Calculate acceleration and speed of block

AI Thread Summary
The discussion revolves around calculating the acceleration and speed of a block on a ramp, with a focus on why a negative acceleration value is obtained. The user derived the equation for acceleration, resulting in a value of -5 m/s², and calculated the final speed as 5.48 m/s. Clarifications were sought regarding the variable "F" in the equations, particularly in the context of friction being assumed as zero. Participants pointed out the inconsistency of including friction in the equations if it is not present. The conversation emphasizes the importance of clear definitions and assumptions in physics calculations.
chwala
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Homework Statement
A block of wood of mass ##4## kg is released from rest on a plane inclined at ##30^0## to the horizontal. Assuming that the surface is modelled as smooth (no friction), calculate the acceleration of the block, and its speed after it has moved ##3## m.
Relevant Equations
Mechanics
Pretty straight forward, ...reason of posting is to check why i am having a negative value for ##a##.

From my study, i know that

##R(||)## to plane

##F - 40 \cos \dfrac{π}{3} = 4a##

##a = -5 m/s^2##

or can i as well have the equation ( friction and tension are at equilibrium) as,

##40 \cos \dfrac{π}{3} - F = 4a##

For second part,

##v^2 =u^2 +2as##

##v^2= 2×5×3##

...

##v = 5.48 m/s## to two decimal places.
 
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chwala said:
Pretty straight forward, ...reason of posting is to check why i am having a negative value for a.
You've chosen down the ramp to be the negative direction!

What is "F" supposed to be in your equation?
 
Doc Al said:
You've chosen down the ramp to be the negative direction!

What is "F" supposed to be in your equation?
Friction which is ##0##.
 
chwala said:
Assuming that the surface is modelled as smooth (no friction)
If friction is 0, why include it in your equation?
 
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