7.1 Problem 1: Three glasses are placed by a waiter on a light-weight tray. The first glasshas a mass of M = 575 g and is located R = 17 cm from the center of the tray at anangle 01 = 45 degrees above the positive x-axis. The second glass has a mass of M2 =325 g and is located R2 = 22 cm from the center of the tray at an angle 02 = 45 degreesbelow the positive x-axis. The third glass has a mass of M3 = 225 g and is located R3 =17 cm from the center of the tray at an angle 03 = 45 degrees above the negative x-axis.A fourth glass of mass M4 = 875 g is to be placed on the tray so that the center of massis located at the center of the tray.(m3RR,Rm,Otheexpertta.comPart (a) Write a symbolic equation for the horizontal position from the central x-axis that the fourth glass must be placed so that the horizontalcenter of mass of the four glasses is at the center of the tray.Expression :X4 =Select from the variables below to write your expression. Note that all variables may not be required.cos(a), cos(Ф), cos(0), cos(@1, cos(@1), cos(®), cоs(@ 3), sin(a), sin(Ф), sin(®), sin(®), sin(®2), sin(®з), Mj, M2, Мҙ, М4, R1, Rz, RgPart (b) Calculate the numeric value of the horizontal position from the central x-axis of the fourth glass in cm.Numeric : A numeric value is expected and not an expression.X4 =.Part (c) Write a symbolic equation for the vertical position from the central y-axis that the fourth glass must be placed so that the vertical center ofmass of the four glasses is at the center of the tray.Expression :Y4 =Select from the variables below to write your expression. Note that all variables may not be required.cos(6), cos(01), cos(02), cos(03), sin(8), sin(01), sin(0,), sin(03), M1, M2, M3, M4, R1, R2, R3Part (d) Calculate the numeric value of the vertical position from the central y-axis of the fourth glass in cm.Numeric : A numeric value is expected and not an expression.Y4 =Part (e) Calculate the distance that the fourth glass is away from the center of the tray in cm.Numeric : A numeric value is expected and not an expression.R4 =Part (f) Calculate the angular position of the fourth glass relative to negative x-axis in degrees.Numeric : A numeric value is expected and not an expression.04 =

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Answered: itive x-axis. The third glass has e…

itive x-axis. The third glass has e center of the tray at an angle of mass M4 = 875 g is to be pla ne center of the tray.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter6: Momentum, Impulse, And Collisions

Section: Chapter Questions

Problem 46P: A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three...

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A water molecule consists of an oxygen atom with two hydrogen atoms bound to it (Fig. P8.36). The angle between the two bonds is 106. If the bonds are 0.100 nm long, where is the center of mass of the molecule? Figure P8.36
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?
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