How to find minimum possible mass

In summary, the conversation discusses the use of the integral to find the impulse and momentum change of an unknown mass in a collision. It also raises questions about the minimum required for finding the solution and the use of energy in the problem.
  • #1
ssarpal
7
1
Homework Statement
A block of mass m moving at a speed 4 m/s collides with a block of mass 2 Kg initially at rest. The force during collision varies as the function F = A*sin^2(Bt). The collision lasts for 1 ms.

Find the minimum possible mass m?
##A = 10^4 N##

##B = 1000\pi \hspace{2mm} rad/sec##
Relevant Equations
Change in momentum is equal to the integral of force with respect to time.
lagrida_latex_editor (2).png

Unfortunately, this is not the right answer.
 
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  • #2
The integral gives you the impulse ##J## which is the momentum change of the unknown mass. After the collision, this mass will still be moving with velocity ##v_1## and the 2 kg will also be moving with velocity ##v_2## because it received impulse ##J## in the opposite direction. Do you see how to tie all this together?
 
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  • #3
ssarpal said:
this is not the right answer.
Did it bother you that you were asked to find a minimum, but you did not go through such a step?
 
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  • #4
kuruman said:
The integral gives you the impulse ##J## which is the momentum change of the unknown mass. After the collision, this mass will still be moving with velocity ##v_1## and the 2 kg will also be moving with velocity ##v_2## because it received impulse ##J## in the opposite direction. Do you see how to tie all this together?
I think that means
##mu_1 = mv_1 +m_2v_2##
where ##u_1## = 4 m/s and ##m_2## = 2 Kg
Am not sure if ##v_1## and ##v_2## are needed to solve this?
 
  • #5
haruspex said:
Did it bother you that you were asked to find a minimum, but you did not go through such a step?
Yes, was wondering where it could be used, am not sure how though.
 
  • #6
ssarpal said:
Yes, was wondering where it could be used, am not sure how though.
Perhaps you need to think about energy?
 
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  • #7
The first thing to ask oneself is: What are the possible final velocities of each object and what is the mass m for each of those velocities?
 
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1. How do you determine the minimum possible mass in a scientific experiment?

The minimum possible mass in a scientific experiment can be determined by conducting multiple trials and finding the lowest recorded mass. This can also be achieved by using precision instruments and techniques to accurately measure the mass.

2. Is there a mathematical formula for finding the minimum possible mass?

There is no specific mathematical formula for finding the minimum possible mass. However, it can be calculated by taking the average of multiple measurements or by using statistical analysis methods.

3. Can the minimum possible mass change over time?

Yes, the minimum possible mass can change over time due to various factors such as environmental conditions, sample degradation, and equipment calibration. It is important to regularly monitor and adjust for these changes in order to obtain accurate results.

4. How does the precision of instruments affect the determination of minimum possible mass?

The precision of instruments plays a crucial role in accurately determining the minimum possible mass. Higher precision instruments can measure smaller mass differences, resulting in a more precise determination of the minimum possible mass.

5. What are some common sources of error when trying to find the minimum possible mass?

Some common sources of error when trying to find the minimum possible mass include human error, equipment error, environmental factors, and sample contamination. It is important to carefully control and monitor these factors in order to obtain reliable results.

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