Daily Archives: August 12, 2019

1271 posts

11.88 … DATA You are a construction engineer working on the interior design of a retail store in a mall. A 2.00-m-long uniform bar of mass 8.50 kg is to be attached at one end to a wall by means of a hinge that allows the bar to rotate freely with very little friction. The bar will be held in a horizontal position by a light cable from a point on the bar (a distance x from the hinge) to a point on the wall above the hinge. The cable makes an angle u with the bar. The architect has proposed four possible ways to connect the cable and asked you to assess them: (a) There is concern about the strength of the cable that will be required. Which set of x and u values in the table produces the smallest tension in the cable? The greatest? (b) There is concern about the breaking strength of the sheetrock wall where the hinge will be attached. Which set of x and u values produces the smallest horizontal component of the force the bar exerts on the hinge? The largest? (c) There is also concern about the required strength of the hinge and the strength of its attachment to the wall. Which set of x and u values produces the smallest magnitude of the vertical component of the force the bar exerts on the hinge? The largest? (Hint: Does the direction of the vertical component of the force the hinge exerts on the bar depend on where along the bar the cable is attached?) (d) Is one of the alternatives given in the table preferable? Should any of the alternatives be avoided? Discuss.

University Physics with Modern Physics lessons by JJtheTutor. Designed to teach students problem solving skills, test taking skills and how to understand the concepts.

11.87 .. DATA You need to measure the mass M of a 4.00-mlong bar. The bar has a square cross section but has some holes drilled along its length so you suspect that its center of gravity isn’t in the middle of the bar. The bar is too long for you to weigh on your scale. So first you balance the bar on a knife-edge pivot and determine that the bar’s center of gravity is 1.88 m from its left-hand end. You then place the bar on the pivot so that the point of support is 1.50 m from the left-hand end of the bar. Next you suspend a 2.00-kg mass 1m12 from the bar at a point 0.200 m from the left-hand end. Finally you suspend a mass m2 = 1.00 kg from the bar at a distance x from the left-hand end and adjust x so that the bar is balanced. You repeat this step for other values of m2 and record each corresponding value of x. The table gives your results. (a) Draw a free-body diagram for the bar when m1 and m2 are suspended from it. (b) Apply the static equilibrium equation gtz = 0 with the axis at the location of the knife-edge pivot. Solve the equation for x as a function of m2. (c) Plot x versus 1>m2. Use the slope of the best-fit straight line and the equation you derived in part (b) to calculate that bar’s mass M. Use g = 9.80 m>s2. (d) What is the y-intercept of the straight line that fits the data? Explain why it has this value.

University Physics with Modern Physics lessons by JJtheTutor. Designed to teach students problem solving skills, test taking skills and how to understand the concepts.

11.68 .. BIO Forearm. In the human arm the forearm and hand pivot about the elbow joint. Consider a simplified model in which the biceps muscle is attached to the forearm 3.80 cm from the elbow joint. Assume that the person’s hand and forearm together weigh 15.0 N and that their center of gravity is 15.0 cm from the elbow (not quite halfway to the hand). The forearm is held horizontally at a right angle to the upper arm with the biceps muscle exerting its force perpendicular to the forearm. (a) Draw a free-body diagram for the forearm and find the force exerted by the biceps when the hand is empty. (b) Now the person holds an 80.0-N weight in his hand with the forearm still horizontal. Assume that the center of gravity of this weight is 33.0 cm from the elbow. Draw a free-body diagram for the forearm and find the force now exerted by the biceps. Explain why the biceps muscle needs to be very strong. (c) Under the conditions of part (b) find the magnitude and direction of the force that the elbow joint exerts on the forearm. (d) While holding the 80.0-N weight the person raises his forearm until it is at an angle of 53.0_ above the horizontal. If the biceps muscle continues to exert its force perpendicular to the forearm what is this force now? Has the force increased or decreased from its value in part (b)? Explain why this is so and test your answer by doing this with your own arm.

University Physics with Modern Physics lessons by JJtheTutor. Designed to teach students problem solving skills, test taking skills and how to understand the concepts.