Problem 3: A mass is sliding on a frictionless surface with a speed v. It runs into a c; linear spring with a spring constant of k, which compresses from position xi to position If. Bt- I I | I l I = thcmpcrllnxnm Part (a) Write a general expression for the force that the spring exerts on the mass, in term ofk and x. Choose the initial position of the front of the spring to be xi=0. Expression F spring : Select from the variables below to write your expression. Note that all variables may not be required. a, 13,6, a, d. g, h,j,k, nLP, t.X, Xf.xi Part (b) Select the equation that correctly describes the work done by the spring to stop the mass. MultipleChoice 1)W=-lxixkadx+l/zmv2 2)w:inxkadx 3)W=-lxixkadxl/zmv2 4)W=-lxindex 5)W=-kx2 6)W:lxixkadx Part (c) Evaluate the relationship in part (b) to arrive at an expression for the work done in terms of known variables. Expression W: Select from the variables below to write your expression. Note that all variables may not be required. (I, B: 63 a1 d: g: ha j: k: m: P7 t3 X1 Xf: xi Part (d) Solve for the numerical value of the work done in Joules given that xi = 0, Xf: 58 cm, and k = 75 N/m. Numeric : A numeric value is expected and not an expression. W: Problem 6: Part of riding a bicycle involves leaning at the correct angle when making a turn; the rst gure in the image carousel shows a rider leaning the bicycle at an angle .9 from the vertical. To be stable, the net force exerted by the ground where it contacts the tire must be on a line passing through the center of gravity. The forces have been summarized with a free-body diagram, as seen in the second gure in the image carousel. The ground exerts a normal force which is equal in magnitude to the combined weight of the bicycle and the rider. The ground additionally exerts a force due to static friction which is parallel to the ground, causing the bicycle to move in a circle. Enter an equation for the tangent of the angle between the bicycle and the vertical in terms of the speed of the bicycle, v, the radius of curvature of the turn, r, and the acceleration due to gravity, 3. Expression tan 9 = Select from the variables below to write your expression. Note that all variables may not be required. [1% 9, 11, d2g1 h, j, k, m, 11, P1 1', S, V Problem 7: A banked highway is designed for trafc moving at v : 87 km/h. The radius of the curve r : 347 m. Part (a) Write an equation for the tangent of the highway's angle ofbanking. Give your equation in terms of the radius of curvature r, the intended speed of the turn v, and the acceleration due to gravity g. Expression tan(6) : Select from the variables below to write your expression. Note that all variables may not be required. [3,75 0,11, d, g: hulk, mm P, 128, v Part (b) What is the angle ofbanking of the highway? Give your answer in degrees. Numeric : A numeric value is expected and not an expression. 6 : Problem 4: Consider a ball of mass m attached to a string of length L, which is being spun around in a horizontal circle as shown in the gure. This image is shown from ' above, so gravity is acting into the page. .' '- _______ -"|'lllccxpcrltuxnm How much work is the string doing on the ball, if it moves with a constant speed v? Expression W : Select from the variables below to write your expression. Note that all variables may not be required. a, B, n, 0, a, d, g, h, j, k, L, m, P, t, v Problem 5: A box of mass m is initially at rest at the top of an inclined plane, which has a height of 5.1 m and makes an angle on = 22D with respect to the horizontal. After being released, it is observed to be traveling at v = 0.65 m/s a distance d after the end of the inclined plane as shown. The coefcient of kinetic friction between the box and the plane is pp = 0.1, and the coefcient of friction on the horizontal surface is hr = 0.2. I tIlccxpcrlluxnm Part (a) What is the speed of the box, in meters per second, just after it leaves the inclined plane? Numeric : A numeric value is expected and not an expression. \"bottom : Part (b) Find the distance, d, in meters. Numeric : A numeric value is expected and not an expression. d