Explanation Given information : The mass of a sphere is 4 kg. Observation: The tension in the cord is the same throughout the cord. Illustrate the free body diagram of the angles in the given system as shown below in Figure 1. Illustrate the free body diagram of the forces acting on the cable system ABC as shown below in Figure 2. Write the given parabolic function. y = 2.5 x 2 (I) Here, y is the vertical distance of point A from the origin and x is the horizontal distance of point A from the origin. Determine the angle θ made with the surface using the relation. tan θ s = d y d x (II) Here, d y d x is the differentiation of given function with respect x . Determine the weight of the sphere W s . W s = m s g (III) Here, the mass of the sphere is m s and the acceleration due to gravity is g . Determine the normal force N exerted on the surface and the mass of block B by applying the Equation of equilibrium. Along horizontal direction : ∑ F x = 0 T A B cos θ A B − N sin θ s = 0 T A B cos θ A B = N sin θ s (IV) Here, the tension force acting on the cord AB is T A B , the angle of cord AB is ϕ A B , the weight of the sack is W . Along vertical direction : ∑ F y = 0 T A B sin θ A B + N cos θ s − W = 0 T A B sin θ A B + N cos θ s = W (V) Determine the mass of the block m B . m B = T A B g (VI) Conclusion : Differentiate the Equation (I) with respect to x . y = 2.5 x 2 d y d x = 2.5 ( 2 x ) d y d x = 5 x Substitute 5 x for d y d x and 0.4 m for x in Equation (II). tan θ s = 5 x θ s = tan − 1 ( 5 × 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freed…

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Chapter 3.3, Problem 37P

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The normal force exerted on the surface and the mass of block B.

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Chapter 3.3, Problem 36P

Chapter 3.3, Problem 38P

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Chapter 3 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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The normal force exerted on the surface and the mass of block B .

Solution Summary: The author illustrates the free body diagram of the forces acting on the cable system ABC by applying the Equation of equilibrium.

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The normal force exerted on the surface and the mass of block B.

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Chapter 3 Solutions