An amusement park features a ride in which the passengers are carried in two cabins mounted at the ends of a long boom, pivoted at the center so that they move in a vertical circle. the center-to-center distance between the cabins is 18 meters.
a.) At what angular speed will the passengers feel "weightless" at the top of the rotation?
I got an answer of 1.04 radians/second but not sure if it's right
B.) At that same angular speed, how much will they feel that they weight at the bottom of the rotation? you can express your answer in terms of units of g, so you don't need to know the masses of the passengers
Any help would be appreciated!
a.) At what angular speed will the passengers feel "weightless" at the top of the rotation?
I got an answer of 1.04 radians/second but not sure if it's right
B.) At that same angular speed, how much will they feel that they weight at the bottom of the rotation? you can express your answer in terms of units of g, so you don't need to know the masses of the passengers
Any help would be appreciated!
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An amusement park features a ride in which the passengers are carried in two cabins mounted at the ends of a long boom, pivoted at the center so that they move in a vertical circle. the center-to-center distance between the cabins is 18 meters.
a.) At what angular speed will the passengers feel "weightless" at the top of the rotation?
If the ride stops, while you are at the top, you are pressed against the lower side of the cabin. The wall of the cabin is supporting your weight. As the speed increases, you feel less force. As the speed increases more, you will feel no force from the wall below you. As the speed increases even more, you will the wall above you pushing you toward the center of the circle.
When you feel no force, the centripetal force must equal the weight.
m * v^2/r = m * g
v^2/r = g
The centripetal acceleration must equal the acceleration due to gravity. At this speed, you feel like you are “weightless”.
v^2/r = g
Tangential velocity = (r * g)^0.5 = (9 * 9.81)^0.5
Angular velocity = Tangential velocity ÷ radius = (9 * 9.81)^0.5 ÷ 9 = 1.044 rad/s
B.) At that same angular speed, how much will they feel that they weight at the bottom of the rotation? you can express your answer in terms of units of g, so you don't need to know the masses of the passengers
At bottom, the cabin is supporting your weight and exerting enough centripetal force to keep you moving in a circle.
Total force = weight + centripetal force
Since the velocity of the cabin is constant, the centripetal force is constant. The centripetal force is equal to the weight.
So the force at the bottom = 2 * weight
At the bottom a person feels like his or her weight has doubled.
When the cabin is half way up, your weight is pulling down and the centripetal force is pushing you horizontal.
Go to the website below to see how the forces change.
http://www.physicsclassroom.com/mmedia/c…
a.) At what angular speed will the passengers feel "weightless" at the top of the rotation?
If the ride stops, while you are at the top, you are pressed against the lower side of the cabin. The wall of the cabin is supporting your weight. As the speed increases, you feel less force. As the speed increases more, you will feel no force from the wall below you. As the speed increases even more, you will the wall above you pushing you toward the center of the circle.
When you feel no force, the centripetal force must equal the weight.
m * v^2/r = m * g
v^2/r = g
The centripetal acceleration must equal the acceleration due to gravity. At this speed, you feel like you are “weightless”.
v^2/r = g
Tangential velocity = (r * g)^0.5 = (9 * 9.81)^0.5
Angular velocity = Tangential velocity ÷ radius = (9 * 9.81)^0.5 ÷ 9 = 1.044 rad/s
B.) At that same angular speed, how much will they feel that they weight at the bottom of the rotation? you can express your answer in terms of units of g, so you don't need to know the masses of the passengers
At bottom, the cabin is supporting your weight and exerting enough centripetal force to keep you moving in a circle.
Total force = weight + centripetal force
Since the velocity of the cabin is constant, the centripetal force is constant. The centripetal force is equal to the weight.
So the force at the bottom = 2 * weight
At the bottom a person feels like his or her weight has doubled.
When the cabin is half way up, your weight is pulling down and the centripetal force is pushing you horizontal.
Go to the website below to see how the forces change.
http://www.physicsclassroom.com/mmedia/c…