Quizlet The Cajun Cliffhanger at Great AMerica is a ride in which occupants line the perimeter of a cylinder and spin in a circl
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Answer:
Centripetal Force is the force that keeps the object's rotation in a circular path and it's always directed towards the center of rotation. Mathematically, it is given as,
From this equation it can be concluded that the centripetal force is proportional to the product of mass and the square of velocity. It is inversely proportional to the object's distance from the center.
Now in the above mentioned case, when the cylinder begins spinning very rapidly and it's speed becomes double. Then by applying the above equation we conclude that " the force will be increased four times if the speed is doubled as it is proportional to square of speed."
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Let's split the problem into two parts, and let's solve it by using conservation of momentum.
1) Let's analyze the moment when the boy tosses the pumpkin. Before this moment, the boy is standing with the pumpkin, so with speed v=0 and therefore the total momentum of the system (boy+pumpkin) is zero.
After he tosses the pumpkin, the boy will start to move with speed
and the pumpkin starts to move with speed 
. The momentum of the boy is 
(with 
being the mass of the boy), while the momentum of the pumpkin is 
(where 
is the mass of the pumpkin). Since the total momentum must be equal to zero (because the total momentum cannot change), then we can write
From which we find
and this is the speed of the boy, and the negative sign means he's moving in the opposite direction of the pumpkin.
2) Now let's focus on the entire system (boy+pumpkin+girl). Initially, the total momentum of this system is zero, because both the boy (holding the pumpkin) and the girl are still. So, the total momentum after the girl catches the pumpkin must be still zero.
After this moment, the boy has a momentum of, while the girl has momentum 
where 
is the girl mass 
is the girl speed. Here we use 
because the girl is holding the pumpkin now. Therefore, the conservation of momentum becomes
and so
and this is the girl's speed, with positive sign so with same direction of the pumpkin initial direction.
1) Let's analyze the moment when the boy tosses the pumpkin. Before this moment, the boy is standing with the pumpkin, so with speed v=0 and therefore the total momentum of the system (boy+pumpkin) is zero.
After he tosses the pumpkin, the boy will start to move with speed
From which we find
and this is the speed of the boy, and the negative sign means he's moving in the opposite direction of the pumpkin.
2) Now let's focus on the entire system (boy+pumpkin+girl). Initially, the total momentum of this system is zero, because both the boy (holding the pumpkin) and the girl are still. So, the total momentum after the girl catches the pumpkin must be still zero.
After this moment, the boy has a momentum of
and so
and this is the girl's speed, with positive sign so with same direction of the pumpkin initial direction.