Physics arc problem-please help!

Question

In the Pirate Boat ride at the amusement park, riders swing back and forth in a pendulum-like "boat." The distance from the boat to the pivot point is 13 m, and the maximum angle the boat reaches is 40 ∘

1. maximum speed the boat attains: 7.9 m/s
2. What is the apparent weight of a 45 kg rider at the bottom of the arc?

Answer 1

The boat swings in a circular arc. The maximum speed is at the bottommost position the boat achieves. At the very bottom of the swing, there are three forces acting on the rider:

1.    The force of gravity on the rider with the value of mg and acting downward.

2.    The centripetal force due to the swing and acting upward that is equal to V^2 /R x mass where V is the maximum velocity and R the radius of the pendulum boat (13 m).

3.    The normal force exerted on the rider which is what is measured as the rider’s apparent weight and is in an upward direction.

The 3 forces balance out and can be expressed as Fc + N = mg where Fc and N are the centripetal force and normal force respectively. As we are interested in the apparent weight, we must solve for N.

N = mg – Fc = 45kg x 9.8 m/s^2 – V^2/R

N = 441 N – 7.9^2 m^2/s^2  / 13 m x 45 kg = 441 N – 216 N = 225 N.