Kinetics of Masses on an Inclined Plane: Explaining Different Movements

[darkmagic]

Homework Statement

Refer to the diagram.

can someone explain why is the 300lb block moves only one-half the distance of the 200lb then the acceleration and velocity also to one half.

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Hi darkmagic!

velocity = dx/dt and acceleration = d²x/dt², so if you halve x, you halve velocity and acceleration also.

(and of course x is halved because the pulley moves only half as far as the string)

 

[darkmagic]

how can you know that the pulley moves only half of the string?

 

[tiny-tim]

When the pulley goes down 1 cm, that makes the string above it 1 cm longer on both sides, which requires 2 cm of string, so the block on the slope moves 2cm.

 

[darkmagic]

ok thanks. another question, how can I know to which the blocks will move and how their acceleration are computed? look at the new attachment.

 

[tiny-tim]

Just ask yourself, does the pulley move? if it does, how many strings are attached? (because each string will have to get longer or shorter by the same distance)

 

[darkmagic]

yes the blocks will move. my problem is in which direction will they move?

 

[tiny-tim]

To find out, write the F = ma equations for each of the three masses.

(and, if the heights of the masses are x y and z, you'll need a linear equation connecting x y and z)