In: Physics

A roller coaster car with its passengers has a mass of 220 kg and it goes through a series of horizontal and vertical curves.

A. Draw the free body diagrams for the car going around a horizontal curve, the bottom of a vertical loop, and the top of a vertical loop in which the cart is upside down. Indicate the direction of the acceleration on each diagram.

B. If the car is moving at 25 m/s what is the smallest horizontal curve it can go around and not exceed a 4.5g limit on acceleration (g = 9.8 m/s2?

C. What speed does the car need at the top of a loop with a radius of 4.5 m in order for the car to experience weightlessness?

D. What is the apparent weight of the car at the bottom of a 4.5 m radius loop at 25 m/s?

A. When the car goes around a horizontal curve, the Normal force and the Gravity force (Weight) are perpendicular to each other at all times, and the Weight never acts as a centripetal force (it never points to the center of the circular path). On the other hand when the car is going through a vertical loop the situation is different, because the line of action of mg is in the radial direction. When the cart is on top, mg is alligned with the Normal force, when the cart is at the bottom, mg is opposite to the Normal:

B. For any circular motion the centripetal acceleration and the velocity at a point in the circumference are related by:

If we want the car not to exceed the 4.5g limit the minimum radius should be:

C. When the cart is at the top of a vertical loop the balance in the radial direction is:

The sensation of weightlessness appears when N=0. In this case:

D. The apparent weight of the cart at the bottom is given by the Normal force. The balance in the radial direction in this case is:

This is about 17 times the real weight of the car

A roller coaster car has a mass of 250 Kg. The car is towed to
the top of a 30 m hill where it is released from rest and allowed
to roll. The car plunges down the hill, then up an 8 m
hill and through a loop with a radius of 8 m. Assuming no friction:
(8 points)
What is the potential energy of the car at the top of the 30 m
hill?
What are the Kinetic Energy...

A roller coaster car with its three passengers (a total of 450̅
kg) is pulled up to the top of a 30.0 meter hill where it is
released at a speed of 1.00 meter per second to begin its hurtle
down the track toward a 15.0 meter diameter loop the loop at the
bottom. Unfortunately, the maintenance crew still has some work to
do on the old rusty roller coaster track and the average frictional
force on the 65.0 meter...

A car of a roller coaster has a total mass of 1000 kg including
the passenger. At position A (the top of the first incline), it
cruises at 2m/s.
Calculate its velocity at position C at the top of the second
incline which is 5 m below the top of the first incline, if there
are no losses due to friction on the track or air drag.
Calculate the average resistance force (due to friction and
drag) between points A...

A roller-coaster track is being designed so that the
roller-coaster car can safely make it around the circular vertical
loop of radius R = 24.5 m on the frictionless track. The loop is
immediately after the highest point in the track, which is a
height h above the bottom of the loop. What is the
minimum value of h
for which the roller-coaster car
will barely make it around the vertical loop?

A roller coaster car with a mass 700 Kilograms starts from rest
at h1 above the ground and slides along a track. The car
encounters a loop of radius 12 m. The bottom of the loop is a
height h2 = 5 m from the ground. What would be the max
height of release h1 for the roller coaster car if the
amount of thermal energy produced between the point of release and
the top of the loop should not...

-A roller coaster cart of mass (m1=127 kg) initially sits at
rest on a track. Once the motor is activated, the cart is
accelerated forward (across level ground) until it reaches the
bottom of a giant circular loop with a radius of (r1=17.5 m). At
this point, the motor is turned off and the cart must "coast" for
the remainder of the ride. Assume the track is frictionless and
ignore air resistance. At the top of the loop, what is...

1) A roller coaster car on the leveled portion of a track is
moving at a speed of 35 m/s, heading toward a hump. Based on the
principle of conservation of energy, predict what is the velocity
of the car on the top of the hump if the lost of energy due to
friction and air resistance is negligiable. The highest point of
the hump is 14 above the leveled track.

1. A 1200 kg roller coaster is given an initial velocity of 28
m/s (not the answer to problem 7) and travels uphill to a
height of 30m above the ground. What is the velocity at the top of
the hill?
2. A 1200 kg roller coaster is given an initial velocity of 28
m/s (not the answer to problem 7) and travels uphill to a
height of 30m above the ground, then drops to a height of 13m above...

A roller-coaster car is starting from rest from the top of the
slope of height H. As it reaches the bottom of the slope, it is
moving at 30 m/s along a straight horizontal track. Using the
principle of conservation of energy,
a. Calculate the height H.
b. Calculate the speed of the roller-coaster car after climbing
the 10 m hill shown in the figure. Ignore friction.
c. What is the change in kinetic energy as the car goes a....

A roller-coaster car speeds down a hill past point A where R1 =
11.6 m and then rolls up a hill past point B where R2 = 15.2 m, as
shown below.
(a) The car has a speed of 20.0 m/s at point A. if the track
exerts a normal force on the car of 2.08 104 N at this point, what
is the mass of the car?
(b) What is the maximum speed the car can have at point...

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