Roller Coaster Design

Weightlessness

Weight is the pull of gravity. Typical weight units are pounds and newtons. (1 pound @ 4.45 newtons). On the moon, gravity pulls with ¹/6 the force compared to the Earth. Therefore, a student on the moon weighs ¹/6 of what she weighs on the Earth.

On the Earth, neglecting air resistance, all objects will speed up at a rate of 9.80 ^m/s every second they fall. That is a speed increase of about 22 mph for every second an object falls.

Time in the Air
(s)

Velocity

(mph)

0
0

1
22

2
44

3
66

4
88

5
110

There are two ways to experience weightlessness. (1) move far enough away from the planets and sun to where their pull is nearly zero. [Gravity acts over infinite distance. One can never completely escape it.] (2) Fall down at a rate equal to the pull of gravity. In other words, accelerate to the Earth speeding up 22 mph every second in the air. In order for a person to feel weight, a person must sense the reaction force of the ground pushing in the opposite direction of gravity.

In the absence of the reaction force a person will sink through the ground.
Many amusement park rides generate the weightless sensation by accelerating down at 22 mph every second.

g’s
Neglecting air resistance, if a rock is dropped, it will accelerate down at 9.8 ^m/s². This means it will speed up by 9.8 ^m/s for every second it falls. If a rock you drop accelerates down at 9.8 ^m/s², scientists say the rock is in a “1 g” environment, [1 g = 9.8 ^m/s² = 22 ^mph/s].

Any time an object experiences the pull equal to the force of gravity, it is said to be in a “one g” environment. We live in a 1 g environment. If a rock whose weight on the Earth is 100 lbs was moved to a 2 g environment then it would weigh 200 lbs. In a 9 g environment it would weigh 900 lbs. In a “NEGATIVE 2 g” environment it would take 200 lbs to hold the rock down on the ground. In a “-5 g” environment it would take 500 lbs to hold the rock down to the ground. If the rock were put into a “zero g” environment then it would be weightless. However, no matter what happens to its weight the rock’s mass would never change. Mass measurement is unaffected by the pull of gravity.

What does it feel like to walk in a 2 g environment? Have students find someone who’s mass is about equal to theirs. Have them give piggyback rides. As they walk around this is what it feels like to be in a 2 g environment. Go outside on the soft ground and have the students step up on something. This is when they will really know what a 2 g environment feels like.
Often engineers will use g’s as a “force factor” unit. The force factor gives a person a way of comparing what forces feel like.

All acceleration can be converted to g’s by dividing the answer, in ^m/s², by 9.8 ^m/s².

Example 6
A roller coaster is propelled horizontally by a collection of linear accelerator motors. The mass of the coaster train is 8152 kg. The train starts from rest and reaches a velocity of 26.1 ^m/s, 55 mph, in 3.00 seconds. The train experiences a constant acceleration. What is the coaster train’s acceleration in g’s?

Solution
m = 8152 kg
v_o = 0 (starts from rest)
v_f = 26.1 ^m/s
t = 3.00 s
a = ?

v_f = v_o + at
26.1 = 0 + a(3.00)
a = 8.70 m/s
in g’s... 8.70 ^m/s² / 9.80 ^m/s² = 0.89 g’s
This means the rider is being pushed back into his seat by 89% of his weight.

by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)

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