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- Let r be a vector with an initial point located on the axis of rotation and with a terminal point located at the point where a force F is applied. Find the torque and explain what the torque is measuring.Problem 15.109 The 2 lb ball located at A is released from rest and travels down the curved path. (Figure 1) Figure 10 ft .O B 1 of 1 Part A HB = If the ball exerts a normal force of 7 lb on the path when it reaches point B, determine the angular momentum of the ball about the center of curvature, point O. Hint: Neglect the size of the ball. The radius of curvature at point B must first be determined. Express your answer to three significant figures and include the appropriate units. Submit ‚μA Value Request Answer < Return to Assignment Units Provide Feedback 6 of 6 ? ReviewProblem 2: A package is dropped from the plane which is flying with a constant horizontal velocity of VA 150 4. Determine the normal and tangential components of acceleration and the radius of S curvature of the path of motion: (a) at the moment the package is released at A, where it has a horizontal velocity of va 150 (b) just before it strikes the ground at B. Dynamics, Hibbeler, Problem 12.141 Answer: a) (a4)n = 32.2 ; (a,)t = 0; pa = 699 ft b) (ag)n = 14 ; (ag); = 29 ; PB = 8506.8 ft VA 1500 ft B
- Two forces F, and F, act along the two sides of an equilateral triangle as shown in Figure Pl1.5. Point Ois the intersection of the altitudes of the triangle. (a) Find the magnitude of a third force F, to be applied at Band along BC that will make the total torque zero about the point O. (b) What If? Will the total torque change if F, is applied not at Bbut at any other point along BC? B A Figure P11.5The angular moomentum of a point with a mass of m, a velocity v, and position r is: L = mr x v. Prove that the rate of change of L, dL/dt is equal to the torque (T = r x F). F is the force on the point.Find the tangential component at and the normal component an of acceleration at the t = 1 if r(t) = (5t-¹, 6 ln(t), 91²) (Express numbers in exact form. Use symbolic notation and fractions where needed.) at (1) = an (1) =
- 12.123 A bucket is attached to a rope of length L – 1.2 m and is made to revolve in a horizontal circle. Drops of water leaking from the bucket fall and strike the floor along the perimeter of a circle of radius a. Determine the radius a when u = 30°.Find the mass and the moment of the lamina with density δ ( x, y) = A, bounded by y = sin x, y = 0, x = 0 and x =π . A = 2x − 5. Sketch graph.Consider a bar that extends from x = 0 m to x = 4 m. The linear mass density of the rod is given by λ(x) = 7 + 7 x (kg/m). Calculate the rotational inertia of the beam about x = 0, in kg m2. (Please answer to the fourth decimal place - i.e 14.3225)
- A sphere is projected with an under twist down a rough inclined plane, show that it will turn back in the course of its motion if 2a w (u – tan α) > 5μu, where u is the initial linear velocity and w the initial angular velocity of the sphere, µ is the coefficient of friction and a is the inclination of the plane. HA hollow, spherical shell with mass 3.00 kg rolls without slipping down a 36.0 ∘slope. Find the acceleration. Find the friction force. Find the minimum coefficient of static friction needed to prevent slipping.A uniform sphere of mass m and radius R rolls without slipping down a plane at an angle θ from thehorizontal. Show that the acceleration along the slope of the center of mass is aCM = (5/7)g sin θ and that the force of static friction needed is fs = (2/7)mg sin θ. What minimum coefcient of friction µs is needed to satisfythe conditions of the problem?