*hard* collisions question
hey! i'm struggling with this question (managed part a - they are travelling in opposite directions) and how to get what they want
any/all help appreciated!
Consider a sphere of mass 𝑚 moving along the positive 𝑥-axis until there is an elastic collision with a sphere of mass 𝑀 at rest. Assume that the radius of both spheres is equal to one and that 𝑀>𝑚
(i) Which direction(s) do the two spheres move in after the collision?
(ii) Assume that after the collision the centre of sphere with mass 𝑀 is at 𝑥=𝑎 when the centre of the sphere with mass 𝑚 is at 𝑥=0
Show that the sphere with mass 𝑀
was initially at 𝑥̃ =[(𝑀−𝑚)𝑎+4𝑚]/[𝑀+𝑚]
(iii) What do you find for 𝑥̃ when 𝑀 is much larger than 𝑚? Explain your result.
any/all help appreciated!
Consider a sphere of mass 𝑚 moving along the positive 𝑥-axis until there is an elastic collision with a sphere of mass 𝑀 at rest. Assume that the radius of both spheres is equal to one and that 𝑀>𝑚
(i) Which direction(s) do the two spheres move in after the collision?
(ii) Assume that after the collision the centre of sphere with mass 𝑀 is at 𝑥=𝑎 when the centre of the sphere with mass 𝑚 is at 𝑥=0
Show that the sphere with mass 𝑀
was initially at 𝑥̃ =[(𝑀−𝑚)𝑎+4𝑚]/[𝑀+𝑚]
(iii) What do you find for 𝑥̃ when 𝑀 is much larger than 𝑚? Explain your result.
Original post by AngryHomer
hey! i'm struggling with this question (managed part a - they are travelling in opposite directions) and how to get what they want
any/all help appreciated!
Consider a sphere of mass 𝑚 moving along the positive 𝑥-axis until there is an elastic collision with a sphere of mass 𝑀 at rest. Assume that the radius of both spheres is equal to one and that 𝑀>𝑚
(i) Which direction(s) do the two spheres move in after the collision?
(ii) Assume that after the collision the centre of sphere with mass 𝑀 is at 𝑥=𝑎 when the centre of the sphere with mass 𝑚 is at 𝑥=0
Show that the sphere with mass 𝑀
was initially at 𝑥̃ =[(𝑀−𝑚)𝑎+4𝑚]/[𝑀+𝑚]
(iii) What do you find for 𝑥̃ when 𝑀 is much larger than 𝑚? Explain your result.
any/all help appreciated!
Consider a sphere of mass 𝑚 moving along the positive 𝑥-axis until there is an elastic collision with a sphere of mass 𝑀 at rest. Assume that the radius of both spheres is equal to one and that 𝑀>𝑚
(i) Which direction(s) do the two spheres move in after the collision?
(ii) Assume that after the collision the centre of sphere with mass 𝑀 is at 𝑥=𝑎 when the centre of the sphere with mass 𝑚 is at 𝑥=0
Show that the sphere with mass 𝑀
was initially at 𝑥̃ =[(𝑀−𝑚)𝑎+4𝑚]/[𝑀+𝑚]
(iii) What do you find for 𝑥̃ when 𝑀 is much larger than 𝑚? Explain your result.
Hi, I understand it has been more than 2 weeks, if you still require help on the problem, do revert back.
For part (ii), what you need is to use the info (speed of M and m) you have obtained from (i) to compute the individual distance travelled by M and m respectively and then obtain 𝑥̃ through simultaneous equations.
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