Finding an expression for acceleration

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To find the acceleration of a 5.21 kg block sliding down a 4.22° slope with initial speed and friction coefficients, the correct expression needs to account for both gravitational and frictional forces. The proposed equation, a = g*sin(θ) - μk*cos(θ), is incorrect because it mixes dimensional terms with dimensionless coefficients. The correct approach involves using Newton's second law to derive the acceleration, ensuring all terms are consistent in units. Further clarification or detailed working steps may be necessary for accurate assistance. Understanding the relationship between forces and acceleration is crucial in solving this problem.
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.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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