Four masses are positioned in the xy-plane as follows:300g at (x=0, y=2.0m),500 g at (-2.0m, -3.0m), 700g at (50cm, 30cm), and 900g at (-80cm, 150cm). Find their center of mass. Show all work in detail

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Hubert KochLv2

19 Nov 2019

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Related questions

A) A 1.0 kg ball is located at the origin and a 2.0 kg ball is at1.0 m away in the x-direction. Where is the center of mass of thesetwo balls.
(Answer in ihat + jhat+ khat form)

B) A 3.0 kg ball is located at (x,y,z)=(0,1.0,0)m and a 4.0 kg ballis located at (1.0,1.0,0) m. Where is the center of mass of thesetwo balls?
(Answer in ihat + jhat+ khat form)

C) Where is the center of mass of all four balls? Determine thistwo ways: (1) find the center of mass of all four balls treatedindividually and then (2) find the center of mass acting as if thesystem was made up of two bodies located at the two centers ofmasses you found above (e.g. a total mass of 1 kg + 2 kg at thelocation of the first center of mass you found above). The tworesults should agree.
(Answer in ihat + jhat+ khat form)

D) Now, let's say that three identical, uniform rods, each 1.00 mlong, are welded perpendicular to one another at a common end so asto represent the positive x-, y-, and z-axes of a Cartesiancoordinate system. Where is the CM of this object?
(Answer in jhat+ khat form)

A mass m on an inclined plane that makes an angle of Î¸ with thehorizontal is attached via a string over a pulley to a mass M thathangs vertically from the edge of the inclined plane. When themasses are released, mass M accelerates vertically downward andmass m accelerates up the ramp. The coefficient of kinetic frictionbetween the mass m and the surface of the inclined plane isu_k.

a.) Draw a diagram of the situation and label all forces andaccelerations. Be
sure to indicate their directions with an arrow.

b.) Draw free body diagrams for each of the two masses. Be sure todraw a coordinate system and indicate the positive and negativedirections. Be sure to resolve any forces that are not acting alongeither the x or y directions of your coordinate system into their xand y components using right triangle trig.

c.) Use your free body diagrams and Netwonâs 2nd law to writeequations for this scenario. Do not use any numbers in theseequations.

d.) Given that m = 20-kg , M = 90-kg , = 30 , and = 0.14 . Find thenormal force acting on mass m.

e.) Find the force of friction acting on mass m.

f.) Find the acceleration of the masses. (You will have to use twoequations.)

g.) Find the tension on the string.

x.Hm

I just need help in the three questionI figure the last question

1)Consider an oxygen molecule (O2) rotating inthe xy plane about the z axis. The axis

passes through the center of the molecule,perpendicular to its length. The mass of each

oxygen atom is 2.66 x 10

-26 kg, and at room temperature the average separation between

the two atoms is

d=1.21 x 10-10 m (the atoms are treated as point masses).a) Calculate

the moment of inertia of the molecule about the zaxis. b) If the angular speed of the

molecule about the

z axis 4.60 x 1012 rad/s, what is its rotational kineticenergy?

Answer: a) 1.95 x 10