a ferriswheel with a radius of 5m has a rider that weighs 30 kg, turns 5 revolution per second. compute the the centripital force when the rider is on the top and bottom of the ferriswheel
Question
a ferriswheel with a radius of 5m has a rider that weighs 30 kg, turns 5 revolution per second. compute the the centripital force when the rider is on the top and bottom of the ferriswheel
Solution
To calculate the centripetal force, we need to use the formula:
F = m * v² / r
where: F is the centripetal force, m is the mass of the object (in this case, the rider), v is the velocity of the object, and r is the radius of the circle.
First, we need to calculate the velocity. The velocity can be calculated using the formula:
v = 2 * π * r * n
where: π is a constant approximately equal to 3.14159, r is the radius of the circle, and n is the number of revolutions per second.
Substituting the given values:
v = 2 * 3.14159 * 5m * 5rev/s = 157.0796 m/s
Now, we can calculate the centripetal force. Substituting the values into the formula:
F = 30kg * (157.0796 m/s)² / 5m = 148352.113 kg*m/s² = 148352.113 N
So, the centripetal force when the rider is at the top of the ferris wheel is 148352.113 N.
When the rider is at the bottom of the ferris wheel, the centripetal force is the same, but it is directed upwards. Therefore, we need to subtract the force of gravity from the centripetal force. The force of gravity can be calculated using the formula:
Fg = m * g
where: Fg is the force of gravity, m is the mass of the object, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the given values:
Fg = 30kg * 9.8 m/s² = 294 N
Subtracting this from the centripetal force:
F - Fg = 148352.113 N - 294 N = 148058.113 N
So, the centripetal force when the rider is at the bottom of the ferris wheel is 148058.113 N.
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