Basic Collision/Pendulum Problem

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In summary, the problem is asking to find the value of mass Mew-M in terms of M and m, so that mass m attains maximum height after an elastic collision with Mew-M. This can be solved by considering conservation of energy and momentum equations and finding the maximum velocity of mass m. The condition for maximum velocity is that the combined mass of Mew-M and m must be equal to M.
  • #1
donwa83
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Ok, I need help with a basic collision problem. Please see the attached image and picture the image as a pendulum.

You bring mass 'M' up a certain height and let it go. It collides elastically with mass 'Mew M." Mass 'm' goes up a maximum height. Find mass 'Mew M' so that mass 'm' can attain the maximum height.

Also:
(1) M Does not equal m.
(2) The answer is not infinitely small, which is what i got :frown:.
 

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  • #2
Why don't you show us how you got the wrong answer? Maybe we can work it out from there.

What things remain conserved in elastic collisions?
 
  • #3
Energy is conserved in a completely elastic collision. I used (1) energy of 'M', (2) collision of 'M' and 'm', (3), collision of 'Mew' and 'm', (4) energy of 'm'


First see attached for description of initial height.

So:

(1) Energy
Mg(L-Lcos[tex]\theta[/tex] )=(1/2)M[tex]V^{2}[/tex]

V = [tex]\sqrt{2gL(1-cos\theta[/tex])




(2) Find the Velocity of 'Mew' after the collision, [tex]V_{3}[/tex], with momentum equation.

[tex]V_{3} = \frac{M(V-V_{2})}{Mew}[/tex]

[tex]V_{2} [/tex] = Velocity of M after collision with Mew




(3) Find the velocity of 'm' after the collision with 'Mew,' [tex] V_{5}[/tex] with momentum equations.

[tex]V_{5} = \frac{M(V-V_{2}) - MewV_{4}}{m} [/tex]

[tex] V_{4} [/tex] = the velocity of 'm' after the collision with 'Mew'





(4) Use energy equation to find Hmax.

[tex] mgHmax = \frac{1}{2} m V_{5}^{2} [/tex]




Am I on the right track? Or am I missing something?
 

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  • #4
You need not worry about the height. The only thing of concern is the KE and V of the mass M at the moment of collision. The values of the KE etc is immaterial, because you have to find mew-m in terms of M and m.

When a mass M collides with another mass, say M', what is the value of M' such that the whole KE of M is transferred to M' ? Think on these lines.
 
  • #5
I got it?

When a mass M collides with another mass, say M', what is the value of M' such that the whole KE of M is transferred to M' ? Think on these lines.

M transfers all its kinetic energy to M' only if M' is the same mass as M! So the answer is Mew-M's mass must be equivalent to the M's mass. Or will 'm' go further if Mew-M was equal to m and not M? M does not equal m.
 
  • #6
Not mew_m' mass but the combined mass of mew_m and m!

Let's assume M comes to rest and gives up all the KE to mew-m and m. Then mew_m and m must add up to M.

You may ask whether that'll ensure the mass m receiving the max energy. You see, not only the KE but the momentum MV of the mass M is also being transferred to mew_m+m. Both conditions combined make m recv the max KE, and so swing up the highest.

(The delay in my first reply was due to a messy piece of algebra I had to before I was satisfied that this was indeed the case.)
 
Last edited:
  • #7
I understand your answer conceptually, but I'm not sure how to solve it algebraically. Should I start with a collision between M and Mew (which will yield the same velocity) and then Mew with m?


Also, initially I was thinking that m must be:

m = [tex]\frac{1}{2}[/tex] M + [tex]\frac{1}{2}[/tex] Mew

Ah, its so open ended without math ! :cry:
 
  • #8
Let MV = p and (1/2)MV^2 = k, for easier wrtining. I'll call mew_m as m1 and its speed as v1 etc.

m1v1^2 + mv^2 = 2k and m1v1 + mv = p. k and p are constants.

Eliminate v1 from the two eqns and maximise v. We want v to be max because m is a constant in the problem, so (1/2)mv^2 will be max.

That'll give you the reqd condition.
 

1. What is a basic collision/pendulum problem?

A basic collision/pendulum problem is a type of physics problem that involves the motion and interaction of objects that collide or swing on a pendulum. These problems typically require the use of Newton's laws of motion and conservation of energy to solve.

2. How do you approach solving a basic collision/pendulum problem?

The first step in solving a basic collision/pendulum problem is to draw a diagram of the situation and label all known quantities, such as masses, velocities, and angles. Then, use Newton's laws of motion and conservation of energy to set up and solve equations to find the unknown quantities.

3. What is the difference between an elastic and inelastic collision?

In an elastic collision, both kinetic energy and momentum are conserved, meaning that the objects bounce off each other with no loss of energy. In an inelastic collision, some of the kinetic energy is lost due to deformation or sticking together of the objects, so only momentum is conserved.

4. How does the length of a pendulum affect its period?

The period of a pendulum (the time it takes for one swing) is directly proportional to the square root of its length. This means that as the length of a pendulum increases, its period also increases.

5. Can a collision/pendulum problem be solved without using calculus?

Yes, simple collision/pendulum problems can be solved using only algebra and basic concepts of physics. However, more complex problems may require the use of calculus to solve for unknown variables and equations.

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