1. In the boom-cable set-up as shown in the figure, determine the tension in the cable and the force exerted on the boom, for the equilibrium of the system. 25% 40° cable pin-connection B cable Figure 2,700 N block
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- Consider the heavy wires with endpoints held at the given temperatures as shown in the image: a) Give the linear system used to model the equilibrium temperatures.Cable AB passes over the small ideal pulley C without a change in its tension. What length of cable CD is required for static equilibrium in the position shown? What is the tension T in cable CD?Two blocks of masses m1 and m2 (m1 > m2) are placed on a frictionless table in contact with each other. A horizontal force of magnitude f is applied to the block of mass m1 in Figure P4.32. (a) If P is the magnitude of the contact force between the blocks, draw the free-body diagrams for each block. (b) What is the net force on the system consisting of both blocks? (c) What is the net force acting on m1? (d) What is the net force acting on m2? (e) Write the x -component of Newton’s second law for each block. (f) Solve the resulting system of two equations and two unknowns, expressing the acceleration a and contact force P in terms of the masses and force. (g) How would the answers change if the force had been applied to m2 instead? (Hint: use symmetry; don’t calculate!) Is the contact force larger, smaller, or the same in this case? Why?
- In order to ensure the stability of the crane, you decide to analyze the vibrations the crane would undergo in a windy environment. For a preliminary analysis, the crane is modelled as a mass-spring system comprising three springs. The following equations are derived in the first test condition:5) Consider four points A, B, C, and D whose geometrical locations correspond to the corners of a square with sides of length 1 mm. Calculate the potential differences (in mV) VAB, VBA, VAC, VCA, VAD, VDA, VBC, VCB, VBD, VDB, VCD, VDC between the points in a uniform electric field of 3 V/m parallel to the two sides (and perpendicular to the other two) of the square. (Show your work)