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(c) A ladder with length L and mass m rests against a wall. Its upper end is a distance h above the ground (Figure 13.3). The center of gravity of the ladder is one-third of the way up the ladder. A fire fighter with mass M climbs halfway up the ladder. Assume that the wall, but not the ground, is frictionless. Write the sum of the forces in (i) x-direction and (ii) y-direction and (iii) the expression for the sum of the torque about the point where the ladder makes contact with the ground(O).
(a) A 5.00 kg block is moving at vo= 6.00m/s along a frictionless, horizontal surface towards a spring with a force constant k = 500 N/m that is attached to a wall (Figure 13.5). The spring has negligible mass. Find(i) the maximum distance the spring will be compressed and (ii) the spring is compressed by no more than 0.150 m, what should be the maximum value of vo? (4 marks)
(b) A steel railroad track is 1000 m long. When its temperature is raised from -30 oto + 30 othermal expansion causes the length of the track to increase by .01%. What compressive force per unit area would be required to keep the track from expanding? (Hint: Calculate the force that would be required to compress it back to its original length. Young's modulus for steel is 2 x 1011N/m2.
(c) A hydraulic press contains 0.25m3(250 L) of oil. Find the decrease in volume of the oil when it is subjected to a pressure increase, âˆ†p = 1.6 x 107 Pa. The bulk modulus , B of oil is 5.0 x 109 Pa and its compressibility K = 1/B = 2.0 x 10-10 Pa-1.