Answer :
The eraser on the tilted clipboard needs a minimum static friction coefficient of 0.3907. No option matches; The correct answer is (O) Not enough information to tell.
- In this problem, we are given that an eraser rests on a clipboard that is tilted at an angle of 23° with the ground. Also, the eraser is not sliding down the clipboard. We need to find the minimum coefficient of static friction required to hold the eraser in its place.
- The coefficient of static friction is given by the formula:f_s = (μ_s)N, where f_s is the force of static friction, μ_s is the coefficient of static friction and N is the normal force acting on the object.
- In this case, the normal force acting on the eraser is equal to its weight. Thus, the normal force acting on the eraser is given by: N = mg, where m is the mass of the eraser and g is the acceleration due to gravity. Substituting the values of N and θ in the above equation, we get f_s = mg sin θ
- Thus, the minimum coefficient of static friction needed to hold the eraser in place is given by:μ_s = f_s / N = (mg sin θ) / (mg) = sin θ = sin 23° = 0.3907 (approx.)
- Therefore, the minimum coefficient of static friction needed for the eraser to stay in its place is 0.3907. The closest option given is 0.26, which is not equal to the value obtained in the calculation. Hence, the correct answer is option (O) Not enough information to tell.
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Final answer:
To prevent sliding, the minimum coefficient of static friction required between the eraser and the clipboard, calculated using forces and equilibrium principles, is approximately 0.42.
Explanation:
The minimum coefficient of static friction between the eraser and the clipboard required to prevent the eraser from sliding down can be calculated using the concept of forces and equilibrium. We know that the vertical equilibrium condition is given by: Friction Force = Weight * sin(θ). Since the eraser is not sliding, the friction force equals the static friction i.e. F = μ * N. Also, Normal Force N = Weight * cos(θ).
Substituting these in the equilibrium condition, we get: μ * Weight * cos(θ) = Weight * sin(θ). Simplifying, we find μ = tan(θ). Substituting θ = 23° gives us μ = tan(23°), which is approximately 0.42. Therefore, the minimum coefficient of static friction required is 0.42.
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