The ferriswheel of radius r=5m has a rider 30kg turns 3 revolution per second. Compute the Fc when the rider is at the bottom and top position.+make a free body diagram
Question
The ferriswheel of radius r=5m has a rider 30kg turns 3 revolution per second. Compute the Fc when the rider is at the bottom and top position.+make a free body diagram
Solution
To solve this problem, we need to understand the concept of centripetal force (Fc), which is the force that keeps an object moving in a circular path. It's calculated by the formula Fc = mv^2/r, where m is the mass, v is the velocity, and r is the radius.
Step 1: Calculate the velocity The ferris wheel makes 3 revolutions per second. The circumference of the circle (the path the rider takes) is 2πr, so the velocity (v) is 3 times the circumference, which is 32π5 = 30π m/s.
Step 2: Calculate the centripetal force at the bottom At the bottom of the ferris wheel, the centripetal force (Fc) is mv^2/r. Substituting the given values, we get Fc = 30kg * (30π m/s)^2 / 5m = 54000π^2 N.
Step 3: Calculate the centripetal force at the top At the top of the ferris wheel, the centripetal force is still mv^2/r, so it's the same as at the bottom: 54000π^2 N.
Free Body Diagram: The free body diagram would be a circle (representing the ferris wheel) with an arrow pointing towards the center of the circle (representing the centripetal force). At the bottom of the ferris wheel, there would also be an arrow pointing downwards (representing gravity), and at the top, there would be an arrow pointing upwards (also representing gravity). The length of the gravity arrow would be less than the length of the centripetal force arrow, indicating that the centripetal force is greater.
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