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?

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?

Name: Two particles are moving in the x-y plane. Particle #1 has a mass m,
Uploaded: 2024-03-20T06:57:37.000Z
Channel: Bartleby
Description: 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 massm, = 9.00 kg and is located (at any time) by the

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter8: Momentum And Collisions

Section: Chapter Questions

Problem 31P

See similar textbooks

Similar questions

A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass ml = 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities, (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking to be the unknown angle, (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos and v3 sin , respectively, and use the identity cos2 + sin2 = 1 to obtain v3. (g) Divide the equation for v3 sin by that for v3 cos to obtain tan , then obtain the angle by taking the inverse tangent of both sides, (h) In general, would three such pieces necessarily have to move in the same plane? Why?
An astronaut out on a spacewalk to construct a new section of the International Space Station walks with a constant velocity of 2.00 m/s on a flat sheet of metal placed on a flat, frictionless, horizontal honeycomb surface linking the two parts of the station. The mass of the astronaut is 75.0 kg, and the mass of the sheet of metal is 245 kg. a. What is the velocity of the metal sheet relative to the honeycomb surface? b. What is the speed of the astronaut relative to the honeycomb surface?
An unstable nucleus of mass 1.7 ✕ 10−26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1 = 1.0 ✕ 10−27 kg,moves in the positive y-direction with speed v1 = 5.2 ✕ 106 m/s.Another particle, of mass m2 = 9.0 ✕ 10−27 kg,moves in the positive x-direction with speed v2 = 3.0 ✕ 106 m/s.Find the magnitude and direction of the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.)
An unstable nucleus of mass 1.7 ✕ 10−26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1 = 1.8 ✕ 10−27 kg,moves in the positive y-direction with speed v1 = 5.4 ✕ 106 m/s. Another particle, of mass m2 = 9.0 ✕ 10−27 kg, moves in the positive x-direction with speed v2 = 3.2 ✕ 106 m/s. Find the magnitude and direction of the velocity of the third particle. Answer the following:
Three asteroids coated with cosmic slime are moving in the same plane when they collide and stick together. Initially, asteroid A has a mass of 2*107 kg and is moving to the right at a speed of 150 m/s, asteroid B has a mass of 3*107 kg and is moving at 50 m/s towards the lower left at an angle of 60 degrees with respect to asteroid A, while asteroid C has a mass of 5*107 kg and is moving with an unknown speed and angle. After the collision, the resulting single asteroid is moving toward the right at a speed of 50 m/s. Determine the speed and angle of asteroid C prior to the collision.
A 60.5 kgkg astronaut is doing a repair in space on the orbiting space station. She throws a 2.35 kgkg tool away from her at 3.20 m/sm/s relative to the space station. 1. With what speed will she begin to move? Express your answer with the appropriate units. Δv= _______________ 2. In what direction will she begin to move? option (a) She moves in the direction in which she throws the tool. option (b) She moves opposite to the direction in which she throws the tool.
Which one of the following is the y-coordinate of the centre of mass from three homogeneous solid spheres of masses 1 kg, 2 kg and 4 kg that are arranged with their centres at (2i + j + k) meters, (3i – 2 j + 2k) meters and (4i – j – 2k) meters respectively where i, j, and k are unit vectors in the x, y and z directions
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).
Consider a system composed of three masses connected by light rigid rods. The first mass (m1 = 3.00 kg) is positioned 2.75 meters along the y-axis. The second mass (m2 = 4.00 kg) is situated 2.50 meters along the x-axis. The third mass (m3 = 2.50 kg) is located at the coordinates (-4.00, -3.30) meters. This third mass is connected to the first and second masses such that the system's center of mass is at the origin. The entire system rotates around the origin. A constant force with a magnitude of 2.9 N is applied to the left on (m1), and a force of 9.7 N is applied downwards on (m2). What is the resultant angular acceleration of the system about the origin, considering positive angular acceleration out of the page?
A thin metal rod of mass 1.8 kg and length 0.9 m is at rest in outer space, near a space station (see figure below). A tiny meteorite with mass 0.08 kg traveling at a high speed of 210 m/s strikes the rod a distance 0.2 m from the center and bounces off with speed 60 m/s as shown in the diagram. The magnitudes of the initial and final angles to the x axis of the small mass's velocity are θi= 26° and θf= 82°. Afterward, what is the velocity of the center of the rod? (Express your answer in vector form.) Afterward, what is the angular velocity ω→ of the rod? (Express your answer in vector form.)
A system of three particles with masses m1 = 3.0 kg, m2 = 4.0 kg and m3 = 8.0 kg is placed on a two dimensional xy plane. The scales on the axes are set by xs = 2.0 m and ys = 2.0 m. (a) Find out the x coordinate of the system’s center of mass.(b) Find out the y coordinate of the system’s center of mass.(c) Find out the acceleration of the system if an external force of 5 N acts on it.
Three pieces of putty are launched at one another. They are all aimed at the origin of a Cartesian coordinate systemand are launched so that they collide at the same time. The first piece with mass m1 = 7.5 kg comes in from the rightalong the x-axis with speed v1 = 6.3 m/s. The second piece with mass m2 = 2.8 kg comes from above along the y-axis with a speed v2 = 29.2 m/s. At what angle with respect to the positive x-axis must the third piece of putty come inso that when all three hit and stick together, they remain at rest? (in deg)