Finding an expression for acceleration

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SUMMARY

The discussion centers on calculating the acceleration of a 5.21 kg block sliding down a slope at a 4.22° angle. The initial speed is 1.45 m/s, with static and kinetic friction coefficients of μs = 0.500 and μk = 0.100, respectively. The incorrect expression provided for acceleration, a = g*sin(θ) - μk*cos(θ), fails due to dimensional inconsistency. The correct approach requires incorporating gravitational force components and frictional forces to derive a valid expression for acceleration.

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Mitza
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Homework Statement



A 5.21 kg block is sliding down a slope at an angle of 4.22° to the horizontal.

The block is initially moving down the slope at a speed of 1.45 m s−1 and the coefficients of friction between the block and slope are, μs = 0.500, and μk = 0.100.

Find an expression for the acceleration of the block down the slope, a. (Your expression should give a positive value when the block is accelerating down the slope)

2. The attempt at a solution

I came up with the equation;

a=g*sin(θ)-μk*cos(θ)

However, I've been told this is incorrect so I don't really know what else to do?

Thanks in advance for any help!
 
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Mitza said:
a=g*sin(θ)-μk*cos(θ)

However, I've been told this is incorrect
It is clearly wrong because of the two terms on the right one is an acceleration but the other is dimensionless. Did you omit something in writing it out?
If still stuck, please post your working.
 

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