Resolving Forces: Acceleration & Speed of 4kg Block on Inclined Plane

AI Thread Summary
To calculate the acceleration of a 4 kg block on a frictionless incline of 30 degrees, the component of the gravitational force acting down the slope is determined using F = ma. This results in an acceleration of approximately 5.3 m/s². To find the speed after the block has moved 3 meters, the equation v² = u² + 2as is applied, yielding a final speed of about 7.4 m/s. The calculations confirm the relationship between acceleration, distance, and final speed in the context of inclined motion. This approach effectively demonstrates the principles of dynamics in a frictionless environment.
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Homework Statement



A block of wood of mass 4 kg is released from rest on a plane inclined at 30 degrees to the horizontal. Assuming that the surface can be modeled as smooth (no friction) calculate the acceleration of the block, and its speed after it has moved 3m

Homework Equations


equations of motion


The Attempt at a Solution



http://img174.imageshack.us/img174/2632/36018360et2.jpg
 
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Apply F = ma down the slope by calculating the component of the weight down the slope to find the accleration. Then use v^2 = u^2 + 2as to find the velocity v after s = 3 metres. Hope this helps.
 

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