A roller coaster with people on board has a total mass of 4500 kg and starts at a height of 22 meters with a speed of 2.0 m/s. 50 kJ of work is done by friction on the way to the bottom of the ride. What is the speed at the bottom of the ride?
20
similar technique as previous question
To determine the speed of the roller coaster at the bottom of the ride, we will need to apply the principles of conservation of energy.
First, let's calculate the potential energy of the roller coaster at the beginning of the ride using the equation:
Potential Energy = mass * acceleration due to gravity * height
Potential Energy = 4500 kg * 9.8 m/s^2 * 22 m
Potential Energy = 977,400 J
Next, we need to account for the work done by friction during the ride. The work done by friction is given as 50 kJ (kilojoules), which can be converted to joules by multiplying by 1000:
Work done by friction = 50 kJ * 1000
Work done by friction = 50,000 J
Now, let's determine the kinetic energy of the roller coaster at the bottom of the ride, which can be calculated using the equation:
Kinetic Energy = Potential Energy at the beginning + Work done by friction
Kinetic Energy = 977,400 J + 50,000 J
Kinetic Energy = 1,027,400 J
Finally, we can use the equation for kinetic energy to determine the speed of the roller coaster at the bottom of the ride:
Kinetic Energy = (1/2) * mass * velocity^2
Rearranging the equation, we find:
velocity^2 = (2 * Kinetic Energy) / mass
velocity^2 = (2 * 1,027,400 J) / 4500 kg
velocity^2 = 456,311.11 m^2/s^2
Taking the square root of both sides, we get:
velocity = √456,311.11 m^2/s^2
velocity ≈ 676.3 m/s
Therefore, the speed of the roller coaster at the bottom of the ride is approximately 676.3 m/s.