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Homework 2-1

Homework 2-1. Locate the centroid of a semicircle. y. r. x. Homework 2-2. Determine the reactions at A, B and C. Neglect the weight of rod. Homework 2-3. Determine the reactions at the ball and socket joint A and the tension in cables BD and BE. Example.

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Homework 2-1

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  1. Homework 2-1 Locate the centroid of a semicircle. y r x

  2. Homework 2-2 Determine the reactions at A, B and C. Neglect the weight of rod.

  3. Homework 2-3 Determine the reactions at the ball and socket joint A and the tension in cables BD and BE.

  4. Example The plate has a mass of 50 kg/m2. Determine the force in each cable, if it is suspended in the horizantal plane.

  5. Example The shaft is supported by journal bearings at A and B. A key is inserted into the bearing at B in order to prevent the shaft from rotating about and translating along its axis. Determine the x, y, z components of reaction at the bearings when 600 N force is applied to arm.

  6. Friction In the previous sections, the surfaces of contact between two bodies were considered to be perfectly smooth. Because of this, the force interaction between bodies always acts normal to the surface at points of contact. In reality, however all surfaces are rough. Therefore a tangential force must also be considered besides the normal force at the bodies contacting surface. The tangential force is caused by friction.

  7. Friction Wx=Ph If x=a/2, the block is verge of tipping. Static Friction: Fs=μsN Kinetic Friction: Fk=μkN W P a/2 a/2 h O F x N F Time static dynamic

  8. Friction • Friction is defined as a force of resistance acting on a body. • Friction force always acts tangent to the surface at points of contact with other bodies in a direction opposed to the relative motion. • The magnitude of maximum static frictional force is independent of the area of contact. • Generally μs<1, except special cases such as aluminum on aliminum.

  9. Friction • Typical values for μk are approximately 25 percent smaller than static friction values.

  10. Example Beam AB is subjected to a force of 800 N and is supported at B by a post BC. If the coefficient of friction at B and C are μB=0.2 amd μC=0.5, determine the force P needed to pull the post out from under the beam. Neglect the weight of the members and the thickness of the post.

  11. Example Determine the tension in the cable for equilibrium of the lower block.

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