Problem 1

A Bar Suspended by Two Vertical Strings - Calculations - Self Assessment tring A S d | my ! - x L String B The figure shows a model of a crane that may be mounted on a truck.A rigid uniform horizontal bar of mass m; = 90.0 kg and length L = 5.00 m is supported by two vertical massless strings. String A is attached at a distance d = 2.00m from the left end of the bar and is connected to the top plate. String B is attached to the left end of the bar and is connected to the floor. An object of mass m2 = 3500 kg is supported by the crane at a distance =4.80 m from the left end of the bar. Throughout this problem, positive torque is counterclockwise and use 9.80 m/s2 for the magnitude of the acceleration due to gravity. Suggestion: Self Assessment v PartA Find Ty, the tension in string A. Express your answer in newtons using three significant figures. View Available Hint(s) ..o % Incorrect; Try Again; 3 attempts remaining v PartB Find Ty, the magnitude of the tension in string B. Express your answer in newtons using three significant figures. View Available Hint(s) M. .. 7=0; v Choosing the pivot point to be the BOTTOM end of the ladder, which is the correct equation? Open the hints for steps. P View Available Hint(s) 0+0+P*b - w*a - W zg * /2 =0 0+0+P*b +w*a + W\\ a4 * /2 = 0 0+0+P*b - w*a - W zg * =0 040 - P*b - w*a - W| .4 * /2 =0 040 - P*b - w*a - W ,q*c=0 0+0+P*b - w*a + W og * /2=0 0+0+P*b + W*a - W 4q * /2=0 Previous Answers All attempts used; correct answer displayed Part D V Solve for FN, the magnitude of the normal force by the floor. Keep 2 digits after the decimal point, in Newtons. FN = 706.00 N Submit Previous Answers Correct Part E Solve for P, the magnitude of the force by the wall Keep 2 digits after the decimal point, in Newtons. VI AEd ? P = N Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining Part F Complete previous part(s)MR Review This problem is related to Lab "Static Equilibrium Lab" Use your intuition to try to answer the following question. If your intuition fails, work the rest Learning Goal: of the problem and return here when you feel that you are more comfortable with torques. To make the connection between intuitive understanding of a seesaw and the standard formalism for torque. This problem deals with the concept of torque, the "twist" that an off-center force applies to a body that tends to v PartA make it rotate. (Figure 1) . Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child, Jacques, simply sinking to the ground. Given that Jacques, whose weight is W = 65.0 N , is sitting at distance L = 0.70 m to the left of the pivot, at what distance L; should Marcel place Gilles, whose weight is w = 41.0 N , to the right of the pivot to balance the seesaw? Keep 2 digits after the decimal point, in meters. P View Available Hint(s) Li=111m Previous Answers Figure 10f3 (> + Correct Now consider this problem as a more formal introduction to torque. The torque of each child about the pivot point is the product of the child's weight and the distance from the pivot to the child's center of mass (center of gravity.) The sign of the torque is taken to be positive by convention if it would cause a counterclockwise rotation of the seesaw. The distance is measured perpendicular to the line of force and is called the lever arm. v PartB v Write the torque T about the pivot due to the weight w = 41.0 N of Gilles on the seesaw, use L as space holder. Include a proper sign. Marcel wants the seesaw to balance, which means that there can be no angular acceleration about the pivot. For the angular acceleration to be zero, the sum of the torgues about the pivot must equal zero: Y. r=0. v PartC v Apply Z 7 = 0, which of the following equations ( in terms of W, w, L and L) is correct? Consider only the torques exerted by the children. P View Available Hint(s) WL + w*L1=0 -W*L - w*L{=0 WL - W*L,=0 Previous Answers v Correct If you did not solve for the distance L required to balance the seesaw in Part A, do so now. The equation E 7 = (0 applies to any body that is not rotationally accelerating. Combining this equation with E F' = 0 (which applies to any body that is not accelerating linearly) gives a pair of equations that are sufficient to form the basis of statics. The art of applying these equations to large or complicated structures constitutes a significant part of mechanical and civil engineering. Gilles has an identical twin, Jean, also of weight w = 41.0 N . The two twins now sit on the same side of the seesaw, with Gilles at distance L = 1.24 m from the pivot and Jean at distance L3 = 0.72 m . (Figure 2) Part D V Where should Marcel position Jacques to balance the seesaw? Keep 3 digits after the decial point, in meters. View Available Hint(s) Jacques on the left side Lnew = 1.236 m new location Submit Previous Answers CorrectBad news! When Marcel finds the distance L, from the previous part, it turns out to be greater than Lenq = 1.290 m , the distance from the pivot to the end of the seesaw. Hence, even with Jacques at the very end of the seesaw, the twins Gilles and Jean exert more torque than Jacques does. Marcel now elects to balance the seesaw by pushing sideways on an ornament (shown in red) that is at height A = 0.30 m above the pivot. (Figure 3) v PartE With what force in the rightward direction, F}, should Marcel push? If your expression would give a negative result (using actual values) that just means the force should be toward the left. Keep 2 digits after the decimal point, in Newtons. P View Available Hint(s) F, = N STV Tl 1 Previous Answers X Incorrect; Try Again; 3 attempts remaining