A 300kg roller coaster at an amusement park is at rest on...

A 300 kg roller coaster at an amusement park is at rest on top of a 30 m hill (Point A). The car starts to roll down the hill and reaches point B, which is 10 m above the ground, and then rolls up the track to point C, which is 20 m 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 location where potential energy = 0) 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?

Transcript

00:01 So in this question it has been asked that there is a specific type of roller coaster in an amusement park with three different points named a with height 30 meter, b with height 10 meter and c with height 20 meter.

00:21 And we have a roller coaster of mass m is equals to 300 kg.

00:30 This roller coaster goes from a to b and finally at c.

00:36 Now for question number a, we'll have to find the velocity of the roller coaster at point c.

00:45 Now, we know that ea will be equals to e .c from conservation of energy.

00:54 Now, putting in the values, we will see the value of ea is potential energy, that is mg times the height of aha, plus the kinetic energy of a, will be equals to potential energy at c, that is mg times the height of c, that is hc, plus the kinetic energy at c, that is, half mv square.

01:17 Now we know that the roller coaster was at rest at a, therefore the kinetic energy at a will be 0.

01:25 Therefore, we can write the new equation as mg times ha is equals to mg times hc plus half times mv square.

01:35 Now putting in the values we see the value of mass as 300 kilograms times the value of acceleration due to gravity that is 9 .8 times the height of a that is 30 meters will be equals to the value of mass that is 300 kilograms times the gravitational acceleration that is 9 .8 times the height of c that is 20 meter plus half times the mass that is 300 kilograms times velocity square.

02:03 We need to figure out the value of velocity.

02:06 Now upon further calculation we find velocity square as 9 .8 times 30 minus 20 times 2.

02:15 And upon further calculation we will see that the velocity value is 14 meter per second.

02:24 So this is our required value of velocity of the roller coaster at point c.

02:29 Now for question number b, we'll have to find the mechanical energy at b, that is eb.

02:35 Now once again, we can write e .a is equals to e b, that too from conservation of energy.

02:47 Now putting in the values of ea, we see mass times acceleration due to gravity times the height of a that is ha plus kinetic energy at a will be equals to energy at b.

03:00 Now we know that kinetic energy of a is 0 as the roller coaster started from rest at a.

03:11 So now putting in the values we find mass as 300 kilograms times acceleration due to gravity as 9 .8 times the height of a is 30 meters is equals to eb...

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