Question

A 300kg roller coaster at an amusement park is at rest on top of a 30m hill (Point A). The car starts to roll down the hill and reaches point B, which is 10m above the ground, and then rolls up the track to point C, which is 20m above the ground.

a) Assuming no energy is lost and using energy arguments, how fast is the cart moving at point C?

b) What is the total mechanical energy of the roller coaster at point B (Use the ground as the locaiton where potential energy=0)

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If the final speed at point C is actually measured to be 12 m/s,

a) How much energy is lost?

b) Where did this energy go?

Answer 1

SECTION (1):

PART (a):

Mass of the roller coaster, m = 300 kg

at point A:

Height, h = 30 m

Speed, V = 0 m/s

Therefore, Total energy at point A:

Where g is acceleration due to gravity.

at point C:

Height, h₁ = 20 m

Total energy at point C = Total energy at point A (law of conservation of energy)

Total energy at point C:

Also, we have:

Let V be the final speed of the roller coaster.

Cancelling out m:

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

PART (b):

at point B:

Total energy at point B = Total energy at point A (law of conservation of energy)

Total energy at point B:

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

SECTION (2):

PART (a):

at point C:

Height, h₁ = 20 m

Speed, V = 12 m/s

Total energy at point C:

We have, Total energy at A, TE_A = 88200 J

Therefore Energy lost () is given by:

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

PART (b):

There is several ways through which energy lose may happen. Some of them are:

• Frictional loss of energy major cause of loss of energy).
• As sound energy.
• As heat energy/thermal energy.
• As light energy (in case of sparks) etc.