Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_124

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Determine the value of the force required to move the 50-kg block to the right. For the values and , plot your results over the range , and interpret the results at . State the value of for . Neglect the effects of the diameter of the rod at A. Problem 6/124 (a) General expression for force as a function of ● Calculation Process 1. Present Final Formula: We analyze the equilibrium of the rod and the block. Let the rod have length . The collar at exerts a normal force and a friction force . The rod pushes the block at with force components and . The equilibrium of the block on the verge of slipping to the right yields the required force : 2. Substitute Values: Substitute , , , and : 3. Partial Operations: Simplify the constants in the numerator and denominator: Numerator constant: Coefficient of : Constant in denominator: The simplified function is: P μ = 1 0.60μ = 2 0.300≤x≤10 m x=0Px=3 m Px L= x+2 22 AN A F = A μ N 2A BR x R y P P= −μ x+2(1+μ μ )x−4μ 2 2 121 μ mg(x+4) 1 2 m=50 kgg= 9.81 m/s 2 μ = 1 0.60 μ = 2 0.30 P= −0.30x+2(1+0.60⋅0.30)x−4(0.60) 2 0.60(50⋅9.81)(x+4) 2 0.60⋅490.5=294.3 x2(1+0.18)=2.36 4⋅0.60=2.4 P(x)= −0.3x+2.36x−2.4 2 294.3(x+4) 2 4. Final Calculation: Identify the range of validity by finding the roots of the denominator: Movement to the right is only possible for positive in the range . ● Final Conclusion: The force required is given by for the physically valid range of motion. (b) Calculation of force at 1.