A uniform horizontal beam with a length of 8.00 m and a weight of W_b = 200 N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of φ = 53^° with the beam. A person of weight W_p = 600 N stands a distance d = 2.00 m from the wall. Find the tension in the cable as well as the magnitude and direction of the force exerted by the wall on the beam.

Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude f due to the other. with time, charge gradually leaks off of both spheres. when each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i.e., a subspace of r 3 ). explain your reasoning

Air initially at 0.75 bar, 1000 k, and occupying a volume of 0.12 m^3 undergoes two processes. process 1-2: the air is compressed isothermally until the volume is halved. process 2-3: the air undergoes a constant pressure process until the volume is halved again. assume ideal gas behavior. a) determine the mass of the air, in kg. b) the work and the heat transfer for each of the two processes, in kj. (100 kj = 1 bar . m^3)