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TBES 5 Finals Topic - A SAMPLE PROBLEMS
Civil Engineering (BSCE 01)
Ateneo de Davao University
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STATICS OF RIGID BODIES
TBES 5
SESSION 7 – FRICTION
Lecture: Static case Coulomb proposed the following law: If there is no relative motion between two surfaces that are in contact, the normal force N and the friction force F satisfy the following relationship. Impending sliding Consider the static case in which the friction force equals its limiting value; that is, For this condition, the surfaces are on the verge of sliding, a condition known as impending sliding. When sliding impends, the surfaces are at rest relative to each other. However, any change that would require an increase in the friction force would cause sliding. The direction for Fmax can be determined from the observation that Dynamic case If the two contact surfaces are sliding relative to each other, the friction force F is postulated to be Problem: Situation 1 1. If the P=50N, what is the frictional force between the plane and the block? 2. If the P=100N, what is the frictional force between the plane and the block? 3. What is the minimum value of P that will cause the block impends to move? Situation 2 The device shown is designed to position pieces of luggage on a ramp. The suitcase weighs 50kg. The coefficients of friction between the suitcase and ramp are μs=0 and μk=0. 4. Will the suitcase remain stationary on the ramp when the device exerts no force on it? 5. What force must the device exert to push the suitcase up the ramp? Situation 3 The uniform stone in the figure shown has a mass of 500kg and is held in the horizontal position using a wedge at B. The coefficient of static friction is 0 at the contact surfaces. 6. Determine the minimum force P needed to remove the wedge. Assume that the stone does not slip at A.
Situation 4 The uniform 50-kg plank in Figure is resting on friction surfaces at A and B. The coefficients of static friction are shown in the figure. If an 80-kg man starts walking from A toward B. 7. Determine the distance x when the plank will start to slide. Situation 5 The man in figure is trying to move a packing crate across the floor by applying a horizontal force P. The center of gravity of the 250-N crate is located at its geometric center. 8. Does the crate move if P = 60 N? The coefficient of static friction between the crate and the floor is 0. 9. Calculate the force P required to cause tipping of the packing crate. 10. Determine the minimum coefficient of static friction that permits tipping. STATICS OF RIGID BODIES TBES 5 SESSION 8 – RESULTANT OF FORCE SYSTEM IN SPACE Lecture: the components of the forces show in the figure can be obtained by: Where θx, θy, and θz are the angles between A and the positive coordinate axes. The scalar components can be positive or negative, depending upon whether the corresponding vector component points in the positive or negative coordinate direction. The magnitude of A is related to its scalar components by If θ is not given we can use the dimension of the forces in the system. cosθx =
x
d
cosθy =
y
d
cosθz =
z
d
Where d = √ x 2 + y 2 + z 2
Problem:
If F 3 =9kN, θ=30⁰ and Φ=45⁰, determine the magnitude and direction of angles of the resultant force.
The magnitudes of the three forces acting on the plate are T 1 =100kN, T 2 =80kN and T 3 =50kN. Replace these forces with a single equivalent force R.
Replace the three forces acting on the guy wires by single equivalent force acting on the flagpole. Use T1 = 1000 N, T2 = 2000 N, and T3 = 1750 N.
Calculate the tension in each of the three cables that support the 1500-kN weight.
The horizontal boom OC, which is supported by a ball-and-socket joint and two cables, carries the vertical force P=8000N. Calculate TAD and TCE, the tensions in the cables, and the components of the force exerted on the boom by the joint at O. (neglect the weight of the boom)
The nonhomogeneous plate weighing 60kN has its center of gravity at G. It is supported in the horizontal plane by three vertical cables. Compute the tension in each cable using the given FBD. 4. The bent bar of negligible weight is supported by a ball-and-socket joint at O, a cable connected between A and E, and a slider bearing at D. The bar is acted on by a wrench consisting of the force P and couple C, both parallel to the z-axis. Determine the components of bearing reaction at D and the force in the cable.
TBES 5 Finals Topic - A SAMPLE PROBLEMS
Course: Civil Engineering (BSCE 01)
University: Ateneo de Davao University
