A roller-coaster car with a mass of 500 kg starts at rest from point A, which is 46 m above the ground. At point B, it is 23 m above the ground.
What is the formula for this problem
To find the speed of the roller-coaster car at point B, we can use the principle of conservation of energy. At point A, the roller-coaster car has potential energy due to its height above the ground. As it moves from point A to point B, this potential energy is converted into kinetic energy.
The potential energy (PE) of an object is given by the equation:
PE = m * g * h
Where:
m is the mass of the object (500 kg)
g is the acceleration due to gravity (9.8 m/s²)
h is the height above the ground (46 m at point A and 23 m at point B)
The formula for kinetic energy (KE) is:
KE = 0.5 * m * v²
Where:
v is the speed of the object
According to the law of conservation of energy, the total energy remains constant, so the potential energy at point A is equal to the kinetic energy at point B. Therefore:
PE at A = KE at B
m * g * hA = 0.5 * m * v²B
Since the mass (m) appears on both sides of the equation, we can simplify:
g * hA = 0.5 * v²B
Now we can solve for the speed (v) at point B:
v²B = (2 * g * hA) / 1
vB = √(2 * g * hA)
Plugging in the values:
vB = √(2 * 9.8 * 46)
Simplifying:
vB = √(901.6)
vB ≈ 30.03 m/s
Therefore, the speed of the roller-coaster car at point B is approximately 30.03 m/s.