Kinematics - marbles rolling down a ramp and into sand

[jsmith613]

Kinematics -- marbles rolling down a ramp and into sand

Homework Statement

14) The student carries out an experiment to investigate momentum and collisions. A ball bearing is rolled down a ramp clamped at the edge of a bench. The ball bearing makes a head-on collision with a marble at the bottom of the ramp.

The ball bearing and the marble both move forward in the initial direction of the ball bearing after the collision, landing in a tray containing a layer of sand.

(a) Initially the ball bearing rolls down the ramp without the marble in a place. The ball bearing falls a vertical distance of 1.2m and lands a horizontal distance 95cm forward of the end of the ramp. Show that the speed of the ball bearing leaving the ramp is about 2ms^-1
I worked this out, CORRECTLY as 1.9 ms^-1

(b) When the ball bearing is rolled down the ramp with the marble in place, it knocks the marble forwards. The ball bearing lands a horizontal distance 64cm forward of the end of the ramp, and the marble lands a further 93cm forward from this position. Calculate the ratio of masses of the ball bearing and he marble

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PART (b) IS THE QUESTION ON WHICH I AM STUCK

Homework Equations

v² = u² + 2as

The Attempt at a Solution

so

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

m₁u₁ = 1.9m₁
m₂u₂ = 0

1.9m₁ = m₁v₁ + m₂v₂
BUT I cannot find v₁ OR v₂ as I don't know the distance the balls FALL

 

[SHISHKABOB]

isn't it 1.2 meters?

 

[jsmith613]

isn't it 1.2 meters?

no that is the distance between the top and bottom of the ramp NOT the bottom of the ramp and the floor

(imagine a ramp standing on a table - the 1.2 m deals with the height of the ramp)

part (b) deals with the height above the ground - THERE MAY BE another way to do it but i figured my method was most logical!

 

[SHISHKABOB]

oh so like this? and the ramp is 1.2 meters high from top to table?EDIT: actually now that I read this part more carefully: "The ball bearing falls a vertical distance of 1.2m"

it seems to say that the 1.2 meters is the height from the tray to the bottom of the ramp

 

[jsmith613]

oh so like this? and the ramp is 1.2 meters high from top to table?EDIT: actually now that I read this part more carefully: "The ball bearing falls a vertical distance of 1.2m"

it seems to say that the 1.2 meters is the height from the tray to the bottom of the ramp

the diagram is exactly what is in the book and although it is unlabelled it would seem that the inital suggestion is correct :)
(i.e: the BOOK diagram is unlabelled)

 

[gneill]

If you know the speed that the solo ball bearing left the ramp horizontally, and you know how far it traveled horizontally before it hit the sand, then surely you can work out the height of the drop from table to sand...

 

[jsmith613]

If you know the speed that the solo ball bearing left the ramp horizontally, and you know how far it traveled horizontally before it hit the sand, then surely you can work out the height of the drop from table to sand...

actually that cannot be correct because the ball will lose speed when it hits the marble :S
if it helps the MS got an answer of 5.3 although I have no clue how :S

 

[SHISHKABOB]

actually that cannot be correct because the ball will lose speed when it hits the marble :S
if it helps the MS got an answer of 5.3 although I have no clue how :S

the height of the table is not going to change depending on if the ball is alone or if it is hitting a marble :)