Kinematics - marbles rolling down a ramp and into sand

• jsmith613
In summary: the height of the table is not going to change depending on if the ball is alone or if it is hitting a marble :)
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 verticle 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

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

isn't it 1.2 meters?

SHISHKABOB said:
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!

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 verticle 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

Attachments

• marble ramp.png
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SHISHKABOB said:
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 verticle 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)

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...

gneill said:
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

jsmith613 said:
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 :)

What is the relationship between the height of the ramp and the distance the marble travels?

The height of the ramp affects the potential energy of the marble. The higher the ramp, the greater the potential energy, which translates into a greater kinetic energy and therefore a longer distance traveled by the marble.

How does the angle of the ramp affect the speed of the marble?

The angle of the ramp affects the acceleration of the marble. The steeper the ramp, the greater the acceleration and therefore a higher speed of the marble.

What factors affect the amount of friction between the marble and the ramp?

The factors that affect the amount of friction include the material of the ramp and the surface of the marble, as well as any external forces such as air resistance.

How does the mass of the marble affect its motion down the ramp?

The mass of the marble affects the force of gravity acting on it and therefore its acceleration. A heavier marble will have a greater force of gravity and therefore a greater acceleration down the ramp.

What is the relationship between the speed of the marble at the bottom of the ramp and the depth of the sand it lands in?

The speed of the marble at the bottom of the ramp is determined by its initial speed and the distance traveled. The depth of the sand it lands in will affect the distance traveled and therefore the final speed of the marble.

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