Final answer:
The weight of the passenger at the top of the loop of a roller coaster can be found by summing the weight of the passenger and the centripetal force. In this case, the weight is 784 N and the centripetal force is 1024 N, resulting in a total weight of 1808 N.
Step-by-step explanation:
To find the weight of the passenger at the top of the loop, we need to consider the forces acting on the passenger. At the top of the loop, the only force acting on the passenger is the normal force, which is perpendicular to the surface. The weight of the passenger is the gravitational force acting downwards. In this case, the normal force is equal to the sum of the weight and the centripetal force.
First, let's find the centripetal force. The centripetal force is given by the equation:
Fc = m * (v^2 / r)
Where Fc is the centripetal force, m is the mass of the passenger, v is the velocity of the coaster, and r is the radius of the loop.
Plugging in the values, we have:
Fc = 80 kg * (22 m/s)^2 / 15 m
Fc = 1024 N
Next, we can find the weight of the passenger using the equation:
W = m * g
Where W is the weight, m is the mass of the passenger, and g is the acceleration due to gravity.
Plugging in the values, we have:
W = 80 kg * 9.8 m/s^2
W = 784 N
Finally, we can find the normal force by adding the weight and the centripetal force:
Normal Force = Weight + Centripetal Force
Normal Force = 784 N + 1024 N
Normal Force = 1808 N
Therefore, the weight of the passenger at the top of the loop is 1808 N.