Three small identical spheres A, B, and C, which can slide on a horizontal, frictionless surface, are attached to three strings of length l which are tied to a ring G. Initially the spheres rotate clockwise about the ring which moves along the x axis with a velocity vo. Suddenly the ring breaks and the three spheres move freely in the xy plane. Knowing that
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Vector Mechanics for Engineers: Dynamics
- 6. A particle of mass m is projected from point A with an initial velocity v, perpendicular to OA and moves under a central force F along an elliptical path defined by the equation r =- Show 2- cos 0 that Fis inversely proportional to the square of teh distance r from the particle to the center of teh force 0. m Aarrow_forward3. A bomb which is initially at rest explodes into three fragments. Fragment A of known mass ma moves at a known angle of 8 measured clockwise with respect to the positive y-axis with a known speed |val. Fragment B of unknown mass (but let's call it m3 ) moves at a known angle o measured counterclockwise with respect to the negative x-axis with a known speed |is|. A third fragment C of known mass mc moves off along the negative y-axis with an unknown speed (let's call it |vc]). Only the forces between the fragments are significant during the collision. a. Draw a diagram that shows the initial and final states of the bomb fragments. Label the velocity vectors and known angles. b. Define what you would like to include in your system. c. Write a Newton's 2nd Law equation for this system. d. Determine the speed of fragment C and the mass of fragment B in terms of the known quantities.arrow_forwardA 1.8-kg collar A and a 0.7-kg collar B can slide without friction on a frame, consisting of the horizontal rod OE and the vertical rod CD, which is free to rotate about its vertical axis of symmetry. The two collars are connected by a cord running over a pulley that is attached to the frame at O. At the instant shown, the velocity vA of Collar A has a magnitude of 2.1 m/s and a stop prevents collar B from moving. The stop is suddenly removed and collar A moves toward E. As it reaches a distance of 0.12 m from, the magnitude of its velocity is observed to be 2.5 m/s. Determine at that instant the magnitude of the angular velocity of the frame and the moment of inertia of the frame and pulley system about CD.arrow_forward
- A 450-g ball B is moving along a horizontal circular path at a constant speed of 4 m/s. Determine (a) the angle 0 that the cord forms with the vertical line AC, (b) the tension in the cord 2. 1.8 marrow_forwardA particle of mass 2.6 kg is attached to two cables CB and CA as shown. it revolves in a horizontal circle of radius 1.3 m at a constant speed of 8.45 m/s.arrow_forwardThe two spheres shown collide. the weight of the first sphere (W1) is 40 N while that of the second is (W2) is 30N. assuming that the second sphere's velocity (v2) is 14 m/s and the first sphere's velocity (v1) is 16 m/s along the their respective angles. theta 1(θ1)=30 degrees and theta 2(θ2)=60 degrees. Assume velocities along y will be equal before and after impact. The coefficient of restitution is 0.57. A.) Determine the velocity of the 30N sphere after impact (m/s) B.) Determine the Velocity of the 40N sphere after impact (m/s) C.) Determine the angle of the velocity after impact of the 40N sphere with the horizontal (degrees) D.) Determine the angle of the velocity after impact for the 30N sphere with the vertical (degrees)arrow_forward
- A torpedo was fired at a target ship by a submarine. The torpedo monitor of the target ship detects that 10 seconds pass between the moments when the explosion noise emitted by the water and air is heard. The torpedo travels in a linear orbit in the water. The propagation speed of sound in air is known as 340 m/s and the propagation velocity in water is 1430 m/s. Calculate the distance between the target ship and the torpedo accordingly.arrow_forwardA brass (nonmagnetic) block A and a steel magnet B are in static equilibrium in a brass tube under the magnetic repelling force of another steel magnet, C. The magnet B is located a distance x =d, from C. If block A is suddenly removed, and the acceleration of block B is: k a =-g+ where g andk are known constants. Determine: a. the velocity, v, as a function of the position x and the known parameters (g,k,d,), and b. the position, x, when the velocity is maximum in terms of the known parameters (g,k,d,). Вarrow_forwardA particle, of mass 9 kg, is attached to two identical springs. The other ends of the springs are attached to fixed points, A and B, which are 1.2 metres apart on a smooth horizontal surface. The springs have modulus of elasticity 45 N and natural length 0.4 m. The particle is released from rest at a distance of 0.5 metres from B and moves on the line AB. The midpoint of AB is C. At timet seconds after release, the displacement of the particle from C is x metres, where the direction from A to B is taken to be positive. www C www В (а) Show that the resultant force on the particle, at time t, is -225x newtons. (b) Hence show that the particle moves with simple harmonic motion. (c) State the period of this motion. (d) Find the speed of the particle when it is 0.05 metres from C. (e) Write down an expression for x in terms of t.arrow_forward
- Dynamic Lecture: The 2 kg BC ring can only move left and right on the frictionless rigid arm. Ring BC is connected to springs with spring constants k = 300 N / m and k ′ = 200 N / m at points AB and CD. The unstretched length of both springs is 600 mm. Since it is known that the springs are not tensioned and starts from rest, find the velocity of the ring BC at the moment when the external force F is applied 200 mm.arrow_forwardEnds of three light identical rods each of length l are connected to a light pivot that enables them to rotate in any direction. At the other ends of the rods, three particles A, B and C of masses m, 2m and 3m respectively are affixed. Initially the rods are coplanar, angle between any two is 120 and the particles are at rest. Now the particle C is given a velocity u perpendicular to the rod connected to it and in the plane of the rods as shown in the figure. Ignore gravitational interaction between the particles. What are the moduli of acceleration of the particles A, B and C immediately after the particle C is given velocity u?arrow_forwardEquations for the conservation of energy must be used, the speed that bodies of mass m1 and m2 have after they have traveled a distance "d". Obviously, they must consider the pulley with mass M and radius R. It is necessary to proceed in the case that the masses are equal, and the angles are different. And show the answer with pictures. m₂ m2arrow_forward
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