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Get Full Access to University Physics - 13 Edition - Chapter 7 - Problem 46p
Get Full Access to University Physics - 13 Edition - Chapter 7 - Problem 46p

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# CP Riding a Loop-the-Loop. A car in an amusement park ride ISBN: 9780321675460 31

## Solution for problem 46P Chapter 7

University Physics | 13th Edition

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Problem 46P

CP Riding a Loop-the-Loop. A car in an amusement park ride rolls without friction around a track (Fig. P7.42). The car starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle. (a) What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B)? (b) If ?h? = 3.50 R and ?R? = 14.0 m, compute the speed, radial acceleration, and tangential acceleration of the passengers when the car is at point C , which is at the end of a horizontal diameter. Show these acceleration components in a diagram, approximately to scale.

Step-by-Step Solution:

Solution 46P Introduction At top the car will not fall if the velocity at the top of the hoop is such that the centrifugal force is equal to the gravity. We will use this information to calculate the velocity of the car at the top point. From the velocity we can calculate the energy at that point. The required energy will be supplied by the potential energy because of the starting height of the car. We will calculate the required height from the required potential energy of the car. Now by using the given values we will calculate the velocity and acceleration at the specified point. Step 1 The car will not fall from the top of the hoop, if the velocity of the car at the top of the hoop is such that, the centrifugal force is equal to the weight of the car. Suppose v is the velocity of the car at the top point. Hence the centrifugal force is Here m is the mass of the car. Now the weight of the car is Hence we have Hence the kinetic energy at that point is And the potential energy of the car at that point is Hence the total energy at that point is Now if the starting height of the car is h, then we have Hence the height h will be 2.5R.

Step 2 of 2

##### ISBN: 9780321675460

The answer to “CP Riding a Loop-the-Loop. A car in an amusement park ride rolls without friction around a track (Fig. P7.42). The car starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle. (a) What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B)? (b) If ?h? = 3.50 R and ?R? = 14.0 m, compute the speed, radial acceleration, and tangential acceleration of the passengers when the car is at point C , which is at the end of a horizontal diameter. Show these acceleration components in a diagram, approximately to scale.” is broken down into a number of easy to follow steps, and 120 words. University Physics was written by and is associated to the ISBN: 9780321675460. This full solution covers the following key subjects: Car, Loop, point, acceleration, around. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. This textbook survival guide was created for the textbook: University Physics, edition: 13. Since the solution to 46P from 7 chapter was answered, more than 594 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 46P from chapter: 7 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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