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Vector Mechanics For Engineers
- A jet engine is attached to the wing of an airplane by a security screw (Figure A, marked in black) with a diameter of 40 mm whose purpose is to ensure that if, following a malfunction, the engine exerts too great a horizontal force F on the wing - the screw will break and the engine will detach from the wing, thus the wing will remain intact It is known that the weight of the engine is 3000 kg. A. When the engine exerts a force F of 10 kn, what types of stresses act on the screw? B. When the engine exerts a force F of 10 kn, what is the stress acting on the screw according to the Tarska criterion C. What types of deformations exist in the material when the engine applies a force F of [50] KN d. What is the maximum force F that the motor can apply to a screw without the screw breakingarrow_forward5. A car is driving down the road and goes over a speed bump. The car has a solid circular drive shaft that is subjected to a tensile axial force of F = 400 kN, a bending moment of M = 10.0 kN·m, and a torque of T = 18.0 kN·m as a result of the bump. The shaft has a diameter d = 10.0 cm and mechanical properties of E = 200 GPa, v = 0.35 and σ = 200 MPa. a. What and where is the maximum stress? Hint: use the principle of superposition. b. What are the principal stresses and their directions? c. If it is a ductile steel, will the shaft yield? d. If it is a brittle steel, will the shaft fail? F M T Marrow_forwardStiffness is the property that enables material to withstand high stress without great strain. it is a resistance to any sort of deformation and is a function of the modulus of elasticity, E of the material True or falsearrow_forward
- Two blocks of mass m = 2.00 kg are connected by a vertical string of negligible mass and unknown tension Tm are hanging vertically. The higher one of these two masses is directly attached to another string of negligible mass and unknown tension T that goes over a frictionless pulley of negligible mass and is connected to a third block of mass M = 6.00 kg. The heavier block is free to slide on an incline (of angle 0 = 30.0° w.r.t. the horizontal) with coefficients of kinetic friction of µA = 0.120 and static friction µ,=0.150 between the block and the incline. The system is released from rest. !! M a) Please perform a test to determine which way the system would like to move in the absence of any friction. b) Please perform a test to determine whether the system will be able to overcome the maximum of static friction and be able to move, or remain at rest instead. c) Determine the magnitude of the normal force N exerted on the third block by the incline. d) Determine BOTH the magnitude…arrow_forwardA box with a mass of 3m is on frictionless ground, attached to a wall (on the left-side of the box) by a spring with constant k. Inside the box (on the frictionless floor of the box), is a block of mass m. The block is also attached to the left-side of the box (but inside it), by a second spring, with a spring constant 2k/5.1) What are the F = ma equations for the box and the block? (Remember how the motion of each, affects each other)2) What are the matrices K and M for the system?3) What are the normal frequencies of the system?4) Describe the motion of the masses. In phase? Out of phase? Does one mass oscillate with a higher amplitude than the other?arrow_forward3. A particle of mass m is at rest at the end of the spring (force constant k) hanging from a fixed support. At t=0, a constant downward force F is applied to the mass and acts for a time to. Show that after the force is removed, the displacement of the mass from its equilibrium position (x=xo, where x is down) is F -[cos @, (t-t,)- cos w,t] k x- X, where w = k / m.arrow_forward
- A circular rod and a 0.1-in.-thick rectangular bar are both made of a plastic material that has an elastic modulus of E = 2.3 GPa and a Poisson’s ratio of ν = 0.33. The rod and the bar are initially the same length L. After a particular load is applied, the 3.6-in.-wide rectangular bar is elongated by some amount ΔL and its width is reduced by 0.096 in. If the 1.3-in. diameter rod is stretched by the same amount ΔL, determine its change in diameter. Expansion is positive, while contraction is negative.arrow_forwardUnder some circumstances when two parallel springs, with constants k₁ and k2, support a single mass, the effective spring constant of the system is given by k = 4k1k₂/(k₁ + k₂). A mass weighing 20 pounds stretches one spring 4 inches and another spring 2 inches. The springs are attached to a common rigid support and then to a metal plate. As shown in the figure, the mass is attached to the center of the plate in the double-spring arrangement. k₂ II k = 20 lb Determine the effective spring constant of this system. lb/ft Find the equation of motion x(t) if the mass is initially released from the equilibrium position with a downward velocity of 6 ft/s. (Use g for the acceleration due to gravity.) 32 ft/s² x(t) = ftarrow_forwardProblem (2) A vibration isolation unit consists of two blocks of hard rubber bonded to a plate AB as shown. A force of magnitude P = 24 kN causes a deflection ô = 1.5 mm of the plate AB. (a) 150 mm J00 mm Determine the modulus of rigidity (G) of the rubber used. If a rubber having G= 19 MPa is used (b) and denoting P the magnitude of the force applied to AB and by ô the corresponding deflection, determine the equivalent spring constant k = P/d of the system. 30 mm 30 mmarrow_forward
- The rigid bar AC is supported by two axial bars (1) and (2). Both axial bars are made of bronze [E = 100 GPa; a = 18 × 10-6 mm/mm/ °C). The cross-sectional area of bar (1) is A1 = 184 mm2 and the cross-sectional area of bar (2) is A2 = 380 mm2. After load P has been applied and the temperature of the entire assembly has increased by 38°C, the total strain in bar (2) is measured as 1240 µɛ (elongation). Assume L1 = 1290 mm, a = 590 mm, b = 820 mm, and L2 = 2000 mm. Determine: (a) the magnitude of load P. (b) the vertical displacement of pin A. L2 (1) L1 B a P Answers: (a) The magnitude of P = i kN. (b) The vertical displacement of pin A = i mm (down).arrow_forwardThe 33-Mg freight car A and 11-Mg freight car B are moving towards each other with the velocities shown. (Figure 1) Figure 20 km/h k = 3 MN/m 10 km/h am B 1 of 1 Part A Determine the maximum compression of the spring mounted on car A. Neglect rolling resistance. Express your answer to three significant figures and include the appropriate units. View Available Hint(s) Smax = Submit Provide Feedback Value Units 2 ? Review Next >arrow_forwardA car has broken down in the middle of a road. Eva wants to help tow thecar to a mechanic with her 4WD. To avoid the car from slamming into Eva’s 4WD, they attach the front of the car to the back of Eva’s 4WD by a stiff spring.The broken car weighs 2000kg. The spring has a natural unstretched length of 2m and a spring constant of k = 80000N/mFor this particular gravel road, the magnitude of the drag force is proportional to the weight of the car and the speed of the car. The direction of the drag force is always opposite tothe direction of movement. This can be written asD = −cM v For this particular road we can take c = 4. Let x(t) be the position of the front of the broken car and let y(t) be the position of the back of Eva’s 4WD. We will assume that the position of Eva’s car is a known function of time.(1) By considering Newton’s law applied to the broken car, write down an ordinary differential equation for the motion of the broken car They are planning to travel at a constant…arrow_forward
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