Question

A 500-kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop (see figure). (a) How fast is this roller coaster moving at point B? (b) How hard does it press against the track at point B? (c) If the length of the track between points A and B is 50.0 m, what is the maximum constant friction force that the roller coaster can experience and still make it safely around the loop? 25.0 m 3.00 m 4.00 m 12.0 m

          A 500-kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop (see figure). (a) How fast is this roller coaster moving at point B? (b) How hard does it press against the track at point B? (c) If the length of the track between points A and B is 50.0 m, what is the maximum constant friction force that the roller coaster can experience and still make it safely around the loop?
25.0 m
3.00 m
4.00 m
12.0 m

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A 500-kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop (see figure). (a) How fast is this roller coaster moving at point B? (b) How hard does it press against the track at point B? (c) If the length of the track between points A and B is 50.0 m, what is the maximum constant friction force that the roller coaster can experience and still make it safely around the loop?
25.0 m
3.00 m
4.00 m
12.0 m

Added by Lauren G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Ivan Kochetkov

12/26/2022

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(a) The roller coaster is moving at point B at a speed of . Show more…

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A 500-kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop (see figure). (a) How fast is this roller coaster moving at point B? (b) How hard does it press against the track at point B? (c) If the length of the track between points A and B is 50.0 m, what is the maximum constant friction force that the roller coaster can experience and still make it safely around the loop? 25.0 m 12.0 m 4.00 m 3.00 m

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Transcript

00:01 Hello, here we have to solve the following problem.

00:03 Mass of the roller coaster is 500 kilograms and this roller coaster starts from the height.

00:10 Point h, which is 25 meters height.

00:15 So, first in question a, we have to determine how far it's moving at point b.

00:27 Kinetic potential energy at the position a equals to kinetic energy at the position b.

00:35 Plus potential energy the same position which is mg, hb and height of the point b is 12 meters.

01:05 Let's calculate it.

01:18 That is 16 meters per second.

01:23 Now let's move on to question b.

01:28 In question b, we have to find the reaction at point b.

01:35 Let's sketch the forces.

01:37 Which are acting at this point.

01:40 This normal reaction is downwards, gravity is downwards, and the centripetal acceleration is downwards and radius at this point, rb, is 6 meters as we can notice.

01:53 Therefore, mg plus normal reaction is mass times v squared over radius of this loop.

02:32 Let's calculate it.

03:07 Actually, here, yeah, we have to change the signs of course.

03:13 So let's fix a small typo and let's complete this calculation.

03:24 So this force is 1 .64 times 10 power by 4 newtons...

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