Math  /  Geometry

Question34. (III) A small block of mass mm rests on the rough, sloping side of a triangular block of mass MM which itself rests on a horizontal frictionless table as shown in Fig. 5-44. If the coefficient of static friction is μ\mu, determine the minimum horizontal force FF applied to MM that will cause the small block mm to start moving up the incline.
FIGURE 5-44 Problem 34.

Studdy Solution
The horizontal force F F is related to the acceleration a a by: F=Ma F = M a
Substitute the expression for a a from STEP_7: F=M(g(μcos(θ)+sin(θ))cos(θ)μsin(θ)) F = M \left( \frac{g (\mu \cos(\theta) + \sin(\theta))}{\cos(\theta) - \mu \sin(\theta)} \right)
The minimum horizontal force F F required is: F=M(g(μcos(θ)+sin(θ))cos(θ)μsin(θ)) F = M \left( \frac{g (\mu \cos(\theta) + \sin(\theta))}{\cos(\theta) - \mu \sin(\theta)} \right)

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