How Does Newton's Cradle Demonstrate Conservation Laws in Physics?

[tnutty]

Homework Statement

Imagine a regular Newtons cradle (google it). The problem gives a the following information.
All the spherical ball have the same mass. Ball 1, m_1 is initially raised at height H_i.

A) Consider a stack consisting of just two balls. Let the speed of the first ball just before the collision be V_o. Solve V_f in terms of H. Solve for V_0 in terms of H.

ANS : Using the conservation of energy equation I got H = 0.5V_f^2 / g.


B) Just after the collision , the first ball bounces back at speed V_1, and the second ball moves forward at speed V_2. State the law of conservation of momentum for the general cases of masses m_1 and m_2 in terms of speed V_1 , V_2, and V_f ?

not sure what this is asking. Is is just m_1*V_1 + m_2*V_2 = m_1*V_1f + m_1 * V_1f


C) State the law of conservation of energy for elastic collision for the general case of masses m_1 and m_2 in terms of speed V_1, V_2, and V_f?

Is it just 1/2(m_1*V_1 + m_2*V_2) = (m_1*V_1f + m_1 * V_1f) 1/2

D) Solve for the speeds V_1 and V_2 for the special case that m = m, and m_2 = 2 M using the equations from part b and c above. Show that your solution satisfies the conservation of momentum and energy during the collision.
NEED HELP ON THIS PART!

E) To What height,H_1 will the first mass rebound after the elastic collision? To what maximum height, H_2, will the second mass rise before falling back.

Intuitively , H_1 rebounds to height 0.
And not sure about the next part.

 

[tiny-tim]

B) Just after the collision , the first ball bounces back at speed V_1, and the second ball moves forward at speed V_2. State the law of conservation of momentum for the general cases of masses m_1 and m_2 in terms of speed V_1 , V_2, and V_f ?

not sure what this is asking. Is is just m_1*V_1 + m_2*V_2 = m_1*V_1f + m_1 * V_1f

Hi tnutty!

That's correct … except shouldn't you have put one of them = 0?

C) State the law of conservation of energy for elastic collision for the general case of masses m_1 and m_2 in terms of speed V_1, V_2, and V_f?

Is it just 1/2(m_1*V_1 + m_2*V_2) = (m_1*V_1f + m_1 * V_1f) 1/2

hmmm … what's in your brain may be correct, but what you've written is the same as for momentum

D) Solve for the speeds V_1 and V_2 for the special case that m = m, and m_2 = 2 M using the equations from part b and c above. Show that your solution satisfies the conservation of momentum and energy during the collision.
NEED HELP ON THIS PART!

Find either V1 or V2 from the first equation, and substitute that value into the second equation

 

[tnutty]

Part C is 1/mv^2 for each with initial and final.

pard D) How do you find v_!1?

And how would you find at what H_1, and H_2 the ball reaches, if the mass
ratio of m1/m2 = 1/3, or 4/2 ?

 

[tiny-tim]

Part C is 1/mv^2 for each with initial and final.

Do you mean 1/2 mv² ?

pard D) How do you find v_!1?

As I said before: Find either V1 or V2 from the first equation, and substitute that value into the second equation