What Causes Error in Calculating Acceleration on an Inclined Plane?

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AI Thread Summary
The discussion centers on calculating the acceleration of a block sliding down an inclined plane with a given mass, angle, and coefficient of kinetic friction. The initial calculations incorrectly used sine and cosine functions, leading to an erroneous net force and acceleration. The correct approach involves recognizing that the normal force is derived from the cosine of the incline angle, while the gravitational force acting along the incline uses the sine function. After correcting these calculations, the proper net force and acceleration can be determined. Accurate application of trigonometric functions is crucial for solving problems involving inclined planes.
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Homework Statement



A block of mass M = 3 kg is released from rest and slides down an incline that makes an angle q = 32° with the horizontal. The coefficient of kinetic friction between the block and the incline is µk = 0.15.

What is the acceleration of the block down the inclined plane?


Homework Equations


this is the easiste part of 4 part question and i can't get it.


The Attempt at a Solution


OK here's what i know
Normal = 3kg * (9.8sin32)
so friction is

fs = .15*15.58 = 2.34N
so I'm taking x-axis as the incline plane, (pos x = down the plane)
friction opposes the motion, so force runs along neg axis = -2.34N

forces in pos x direction are
3 * 9.8cos32 = 24.93N

24.93N - 2.34N = 22.59N (this is the net force)

Finally F/m = a
22.69/3 = 7.53m/s/s

= wrong.
??
 
Last edited:
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Looks to me like you have sine and cosine reversed. You draw the inclined plane as a right triangle having angle 32 degrees at the bottom. The force of gravity is straight down, the two legs of that triangle are perpendicular and parallel to the inclined plane- the 32 degree angle is the bottom of that triangle. The normal force is given by cos(32), the force along the incline by sin(32).
 
yeah yer right
thanks
 
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