The figure shows a three-particle system, with masses m₁ = 2.5 kg, m2 = 3.9 kg, and m3 = 6.2 kg. What are (a) the x coordinate and (b)the y coordinate of the system's center of mass?y (m)2="0mg1for2mq3x (m)(a)Number1.2936507Unitsm(b)Numberi 1.1Unitsm>

Step 1: Given that m1 = 2.5 kg , m2 = 3.9 kg , m3= 6.2 kg m1 has a coordinates of (0, 0) = (x1,…

Answered: The figure shows a three-particle…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter10: Systems Of Particles And Conservation Of Momentum

Section: Chapter Questions

Problem 21PQ

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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?
The vector position of a 3.50-g particle moving in the xy plane varies in time according to r1=(3i+3j)t+2jt2, where t is in seconds and r is in centimeters. At the same time, the vector position of a 5.50 g particle varies as r2=3i2it26jt. At t = 2.50 s, determine (a) the vector position of the center of mass of the system, (b) the linear momentum of the system, (c) the velocity of the center of mass, (d) the acceleration of the center of mass, and (e) the net force exerted on the two-particle system.
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From what might be a possible scene in the comic book The X-Men, the Juggernaut (mJ) is charging into Colossus (mC) and the two collide. The initial speed of the Juggernaut is vJi and the initial speed of Colossus is vCi. After the collision, the final speed of the Juggernaut is vJf and the final speed of Colossus is vCf as they each bounce off of the other, heading in opposite directions. a. What is the impulse experienced by the Juggernaut? b. What is the impulse experienced by Colossus? c. In your own words, explain how these impulses must compare with each other and how they are related to the average force each superhero experiences during the collision.
A cannon is rigidly attached to a carriage, which can move along horizontal rails but is connected to a post by a large spring, initially unstretchcd and with force constant k = 2.00 104 N/m, as shown in Figure P8.60. The cannon fires a 200-kg projectile at a velocity of 125 m/s directed 45.0 above the horizontal. (a) Assuming that the mass of the cannon and its carriage is 5 000 kg, find the recoil speed of the cannon. (b) Determine the maximum extension of the spring. (c) Find the maximum force the spring exerts on the carriage. (d) Consider the system consisting of the cannon, carriage, and projectile. Is the momentum of this system conserved during the firing? Why or why not?
A rocket has total mass Mi = 360 kg, including Mfuel = 330 kg of fuel and oxidizer. In interstellar space, it starts from rest at the position x = 0, turns on its engine at time t = 0, and puts out exhaust with relative speed ve = 1 500 m/s at the constant rate k = 2.50 kg/s. The fuel will last for a burn time of Tb = Mfuel/k = 330 kg/(2.5 kg/s) = 132 s. (a) Show that during the burn the velocity of the rocket as a function of time is given by v(t)=veln(1ktMi) (b) Make a graph of the velocity of the rocket as a function of time for times running from 0 to 132 s. (c) Show that the acceleration of the rocket is a(t)=kveMikt (d) Graph the acceleration as a function of time. (c) Show that the position of the rocket is x(t)=ve(Mikt)ln(1ktMi)+vet (f) Graph the position during the burn as a function of time.
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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:
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 = 5.0 × 10–27 kg, moves in the positive y - direction with speed v1 = 6.0 × 106 m/s. Another particle, of mass m2 = 8.4 × 10–27 kg, moves in the positive x - direction with speed v2 = 4.0 × 106 m/s. Find the magnitude and direction of the velocity of the third particle.
An object with mass m1 = 3.00 kg is moving along the positive x axis with a speed v1i = 2 m/s straight towards two objects with masses m2 = 2.00 kg and m3 = 4.00 kg, which are initially at rest. When they collide, object 1 comes to rest and object 2 moves away with a speed of v2f = 1.5 m/s at an angle of 50 degrees above the x axis. What is the direction of the velocity of the center of mass of the system comprised of all three objects after the collision? A) Along the x axis B) A an angle of 50 degrees above the x axis C) At an angle of 50 degrees below the x axis D) At an angle > 0 degrees and <50 degrees above the x axis E) At an angle>0 degrees and <50 degrees below the x axis The correct answer is A but I am confused why it is A, if you could explain the justification as to why the answer is option A.

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The figure shows a three-particle system, with masses m₁ = 2.5 kg, m2 = 3.9 kg, and m3 = 6.2 kg. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass? y (m) 2 = " 0 mg 1 for 2 mq 3 x (m) (a) Number 1.2936507 Units m (b) Number i 1.1 Units m >