Two smooth disks A and B, having a mass of 1 kg and 2 kg, respectively, collide with the velocities as shown. If the coefficient of restitution for the disks is e = 0.75, determine the x and y components of the final velocity of each disk just after collision.
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Two smooth disks A and B, having a mass of 1 kg and 2 kg, respectively, collide with the velocities as shown. If the coefficient of restitution for the disks is e = 0.75, determine the x and y components of the final velocity of each disk just after collision.
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- True or False: In a perfectly inelastic collision between two masses, the two masses rebound after the collision. For any question relating to one-dimensional linear momentum, only the velocity is important to consider when objects collide. When we triple the vectorial velocity of an object whose mass is constant, we also triple its moment. In an inelastic collision, the total kinetic energy is conserved. When an object explodes, the sum of the momentum of all the fragments is equal to the momentum of the object before the explosion.Two manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The first has a mass of 2.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. If the two satellites collide elastically rather than dock, what is their final relative velocity? Adopt the reference frame in which the second satellite is initially at rest and assume that the positive direction is directed from the second satellite towards the first satellite.A particle with mass mA = 3.00 kg is located at rA = (2.50 i + 3.50 j) m, and a second particle of mass m2B = 5.00 kg is located at rB = (1.50 i – 3.00 j) m. Find the location of the center of mass of the system relative to the point (1,1).
- A firework with mass M is launched from the origin with initial speed v0 and angle θ0 and travels along the usual parabolic path above flat ground. At the peak of its path, it explodes into two pieces. Piece one has mass .5M and speed v1 in an angle of 30◦ below the horizontal direction and the other piece has mass .5M and speed v2 in an unknown direction. (a) Do the two pieces land at the same time? (Justify your answer) (b) Sketch the motion of the COM and of both pieces. Note any external forces, and describe if p is conserved in x, y or both for the duration of the flight. Also note if the two pieces land at the same distance from the target or describe which one lands closer/further.Problem 3: A particle with mass ma = 3.00 kg is located at ra = (2.50 i + 3.50 j) m, and a second particle of mass m2B = 5.00 kg is located at rB = (1.50 i - 3.00 j) m. Find the location of the center of mass of the system relative to the point (1,1).The sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible mass. The board can rotate around a horizontal axis passing through point O, and a body of mass m2 = 3.9 kg is placed on it at a distance b = 1 m from the axis of rotation. The collision is perfectly inelastic. How high does the body of mass m2 rise after the collision (in m) if a = 0.5 m?
- As shown in the figure, a billiard ball with mass m, is initially at rest on a horizontal, frictionless table. A second billiard ball with mass m, moving with a speed 2.00 m/s, collides with m,. Assume m, moves initially along the +x-axis. After the collision, m, moves with speed 1.00 m/s at an angle of 0 = 54.0° to the positive x-axis. (Assume m, = 0.200 kg and m, = 0.300 kg.) After the collision y sin e Before the collision Py cos e Va cos o y sin o (a) Determine the speed (in m/s) of the 0.300 kg ball after the collision. m/s (b) Find the fraction of kinetic energy transferred away or transformed to other forms of energy in the collision. JAK|An instrument-carrying projectile of mass m1 accidentally explodes at the top of its trajectory. The horizontal distance between launch point and the explosion is x0. The projectile breaks into two pieces that fly apart horizontally. The larger piece, m3, has three times the mass of the smaller piece, m2. To the surprise of the scientist in charge, the smaller piece returns to earth at the launching station. Neglect air resistance and effects due to the earth’s curvature. How far away from the original launching point does the larger piece landYou want to speed up the system of rotating disks. To do this, you throw a ball of mass mb at the two disks that are still rotating together with the same speed (just after they collide). You throw the ball at the disks, and the ball follows the following trajectory as viewed from above. The ball of mass mb approaches the disks at an angle θ with respect to the tangent line to the disk and rebounds at an angle ϕ with respect to the normal. The ball's initial speed is v_0, and its final speed is v_f. What is the new z-component of the angular velocity of the system of rotating disks (they still rotate together) after the collision with the ball? Use these values for the parameters (associated with image 1): v_f=2.13 m/s v_0=14.2 m/s θ=63.2∘ ϕ=68.7∘ m_b=1.59 kg R=2.68 m *Initial scenario if it helps* Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the…