The mass of a roller-coaster car, including its passengers, is 481 kg. Its speed at the bottom of the track in the figure below is 20 m/s. The radius of this section of the track is r1 = 24 m. Find the force that a seat in the roller-coaster car exerts on a 54-kg passenger at the lowest point.
The mass of a roller-coaster car, including its passengers, is 481 kg. Its speed at the bottom of the track in the figure below is 17 m/s. The radius of this section of the track is r1 = 26 m. Find the force that a seat in the roller-coaster car exerts on a 45-kg passenger at the lowest point.
To find the force that a seat in the roller-coaster car exerts on a passenger at the lowest point, we need to use the concept of centripetal force.
The centripetal force is given by the formula:
Fc = (m * v^2) / r
where Fc is the centripetal force, m is the mass, v is the velocity, and r is the radius.
In this case, the mass of the roller-coaster car and the passenger combined is 481 kg, and the speed at the bottom of the track is 20 m/s. The radius of this section of the track is given as r1 = 24 m.
First, let's find the centripetal force acting on the roller-coaster car:
Fc = (m * v^2) / r
= (481 kg * (20 m/s)^2) / 24 m
≈ 8,006.67 N
Now, to find the force that the seat exerts on the passenger, we need to subtract the gravitational force acting on the passenger. The gravitational force is given by:
Fg = m * g
where Fg is the gravitational force, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
For the passenger, whose mass is 54 kg, the gravitational force is:
Fg = 54 kg * 9.8 m/s^2
≈ 529.2 N
Finally, we can find the force that the seat exerts on the passenger:
Fseat = Fc - Fg
= 8,006.67 N - 529.2 N
≈ 7,477.47 N
Therefore, the seat in the roller-coaster car exerts a force of approximately 7,477.47 N on the 54-kg passenger at the lowest point.