Soru
A small block of mass m rests on the rough, sloping side of a triangular block of mass M which itself rests on a horizontal frictionless table as shown in the figure ( Eigure 1) Part A If the coefficient of static friction is ju determine the minimum horizontal force F applied to M that will cause the small block m to start moving up the incline Express your answer in terms of the given quantities and appropriate constants. AId
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Cevap
To determine the minimum horizontal force F required to cause the small block m to start moving up the incline, we need to consider the forces acting on the system.The forces acting on the small block m are:1. Gravitational force (weight) acting downward, equal to mg.2. Normal force acting perpendicular to the incline.3. Frictional force acting parallel to the incline, opposing the motion of the block.The forces acting on the triangular block M are:1. Gravitational force (weight) acting downward, equal to Mg.2. Normal force acting perpendicular to the table.3. Frictional force acting parallel to the table, opposing the motion of the block.To find the minimum horizontal force F required to cause the small block m to start moving up the incline, we need to consider the forces acting on the small block m.The frictional force acting on the small block m is given by the equation:Frictional force = coefficient of static normal forceThe normal force acting on the small block m is equal to the component of the gravitational force acting perpendicular to the incline. This can be calculated using the equation:Normal force = mg * cos(θ)where θ is the angle of the incline.The frictional force acting on the small block m will oppose the motion of the block and will be equal to the coefficient of static friction times the normal force.Therefore, the minimum horizontal force F required to cause the small block m to start moving up the incline is given by the equation:F = frictional force + component of gravitational force parallel to the inclineSubstituting the values, we get:F = coefficient of static friction * normal force + mg * sin(θ)Simplifying further, we get:F = coefficient of static friction * mg * cos(θ) + mg * sin(θ)Therefore, the minimum horizontal force F required to cause the small block m to start moving up the incline is given by the expression:F = coefficient of static friction * mg * cos(θ) + mg * sin(θ)