9. [013 Points] PREVIOUS ANSWERS SERPSElD 7.4.0P.009. 1/6 Submissions Used ASK YOUR TEACHER A light spring obeys Hooke's law. The spring's unstretched length is 33.5 cm. One end of the spring is attached to the top of a doorframe and a weight with mass 7.25 kg is hung from the other end. The final length of the spring is 44.0 cm. (a) Find its spring constant (in N/m). x It appears that you divided the force by the total length of the stretched spring. Note that the magnitude of the spring force is proportional to the stretch of the spring, not the length of the spring. Given the initial and final lengths, how can you find the distance the spring stretches? N/m (b) The weight and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 180 N. Find the length (in m) of the spring in this situation. _x Consider the end of the spring on the right, which exerts a force to the left equal to 180 N. Use F = ekx and your result from part (a), and solve for x. m (c) What If? What would be the length (in rn) of the spring if it were now attached to the vertical portion of the doorfrarne and stretched horizontally by a single person exerting a force of 180 N? _x If a person exerts a force Fat one end of the spring, given the spring is not accelerating, what must be the force that the doorframe exerts on the spring at the other end? Can you make an analogy to the situation in part (b)? m Need Help? W 10. [2/3 Points] PREVIOUS ANSWERS SERPSE1O 7.4.0P.012. 1/6 Submissions Used ASK YOUR TEACHER One end of a light spring with spring constant k1 is attached to the ceiling. A second light spring is attached to the lower end, with spring constant k2. An object of mass m is attached to the lower end of the second spring. (a) By how much does the pair of springs stretch? (Use the following as necessary: k1, k2, m, and g, the gravitational acceleration.) (k1+k2) XtotaI: mg W J (b) What is the effective spring constant of the spring system? (Use the following as necessary: k1, k2, m, and g, the gravitational acceleration.) (kl'kzi 9*\" 11:1\":2 J (c) What If? Two identical light springs with spring constant k3 are now individually hung vertically from the ceiling and attached at each end of a symmetric object, such as a rectangular block with uniform mass density. In this case, with the springs next to each other, we describe them as being in parallel. Find the effective spring constant of the pair of springs as a system in this situation in terms of k3. (Use the following as necessary: k3, M, the mass of the symmetric object, and g, the gravitational acceleration.) k,3 eff2 X Note that in this situation, the weight of the hanging object is split evenly between the two springs, so that the downward force exerted on each spring is g. Use this information to find an expression for kg\". Need Help? M 11. [2/4 Points] DETAILS PREVIOUS ANSWERS SERPSE10 7.43.009. 2/6 Submissions Used A particle is subject to a force FX that varies with position as shown in the following figure. F (N) x(m) 16 (a) Find the work done by the force on the particle as it moves from x = 0 to x = 2.00 m. Ex _, Remember that the expression W = F-AF is only appropriate when the force is constant or A? is very tiny. J 2468101214 (b) Find the work done by the force on the particle as it moves from X = 5.00 m to x = 9.00 m. _.,. (c) Find the work done by the force on the particle as it moves from x = 14.0 m to x : 15.0 m. _x Does the calculation for this part differ in any significant way from the calculation required for part (a)? J (d) What is the total work done by the force over the distance X = 0 to x = 15.0 m? _e . Need Help