On the ride "Spindletop" at the amusement park Six Flags Over Texas, people stood against the inner wall of a hollow vertical cy
linder with radius 2.5 m. The cylinder started to rotate, and when it reached a constant rotation rate of 0.60 rev/s, the floor on which the people were standing dropped about 0.5 m. The people remained pinned against the wall.
a) Draw a force diagram for a person on this ride, after the floor has dropped.
b) What minimum coefficient of static friction is required if the person on the ride is not to slide downward to the new position of the floor?
c) Does your answer in part b) depend on the mass of the passenger? (NOTE: When the ride is over, the cylinder is slowly brought to rest. As it slows down, people slide down the walls to the floor.)
a) Draw a force diagram for a person on this ride, after the floor has dropped.
b) What minimum coefficient of static friction is required if the person on the ride is not to slide downward to the new position of the floor?
c) Does your answer in part b) depend on the mass of the passenger? (NOTE: When the ride is over, the cylinder is slowly brought to rest. As it slows down, people slide down the walls to the floor.)
1 answer:
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Solution :
Given :
Mass of the baseball, m = 200 g
Velocity of the baseball, u = -30 m/s
Mass of the baseball after struck by the bat, M = 900 g
Velocity of the baseball after struck by the bat, v = 47 m/s
According to the conservation of momentum,
(900 x 47) + (200 x -30) = (900 x ) + (200 x
)
36300 = (900 x ) + (200 x
)
..............(i)
The mathematical expression for the conservation of kinetic energy is
................(ii)
Substituting (i) in (ii)
Solving the equation, we get
The negative velocity is neglected.
Therefore, substituting 96 m/s for in (i), we get
= 19
Thus, only impulse of importance is used to find final velocity.
Answer:
Approximately for the train from Boston to NYC Penn Station.
Approximately for the train from NYC Penn Station to Boston.
Explanation:
Convert minutes to hours:
.
.
Calculate average speed of each train:
.
Assume that it takes a time period of for the trains to pass by each other after departure. Distance each train travelled would be:
.
.
Since the trains have just passed by each other, the sum of the two distances should be equal to the distance between the stations:
.
Rearrange and solve for :
.
.
Distance each train travelled in :
.
.