Answer :
The speed of the chair can be found by analyzing the forces acting on it. At the topmost position of the swing ride, the gravitational force is acting downward, and the tension in the cable is acting radially inward. At this position, the tension force is the maximum and provides the centripetal force to keep the chair in circular motion.
To find the speed, we can equate the gravitational force and the centripetal force. The gravitational force is given by the weight of the chair and occupant, which is equal to the mass (172 kg) multiplied by the acceleration due to gravity (9.8 m/s²).
The centripetal force is given by the tension in the cable, which can be calculated using the equation:
Tension = (mass × velocity²) / radius
In this case, the radius is given as 16.5 m and the angle θ is given as 61 degrees. To find the velocity, we need to convert the angle to radians by multiplying it by π/180.
By equating the gravitational force and the centripetal force, we can solve for the velocity:
mass × acceleration due to gravity = (mass × velocity²) / radius
Rearranging the equation, we have:
velocity = √((mass × acceleration due to gravity × radius) / mass)
Simplifying further, we get:
velocity = √(acceleration due to gravity × radius)
By substituting the given values for the acceleration due to gravity (9.8 m/s²) and the radius (16.5 m) into the equation, we can calculate the speed of the chair in meters per second.
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