7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

1/11

Mengjiao ZhangLinzi WangSilu Gao

Centripetal forceand conservation ofkinetic energy andpotential energy

7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

2/11

Q: What is the most thrilling game in the

amusement parks?

A: The Roller coaster!

It deals with danger and fear; roller coastercars go up and down, and go through loops

and twists. The roller Coaster is a highly

exciting entertainment in the amusement

park. However, there are lots of safety

concerns behind roller coaster. Designers of

roller coaster have to apply many physical

concepts to make sure that passengers are

entertained and safe at the same time while

they are on the roller coaster. There are two

basically physics ideas related: centripetal

force and conservation of kinetic energy and

potential energy.

7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

3/11

The roller coaster works by gravity. There are no motors used to power it

during the whole ride. Starting from rest, it simply descends down a steephill, and converts the (stored) gravitational potential energy into kineticenergy, by gaining speed. A small amount of energy is lost because of thefriction. Thats the reason why it is impossible for a roller coaster to returnto its original height after the ride is over.

7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

4/11

According to Newton's secondLaw (F=am), it explains thereason why circular motion occurs. An object acceleratestoward the center of a circle because of the action of a netforce in that direction

Centripetal acceleration: ac = v2/R

Fc = mac Fc= mv2/R FN + W = Fc (W = mg and Fc= mv

2/R)

FN + mg = mv2/R

as the velocity of the roller coaster is greater, the normalforce will be greater so that the roller coaster car will not fallwhen it is going through the loops

7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

5/11

In order to calculate the minimum velocity required

by the roller coaster car to go through the loop. Weassume FN equals to 0.

FN + mg = mv2/R mg = mv

2/R the mass of the roller coaster car (with passengers

on it) does not play a role in here because the masscancels out on both sides

Then the minimum velocity required v = gR

7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

6/11

Mass of the roller coaster: 700kg

Maximum height of the roller coaster: 80 meters

Radius of the loop of the roller coaster: 30 meters

Gravity of earth is also known to be 9.8ms-2 approximately

In order to find the minimum velocity which the roller coastercar must have in order to pass the loop, the above values

have to be substituted into the formula v = gR .

Note the minimum velocity can be calculated regardless ofthe mass of roller coaster

v = gR

V= 9.81 30 V 17.16 ms-1

7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

7/11

At the top, the roller coaster has the largest quantityof potential energy. Potential energy is the energy ofvertical position which dependent upon the mass ofthe object and the height of the object. PE = mass *g * heightAs the cars descend the first drop they lose much ofpotential energy due to their loss of height. Thepotential energy of this car transfer to the kineticenergy subsequently. Kinetic energy is the energy ofmotion which is dependent upon the mass of theobject and it speed. KE = 0.5 * mass * (speed)^2The train of coaster cars speeds up as they loseheight. In that way, their original large potentialenergy (due to their height) transform into kineticenergy (due to their speeds). In the whole process ofthis ride, cars are losing and gaining heightcontinuously. In real world, there is also a small

amount of energy lost due to the friction.The roller coaster illustrate:KEinitial + PEinitial + Wexternal = KEfinal + PEfinal(conservation of mechanical energy)

Related notes:Total energy = KE + PE

= ( 1/2m vf2 - 1/2m vi2)+ ( mghf- mghi)

7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

8/11

In order to explain how does these energy transformation clearly,numerical values will be involved. Assume that the mass of rollercoaster is 700kg. The maximum height of this roller coaster is80meters. How can we find the maximum speed of this roller coasterduring the whole ride? And where does the maximum speed happen?

By conservation of mechanical energy

The total mechanical energy at the maximum height (the roller coasteris immobile)

equals its potential energy = mgh = 700*9.8*80 = 548800 j

When the roller coaster is at the lowest position of the whole ride, itget the maximum speed, because all the potential energy transfers

into kinetic energy.Kinetic energy = 1/2mv^2= 0.5*700*V^2=350V^2=5488000

solve for V= 35.598m/s

7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

9/11

Energy cannot be eliminated or created, itcould only transform from one form to theother.

The design of roller coaster contains physicsconcepts like gravity, centripetal force,acceleration, friction and energy conversion.

7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

10/11

Those basic physics elements are protectingour safety when we are spinning, rising andfalling on that roller coaster.

These data must be carefully collected andcalculated. Physics is a precise science. Rollercoaster is a dangerous facility, one mistake

could cost a huge disaster.

7/29/2019 30 Physics 001 Project 2 (Zhang,_Wang, Gao)'

11/11

"Analysis of Situations in Which Mechanical Energy Is Conserved." The PhysicsClassroom. Web. 21 Apr. 2011..

"Energy Transformation on a Roller Coaster." The Physics Classroom. Web. 21 Apr. 2011..