A block accelerates down an incline angled at $35^{\circ}$ with acceleration magnitude $a = g / 4$ , as shown. What is the coefficient of kinetic friction between the block and incline? Assume the acceleration due to gravity is $a_{y} = - g$ .
0.45
1.2
0.71
0.37

Answer

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$Final Answer: The coefficient of kinetic friction between the block and incline is approximately 0.40. The closest answer choice to this value is 0.37$

Steps

Step 1 ：The acceleration of the block down the incline is given by the equation: $a = g \sin (θ) - μ_{k} g \cos (θ)$

Step 2 ：We are given that $a = g / 4$ and $θ = 35^{\circ}$ , and we are asked to find $μ_{k}$

Step 3 ：We can rearrange the equation to solve for $μ_{k}$ : $μ_{k} = (g \sin (θ) - a) / (g \cos (θ))$

Step 4 ：Substitute the given values into this equation to find the value of $μ_{k}$

Step 5 ：Given that $g = 9.81$ , $a = 2.4525$ , and $θ = 0.6108652381980153$ , we find that $μ_{k} = 0.39501389101934575$

Step 6 ： $Final Answer: The coefficient of kinetic friction between the block and incline is approximately 0.40. The closest answer choice to this value is 0.37$

A block accelerates down an incline angled at 35∘ with acceleration magnitude a=g/4, as shown. What is the coefficient of kinetic friction between the block and incline? Assume the acceleration due to gravity is ay=−g.0.451.20.710.37

Answer

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A block accelerates down an incline angled at $35^{\circ}$ with acceleration magnitude $a = g / 4$ , as shown. What is the coefficient of kinetic friction between the block and incline? Assume the acceleration due to gravity is $a_{y} = - g$ .
0.45
1.2
0.71
0.37