Solving for Distance and Speed in Physics Problems

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To find the distance riders move on a carnival swing fixed at the end of an 8.1-meter beam sweeping through 120 degrees, calculate the arc length using the formula: (angle/360) = (arc length/(2*pi*radius)). For the car negotiating a circular turn at 34 m/s, the maximum static friction force is crucial for maintaining speed; if it reduces by a factor of 3 due to a wet patch, the driver must slow down to avoid losing control. The relationship between centripetal force and speed indicates that a decrease in friction necessitates a proportional reduction in speed to maintain safety. The final arc length for the swing is approximately 17 meters.
winterma
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Hi, I have 2 questions...

1. If a carnival swing is fixed on the end of an 8.1-m-long beam. The swing and beam sweep through an angle of 120 degrees. How do i find the distance through which the riders move?



2. A car is safely negotiating an unbanked circular turn at a speed of 34 m/s. The maximum static frictional force acts on the tires. Suddenly a wet patch in the road reduces the maximum static friction force by a factor of 3. If the car is to continue safely around the curve, to what speed must the driver slow the car?

Thank you very much for your help!

claire
 
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winterma said:
1. If a carnival swing is fixed on the end of an 8.1-m-long beam. The swing and beam sweep through an angle of 120 degrees. How do i find the distance through which the riders move?
Think of the swing as tracing an arc of a circle with a radius of 8.1 m. What's the length of the arc that's swept out? (What fraction of the circle's circumference is 120 degrees?)
2. A car is safely negotiating an unbanked circular turn at a speed of 34 m/s. The maximum static frictional force acts on the tires. Suddenly a wet patch in the road reduces the maximum static friction force by a factor of 3. If the car is to continue safely around the curve, to what speed must the driver slow the car?
The friction force provides the centripetal force that keeps the car going in a circle. The maximum friction force will tell you the how fast the car can go and still stay on the curved road. How does the centripetal force relate to the speed of the car? If the centripetal force drops to 1/3, what must happen to the maximum speed?
 
Question one is a total math question.the formula for solving it comes from the chapter Mensuration. (Angle given)/360 degrees = Arc length( the one you want to find)/2*pi*8.1m. The final answer would be 16.9668m. round off = 17 metres.um,didnt we learn this at grade 10?
 
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