How Does Friction Affect a Ball's Energy and Travel Distance?

[lwymarie]

http://student.shcc.edu.hk/~s021107/rdhg.GIF


a ball of 0.1 kg slides down the track from A and completes the loop without leaving the track. if the ball passes C at 3ms^-1 and D at 4 ms^-2, which of the following is/are correct?

1. energy of the ball at B is 1.1J
2. frictional force acting on the ball is 0.191N
3. the ball will continue to run on the horizontal track for 4. 19 m after passing D


a. 1 only
b. 3 only
C 1 and 2 only
D 1, 2 and 3

 

[HallsofIvy]

Did you read the informational sticky titled "read this". We don't do your homework for you. Show us what you do understand about this and what you have tried so that we can give you hints. Do you know how to calculate (1) potential energy, (2) kinetic energy, (3) total energy?

 

[lwymarie]

i've thought for a long time.. but i still don't know how to solve it..
i hv the basic knowledge to solve this question. however i don't hv the skill to tackle this problem

 

[Werg22]

It is impossible to know unless you have some additional information on lenghts, height and angle.

 

[lwymarie]

And that's why i failed to solve it. However this is a question with 3 asterics, so perhaps there's a way to solve without knowing the dimensions.
Can anyone help me? thx

 

[lwymarie]

Can anyone help me? If no additional information (e.g. dimensions) are given, is it able to solve the problem?

 

[OlderDan]

Can anyone help me? If no additional information (e.g. dimensions) are given, is it able to solve the problem?

The original statement of the problem probably contains an arror

a ball of 0.1 kg slides down the track from A and completes the loop without leaving the track. if the ball passes C at 3ms^-1 and D at 4 ms^-2, which of the following is/are correct?

One of these numbers is a speed and the other is an acceleration. The problem does not state if it is talking about either speed or acceleration, but both are involved in the problem. The diagram shows a symbol suggesting the height of the loop is known, but the number is missing. If there were no friction, and the numbers given in the statement were as they actually appear, or as is more likely they are both supposed to be speeds, then the height of the loop could be deduced, but with friction that cannot be done.

At least go back and check the original problem and make sure you have provided all the information given. Then perhaps we can give you a hint how to approach the problem.

 

[lwymarie]

ah! the height is 0.5m. I'm so sorry that i forget the type the height in my diagram. would you please help me again now? I'm so sorry..

 

[OlderDan]

ah! the height is 0.5m. I'm so sorry that i forget the type the height in my diagram. would you please help me again now? I'm so sorry..

The missing height is not the only problem. I am going to assume that you meant 4ms^-1 rather than 4ms^-2 at D. If you do that, then here is what MIGHT be true. I'm going to leave some blanks for you to fill in, but the outline covers the things you need to think about.

0.191 N could be the frictional force at the end, but unless the coefficient of friction is different in different places on the track, the frictional force has to change. I will assume the coefficient does change to keep the force constant, and let's see what happens. If the friction is 0.191N, and if the distance from D to the end of motion is 4.19m then the work done by friction from point D on is ____, so the energy at point D would have to be _____

The kinetic and potential energies can be calculated at C and D. If the zero of potential energy is taken to be the bottom of the track, then at C (assuming C is at the very top) the total energy is _____. At D the energy is _____, which is consistent with the assumed frictional force and the runout from point D. The energy lost to friction during the descent from C to D is ______. The distance between C and D is _____, so if you figure out the average force over that distance it comes out to be a bit less than .191 N.

So maybe C is not the top exactly. It's hard to tell from the diagram. If the distance from C to D is a bit less, the frictional force could be .191N, but then the energy at C would be a bit less than what is calculated above. I'm sure I could find a point C that would make the energy loss from C to D just right for a frictional force of .191N

The location of point B is unclear, but if the energy there is to be 1.1J, then the energy loss between B and C has to be _____ (a bit more if point C is located after the top). If the friction is constant, the energy lost from B to C has to be a bit more than the energy loss from C to D, which certainly looks possible.

Unless you have more specific information about the location of the points, then everything else is somewhat speculative. It looks like all three statements MIGHT be true, but the idea of a constant frictional force is unusual. It is more likely that there will be a constant coefficient of friction. You can find the coefficient that would be needed for the force to be .191N at the end. If you use that coefficient and calculate the frictional force from the normal force that could be calculated at C you would find the frictional force to be much greater than .191N. But this is a hypothetical problem, so assuming a constant frictional force is OK. Then it becomes a matter of making sense of the rest of it.