A child rides on a Ferris Wheel at the State Fair.
The seat always faces to the right. There are three forces that act on the child,the child’s weight, W, the normal force of the seat,N, and the force of friction between the child and the seat, f.
At which listed location(s) does the gravitational force, W, contribute to the centripetal
force on the child and not oppose it?
a. top
b. Mid way on right side
c. bottom
d. top and bottom
My answer: a
At which position(s) will the magnitude of the normal force, N, be the greatest?
a. top
b. midway to the right
c. bottom
d. midway to the left
e. It is the same at all the listed locations.
My answer: C
If friction were very small and there is no grab bar across the seat, where would the child be in the greatest danger?
a. top
b. midway far right
c. bottom
d. midway far left
e. The danger is the same everywhere.
My answer: e
Are this assumptions correct??
Your first two answers are correct. The last one is not. With the child always facing right, seat cushion friction or a grab bar will have to provide a centripetal force to the left to keep the child accelerating toward the center. Without that force, the child will slide out of the seat. The answer is b.
One might also conclude that the top position is the least safe because the child has the greatest distance to fall, but that will not happen unless the child is crawling about
Your answers are almost correct, but there is a slight error in the second question.
The correct answers are:
1. At which listed location(s) does the gravitational force, W, contribute to the centripetal force on the child and not oppose it?
- Answer: d. top and bottom
The gravitational force (W) contributes to the centripetal force at the top and the bottom of the Ferris wheel, as it acts vertically downward and helps provide the necessary inward force for circular motion.
2. At which position(s) will the magnitude of the normal force, N, be the greatest?
- Answer: a. top
The magnitude of the normal force (N) will be the greatest at the top of the Ferris wheel because the child experiences the greatest apparent weight due to the combined effect of their actual weight and the centrifugal force acting away from the center of the circular motion.
3. If friction were very small and there is no grab bar across the seat, where would the child be in the greatest danger?
- Answer: a. top
If there is no friction and no grab bar, the child would rely solely on the normal force to prevent them from falling out of the seat. At the top of the Ferris wheel, the child experiences the least amount of normal force, making them most vulnerable to falling out.
Your assumptions are correct. Here's a step-by-step explanation of how to arrive at those answers:
For the first question:
1. Recall that the centripetal force is the force that keeps an object moving in a circular path. It always points towards the center of the circle.
2. The weight of the child, W, is always directed downwards towards the center of the Earth.
3. In order for the weight (W) to contribute to the centripetal force rather than oppose it, it needs to be pointing towards the center of the Ferris Wheel.
4. The only location where this occurs is at the top of the Ferris Wheel, where the weight (W) is directed downwards towards the center.
5. Therefore, the answer is a. top.
For the second question:
1. The normal force (N) is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface.
2. At the top of the Ferris Wheel, the child is pushed downwards due to their weight (W). Therefore, the normal force (N) will be greater at the top to counteract the weight.
3. At the bottom of the Ferris Wheel, the child is pushed upwards due to their weight (W). Again, the normal force (N) will be greater at the bottom to counteract the weight.
4. At the midway position on both the right and left sides, the child is neither being pushed downwards nor upwards, so the normal force (N) will be less.
5. Therefore, the answer is a. top and c. bottom.
For the third question:
1. Recall that the force of friction opposes the motion between two surfaces in contact.
2. In this scenario, if friction is very small, it means there is little or no friction between the child and the seat.
3. Without sufficient friction, the child could slide off the seat when the Ferris Wheel is in motion.
4. This danger exists at every position on the Ferris Wheel since there is no friction to prevent the child from sliding.
5. Therefore, the answer is e. The danger is the same everywhere.
Well done on your correct assumptions!