In the instant of the figure, two particles move in an xy plane. Particle P₁ has mass 7.40 kg and speed v₁ = 1.91 m/s, and it is at distance d₁ = 9.52 m from point O (the figure is not drawn to scale). Particle P₂ has mass 2.73 kg and speed v2 = 2.37 m/s, and it is at distance d₂ = 8.89 m from point O. What is the magnitude of the net angular momentum of the two particles about O? P₁O Number i Units ས། ྋ P2
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- = 1. Sphere A has mass ma = 0.05 kg, velocity magnitude va = 2.0 m/s making an angle 30° with the + axis. Sphere B has mass m₁ = 0.03 kg, velocity magnitude Vb = 3.0 m/s and moves along the +y axis. Sphere C has mass mc 0.04 kg, velocity magnitude vc = 4.0 m/s and moves along the +x axis. See figure. They are all approaching the origin as they slide on a frictionless surface. The three spheres arrive at the origin at the same time and stick together. (a) What is the final velocity of the combined object? (b) How does the final kinetic energy compare to the kinetic energy before the collision? y m a m mb XThe carbon isotope 14C is used for carbon dating of archeological artifacts. 14C (mass 2.34 x 10-26 kg) decays by the process known as beta decay in which the nucleus emits an electron (the beta particle) and a subatomic particle called a neutrino. In one such decay, the electron and the neutrino are emitted at right angles to each other. The electron (mass 9.11 x 10-31 kg) has a speed of 5.00 x 107 m/s and the neutrino has a momentum of 8.00 x 10-24 kg • m/s. What is the recoil speed of the nucleus?Two particles are moving in the x-y plane. Particle #1 has a mass m, = 6.40 kg and is located (at any time) by the position vector r, (t) = [0.300 m + (2.00 m/s?)t?jî + 0.200 mj. Particle #2 has a mass m, = 9.00 kg and is located (at any time) by the position vector r,(t) = 0.100 mî + [0.300 m + (0.500 m/s)t + (1.50 m/s?)t?jj. Determine the following at the time t = 1.00 s. (Express your answers in vector form.) (a) location of the center of mass r(t = 1.00 s) = m (b) velocity of the center of mass Vem (t = 1.00 s) = m/s v (c) acceleration of the center of mass a(t = 1.00 s) = m/s?
- CES Chapter 13, Problem 010 GO Two dimensions. In the figure, three point particles are fixed in place in an xy plane. Particle A has mass m, = 5 g, particle B has mass 2.00ma, and particle C has mass 3.00mA. A fourth particle D, with mass 4.00ma, is to be placed near the other three particles. What (a) x coordinate and (b) y coordinate should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero (d = 17 cm)? em em BO plem 1.5d blem oblem roblem Units (a) Number Problem Units (b) Number Problem Click if you would like to Show Work for this question: Open Show WorkThree point particles are fixed in place in an xyz coordinate system. Particle A, at the origin, has mass mA. Particle B, at xyz coordinates (2.00d, 1.00d, 2.00d), has mass 2.00mA, and particle C, at coordinates (-1.00d, 2.00d, -3.00d), has mass 3.00mA. A fourth particle D, with mass 4.00mA, is to be placed near the other particles. In terms of distance d, at what (a) x, (b) y, and (c) z coordinate should D be placed so that the net gravitational force on Afrom B, C, and Dis zero?Consider a system of two particles in the xy-plane. For the first particle, Its mass is m₁ = 1.30 kg Its position is 7¹₁ = (1.202 + 2.203) m Its velocity is ₁ = (2.2002 + 0.100)) m/s For the second particle, Its mass is m₂ = 2.90 kg Its position is 7¹2 = (-3.60% - 2.403) m Its velocity is v₂ = (2.2001 - 2.000)) m/s a. Find the position of the center of mass of the system. 7CM = im+m b. Determine the velocity of the center of mass. UCM = 2 m/s + m/s c. What is the total linear momentum of the system? Pr = kg-m/s + kg-m/s
- To test the speed of a bullet, you create a pendulum by attaching a 3.20 kg wooden block to the bottom of a 1.10 m long, 0.800 kg rod. The top of the rod is attached to a frictionless axle and is free to rotate about that point. You fire a 10 g bullet into the block, where it sticks, and the pendulum swings out to an angle of 38.0°. What was the speed of the bullet? (Treat the wooden block as a particle.)A hockey puck with mass 0.160kg is at rest at the origin on the horizontal, frictionless surfaceof the rink. At t = 0, a player applies a force of 0.250N to the puck parallel to the surface. Hecontinues to apply the force until t = 2.00s. What are the position and speed of the puck at t =2.00?Important note: Unless otherwise stated, your answers must be in Sl units. Three pucks with masses m₁ = 25.0 [g], mB = 50.0 [g], and mc = 75.0 [g] approach the origin as they move on a frictionless table. Puck A moves with speed A = 3.50 [m/s] while puck B moves with speed up = 1.25 [m/s] and is oriented at B = 72.0-below the horizontal as shown. All the pucks arrive at the origin at the same time and stick together, causing it to move at 0.12 [m/s] to the + direction. VC mc y y component of Puck C's momentum: Direction: Magnitude: Angle in degrees: VA VB. MA What must be the and y components of puck C's initial momentum for the described collision to happen? component of Puck C's momentum: MB x What must be the magnitude and direction of puck C's initial velocity for the described collision to happen? What is the change in the system's total kinetic energy?
- Judy has a mass of 72.0kg and stands on slippery ice. She catches her leaping dog (mass 15.0kg),moving horizontally at 3.00 m/s. What is the speed of Judy and her dog after she catches him?4. Sphere A has mass ma = 0.06 kg, velocity magnitude va = 3.0 m/s making an angle = V6 magnitude vc = 25° with the + axis. Sphere B has mass m₂ = 0.04 kg, velocity magnitude 4.0 m/s and moves along the +y axis. Sphere C has mass mc = 0.05 kg, velocity 5.0 m/s and moves along the +x axis. See figure. They are all approaching the origin as they slide on a frictionless surface. The three spheres arrive at the origin at the same time and stick together. (a) What is the final velocity of the combined object? (b) How does the final kinetic energy compare to the kinetic energy before the collision?The diagram shows two identical particles (labeled 1 and 2) that are moving in the x-y plane. The mass of each particle is m = 0.15 kg and they move at the same speed of v = 26.7 m/s. Particle 1 is moving in the positive x direction along the line y = h. Particle 2 is traveling in the negative x direction along the line y = d + h. The diagram illustrates the situation where h = 0.67 m and d = 0.22 m. a.) Write an expression for the magnitude of the net angular momentum of the particles about the origin. b.)What is the answer to part (a) in units of kg⋅m2/s?