Physics problem, elastic collision

[Lawana]

The following problem should be extremely easy, but somehow dd's answer is not matching the expected answer.

 

An object with a mass of 0.10 kg makes an elastic head-on collision with a stationary object with a mass of 0.15 kg. The final velocity of the 0.10 kg object after the collision is 0.045 m/s, in the opposite direction. The final velicity of 0.15 kg object is 0.1m/s. What was the initial velocity of the 0.10 kg object?

 

Help, please.

[regentrude]

You could start like this:

In a collision, linear momentum is conserved. p=mv

So , 0.1kg*v_initial +0.15kg*0 (stationary)= - 0.1 kg*0.045m/s (minus because opposite direction)+0.15kg*0.1m/s

Solve for v_initial=0.105 m/s

 

However, this collision is NOT elastic! In fact, the values make absolutely no sense:

Kinetic energy before collision: 0.5*0.1kg*(0.105m/s)^2=5.5125 exp-4 J

Kinetic energy after collision: 0.5*0.1kg*(0.045m/s)^2+0.5*0.15kg*(0.1m/s)^2=8.5125 exp-4 J

This would mean the energy gets bigger in the collision, which is impossible.

 

I suspect that somewhere there is a typo in the information.

Also, if the wording of the problem is like this, it is overdetermined: you could use either momentum or energy conservation (if it were really elastic). So, if your DD has solved it using energy conservation, she would get a different answer, but her answer would violate the conservation of momentum.

[Lawana]

Thank you! I had the same idea that there was something wrong with the problem, and I also came up with 2 different values using conservartion of momentum and conservation of energy.

 

This problem was made up by dd's physics teacher, who claims the answer is something other than the above, or the 0.13 m/s I got when using conservation of energy.

 

Thanks again.

[regentrude]

Thank you! I had the same idea that there was something wrong with the problem, and I also came up with 2 different values using conservartion of momentum and conservation of energy.

This problem was made up by dd's physics teacher, who claims the answer is something other than the above, or the 0.13 m/s I got when using conservation of energy.

 

Ugggh! I hate it when teachers make up incorrect problems.

Please, please, write out the solutions and show him that this problem is physically impossible.

[Lawana]

Again, thank you so much. It means so much to our community that you are willing to share your knowledge and expertise. I didn't post on the other thread about your dd's success, but I want to express my congratulations as well. How fortunate for your dd that she has you for her mother.

[athomeinMT]

In the teacher's defense, you didn't mention if he told her that the answer was an actual numerical value. I have been known to give my students problems that don't work with the intent that they are to discover that and tell me so. Sometimes you get a group of high school students who just don't want to put the effort into their work to look back at it and see if it makes sense. They want to plug numbers into a formula and give you a value without understanding what they are doing and that is really not learning.

 

This may not be the case, and if so then please disregard my response.

[Lawana]

In the teacher's defense, you didn't mention if he told her that the answer was an actual numerical value. I have been known to give my students problems that don't work with the intent that they are to discover that and tell me so. Sometimes you get a group of high school students who just don't want to put the effort into their work to look back at it and see if it makes sense. They want to plug numbers into a formula and give you a value without understanding what they are doing and that is really not learning.

 

This may not be the case, and if so then please disregard my response.

 

Thanks for your reply. In this case, a numerical answer was needed, as the problem was multiple choice. Unfortunately, none of the answers were right. The teacher ended up telling her students to disregard that particular problem.

 

The fact that this problem was problematic is an anomaly for this teacher. She has taught dd math and science for 5 years now. I really don't know what to make of this. Since she has been competent in everything else, I'm willing to let this one go.