What is the correct formula for solving part b of this problem?

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In summary, the conversation discusses a physics problem involving a solid brass ball rolling along a loop-the-loop track. The first part of the problem involves determining the minimum height from which the ball must be released to ensure it stays on the track at the top of the loop. The second part involves calculating the magnitude of the horizontal force acting on the ball at a certain point on the track. Various equations and formulas are discussed, with the final answer being F = 50/7mg.
  • #1
HobieDude16
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ok, here's a problem that you have to work out with all variables, and i frankly have trouble doing that... i got part a, and i did a lot of work on part b, but can't seem to come up with the right answer... any help appreciated...

In Figure 11-32, a solid brass ball of mass m and radius r will roll without slipping along the loop-the-loop track when released from rest along the straight section. For the following answers use g for the acceleration due to gravity, and m, r, and R, as appropriate, where all quantities are in SI units.

Fig. 11-32
hrw7_11-32.gif


(a) From what minimum height h above the bottom of the track must the marble be released to ensure that it does not leave the track at the top of the loop? (The radius of the loop-the-loop is R. Assume R r.)

(b) If the marble is released from height 6R above the bottom of the track, what is the magnitude of the horizontal component of the force acting on it at point Q?

ok, for part a, i got 2.7R whichi is correct, so then i moved on to part b, and i was told by my TA to start with the formula mg6R = .5mv^2 + .5Iomega^2 + mgR... so i did, and tried to solve for v. i used 2/5mR^2 for I and for omega, used v/R... so if i do that, and solve for v, then i use a=v^2/r and then when i have that, F=ma so i have the idea, i just can't get it right. anybody have any ideas? thanks in advance
John
 
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  • #2
anybody have any ideas?
 
  • #3
maybe i can find some help on another forum or something
 
  • #4
Ok you work with conservation of energy and do, mgh=mgR+7mv^2/10. So at point Q you have F=mv^2/R=(50/7)mg
 
  • #5
awesome, can't believe i didnt think of that, lol
 
  • #6
btw u can find this one in almost every physics book it a classic


mg6R = 1/2mv^2+1/2Iw^2 + mgR

mg6R = 1/2mv^2 + 1/2 (2/5mr^2)w^2 + mgR

6gR = 1/2v^2 + 1/5r^2(v/r)^2+gR

5gR = 7/10 v^2

50/7gR = v^2

F = 50/7mg
 
Last edited:
  • #7
ah, really? its not in ours (since its asked as a question in ours... lol)
 
  • #8
Help...

Hey HobieDude16,

Can you show me how you got part A? I'm learning angular momentum too and I have a similar problem except the ball is not on a ramp. Thanks.
 
  • #9
Hobie sent you a message hope you can help :)
 
  • #10
sqrt(9.8*r)=sqrt(10/7*9.8*(h-2R))
basically, i looked through the book, found examples of a guy riding a bike around a loop, and then found an example of a ball rolling down a hill, and combined and adjusted to work... maybe that might help
 

FAQ: What is the correct formula for solving part b of this problem?

1. What is a variable?

A variable is a quantity or value that can change in an experiment or mathematical equation. It is usually represented by a letter or symbol and can take on different values.

2. Why are variables important in scientific research?

Variables allow scientists to test and manipulate different factors in an experiment to determine their impact on the outcome. They help to control and isolate specific elements to understand their role in the overall process.

3. What is the difference between independent and dependent variables?

An independent variable is a factor that is manipulated or changed by the researcher in an experiment. A dependent variable is the outcome that is measured and affected by changes in the independent variable.

4. How do you control for variables in an experiment?

To control for variables in an experiment, scientists use a control group that is kept under standard conditions while other groups are exposed to different variables. This allows for a comparison of results and helps to isolate the impact of specific variables.

5. What are some common challenges or issues with variables in scientific research?

One challenge with variables in scientific research is ensuring that all other factors are controlled and kept constant, so the only difference between groups is the variable being tested. Another issue is determining which variables are most important to focus on and how to accurately measure and analyze their impact.

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