is 23 m above the ground. [Express your answers in kilojoules (kJ).]
(a) What is the initial potential energy of the car?
Incorrect: Your answer is incorrect. . kJ
(b) What is the potential energy at point B?
kJ
(c) If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 14000 J (14 kJ), what is the kinetic energy of the car at point B?
kJ
To find the answers to these questions, we can use the principles of potential energy and work-energy theorem.
(a) To find the initial potential energy of the car, we need to calculate the gravitational potential energy at the starting point. The formula for gravitational potential energy is:
Potential Energy = mass * gravitational acceleration * height
Given:
mass (m) = 550 kg
height (h) = 46 m
Using the formula, we can calculate the initial potential energy:
Potential Energy = 550 kg * 9.8 m/s^2 * 46 m
Potential Energy = 255080 J
To convert this to kilojoules (kJ), we divide the value by 1000:
Potential Energy = 255080 J / 1000
Potential Energy = 255.08 kJ
Therefore, the initial potential energy of the car is 255.08 kJ.
(b) To find the potential energy at point B, we use the same formula. The only difference is the height value. Given that the car is 23 m above the ground at point B, we can calculate the potential energy at that point:
Potential Energy = 550 kg * 9.8 m/s^2 * 23 m
Potential Energy = 120040 J
Converting this to kJ:
Potential Energy = 120040 J / 1000
Potential Energy = 120.04 kJ
Therefore, the potential energy at point B is 120.04 kJ.
(c) To find the kinetic energy at point B, we can use the work-energy theorem. The work done against friction between the starting point and point B is given as 14000 J.
According to the work-energy theorem, the work done is equal to the change in kinetic energy. Since the initial kinetic energy is zero, we can set up the equation:
Work Done = Final Kinetic Energy - Initial Kinetic Energy
Given:
Work Done = 14000 J
Initial Kinetic Energy = 0
Let's assume the final kinetic energy at point B is K kJ. Converting the work done to kJ:
Work Done = 14000 J / 1000
Work Done = 14 kJ
Now we can rewrite the equation:
14 kJ = K kJ - 0
K = 14 kJ
Therefore, the kinetic energy of the car at point B is 14 kJ.