Question

Consider a system consisting of three particles:

*m*_{1} = **4** kg, _{1} =
**< 11, -6, 12 >** m/s

*m*_{2} = **2** kg, _{2} =
**< -13, 7, -4 >** m/s

*m*_{3} = **3** kg, _{3} =
**< -29, 34, 19 >** m/s

(a) What is the total momentum of this system?

_{tot} = ______ kg · m/s

(b) What is the velocity of the center of mass of this
system?

_{cm} = ______ m/s

(c) What is the total kinetic energy of this system?

*K*_{tot} = _______ J

(d) What is the translational kinetic energy of this system?

*K*_{trans} = ________ J

(e) What is the kinetic energy of this system relative to the
center of mass?

*K*_{rel} = _________ J

One way to calculate *K*_{rel} is to calculate the
velocity of each particle relative to the center of mass, by
subtracting the center-of-mass velocity from the particle's actual
velocity to get the particle's velocity relative to the center of
mass, then calculating the corresponding kinetic energy, then
adding up the three relative kinetic energies. However, there is a
much simpler way to determine the specified quantity, without
having to do all those calculations; think about what you know
about the relationships among the various kinds of kinetic energy
in a multiparticle system. (If you wish, you can check your result
by doing the complicated calculation just described.)

Answer #1

Consider a system of two particles in the xy plane: m1 = 1.95 kg
is at the location r with arrow1 = (1.00î + 2.00?) m and has a
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= (?4.00î ? 3.00?) m and has velocity (3.00î ? 2.00?) m/s.
(a) Plot these particles on a grid or graph paper. Draw their
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Consider a system consisting of three masses on the x
axis. Mass m1 = 1.50 kg
is at x1 = 1.50 m ;
mass m2 = 2.00 kg
is at x2 = 2.30 m ;
and mass m3 = 3.20 kg
is at x3 = 2.70 m .
What is the total gravitational potential energy of this
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A barbell spins around a pivot at its center at
A.
The barbell consists of two small balls, each with mass 450
grams (0.45
kg), at the ends of a very low mass rod of length
d
= 50
cm (0.5
m; the radius of rotation is 0.25
m). The barbell spins clockwise with angular speed 120
radians/s.
We can calculate the angular momentum and kinetic energy of this
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A cylinder of mass 8.0 kg rolls without slipping on a horizontal
surface. At a certain instant its center of mass has a speed of
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(a) Determine the translational kinetic energy of its center of
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J
(b) Determine the rotational kinetic energy about its center of
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J
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2 air carts collide and stick together. cart one is M1
= 0.755 kg and initial speed of 0.435 m/s the cart to right is
initially at rest with mass m2= 0.300kg.
a.find the velocity of the center of mass before the carts Collide
and stick together
b. find the velocity of the center of mass after the carts Collide
and stick together
c. find the kinetic energy of the system before and after the
Collision

Cart 1, with m1= 5.8 kg, is moving on a frictionless linear air
track at an initial speed of 1.8 m/s. It undergoes an elastic
collision with an initially stationary cart 2, with m2, an unknown
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is conserved for cart 1. cart 2. the system of cart 1 and cart 2.
Momentum is not conserved for any of these...

An object with total mass mtotal = 17.4 kg is sitting at rest
when it explodes into three pieces. One piece with mass m1 = 4.9 kg
moves up and to the left at an angle of θ1 = 21° above the –x axis
with a speed of v1 = 25.9 m/s. A second piece with mass m2 = 5.1 kg
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Three particles have the following masses and center of mass
coordinates: m1 = 2.50 kg, (0.150 m, 0.420 m), m2 = 1.50 kg, (0.120
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of the center of mass of the particle system is:
a. (0.04 m, -0.261 m)
b. (0.04 m, -0.261 m)
c. (- 0.04 m, -0.261 m)
d. (- 0.04 m, 0.261 m)

A point object with mass 6 kg and a uniform rigid rod with mass
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frictionless planar surface. Point object hits the rod vertically
with velocity 8 m/s and sticks to the rod.
Part A
Calculate the angular velocity ω about the center of mass just
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Part B
Calculate the ratio of the lost energy to the initial kinetic
energy of...

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