q09.systems of particles
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Q09. Systems of Particles
1. At the same instant that a 0.50-kg ball is dropped from 25 m
above Earth, a second ball, with a mass of 0.25 kg, is thrown
straight upward from Earth's surface with an initial speed of
15 m/s. They move along nearby lines and pass each other
without colliding. At the end of 2.0 s the height above
Earth's surface of the center of mass of the two-ball system
is:
1. 2.9 m
2. 4.0 m
3. 5.0 m
4. 7.1 m
5. 10.4 m
0
0.5 2516.7
0.5 0.25
kg mY m
kg kg
0
0.25 15 /5.0 /
0.5 0.25
kg m sV m s
kg kg
2
0 0
12.0 2.0 7.06
2Y Y V s g s m
Initial height of CM:
Initial velocity of CM:
Height of CM after 2s :
25m
0.25 kg15 m/s
0.5 kg0.0 m/s
V0
CMg
2. A 320-N hunter gets a rope around a 640-N polar bear.
They are stationary, 10 m apart, on frictionless level ice.
When the hunter pulls the polar bear to him, the polar bear
will move:
1. 1.0 m
2. 3.3 m
3. 10 m
4. 12 m
5. 17 m
0
640 10 20
640 320 3
N mX m
N N
0
1010 3.3
3X m X m m
Initial postion of CM:( Hunter at coord origin)
No external horizontal forces position of CM not changed.
Displacement of bear :
10 m
320 N 640 N
X
CM
X0
3. Two 4.0-kg blocks are tied together with a compressed spring between them.
They are thrown from the ground with an initial velocity of 35 m/s, 45° above
the horizontal. At the highest point of the trajectory they become untied and
spring apart. About how far below the highest point is the center of mass of the
two-block system 2.0 s later, before either fragment has hit the ground?
1. 12 m
2. 20 m
3. 31 m
4. Can't tell because the velocities of the fragments are
not given.
5. Can't tell because the coordinates of the highest point
are not given.
35 m/s45
g
4 kg 4 kg
Distance of free falling in 2.0 s is 2219.8 2 19.6
2m s s m
4. Which one of the following statements is true?
1. the CM of an object must lie within the object
2. all the mass of an object is actually concentrated at its CM
3. the CM of an object cannot move if there is zero net force
on the object
4. the CM of a cylinder must lie on its axis
5. none of the above
1. the CM of an object must lie within the object
2. all the mass of an object is actually concentrated at its CM
3. the CM of an object cannot move if there is zero net force on the object
4. the CM of a cylinder must lie on its axis
5. none of the above
Fnet = 0 V = const
Not true if ( ) ≠ (+ )
5. A 3.0-kg and a 2.0-kg cart approach each other on a horizontal
air track. They collide and stick together. After the collision
their total kinetic energy is 40 J. The speed of their center of
mass is :
1. zero
2. 2.8 m/s
3. 4.0 m/s
4. 5.2 m/s
5. indeterminate
2140 3.0 2.0
2J kg kg V
4 /V m s
6. Object A strikes the stationary object B head-on in an elastic
collision. The mass of A is fixed, you may choose the mass of
B appropriately. Then :
1. for B to have the greatest recoil speed, choose mA = mB
2. for B to have the greatest recoil momentum, choose mB << mA
3. for B to have the greatest recoil kinetic energy, choose mB >> mA
4. for B to have the least recoil speed, choose mB = mA
5. for B to have the greatest recoil kinetic energy, choose mB = mA
1. for B to have the greatest recoil speed, choose mA = mB
2. for B to have the greatest recoil momentum, choose mB << mA
3. for B to have the greatest recoil kinetic energy, choose mB >> mA
4. for B to have the least recoil speed, choose mB = mA
5. for B to have the greatest recoil kinetic energy, choose mB = mA
Momentum conservation
Relative velocity reversal
0B
A A BA
mv v v
m
0A B Av v v
02 A AB
A B
m vv
m m
02
1 /A A
B BA B
m vm v
m m
2 22 0
2
1 2
2B A A
B B
A B
m m vm v
m m
Greatest when B Am m
Greatest when B Am m
greatest when B Am m
7. Blocks A and B are moving toward each other along the x axis.
A has a mass of 2.0 kg and a velocity of 50 m/s, while B has a
mass of 4.0 kg and a velocity of –25 m/s. They suffer an
elastic collision and move off along the x axis. The kinetic
energy transferred from A to B during the collision is :
1. 0
2. 2500 J
3. 5000 J
4. 7500 J
5. 10000 J
Initial total momentum : 2.0 50 / 4.0 25 / 0kg m s kg m s
Momentum conservation vA and vB after collision simply reverse their sign.
KE’s are not changed.
2.0 kg50 m/s
5.0 kg25 m/s
50 m/s 25 m/s
8. Two objects, X and Y, are held at rest on a horizontal
frictionless surface and a spring is compressed between
them. The mass of X is 2/5 times the mass of Y.
Immediately after the spring is released, X has a kinetic
energy of 50 J and Y has a kinetic energy of :
1. 20 J
2. 8 J
3. 310 J
4. 125 J
5. 50 J
Initial total momentum = 0
2 21 1
2 2Y X
Y Y Y X X XX Y
v mK m v m v K
v m
Momentum conservation X X Y Ym v m v
250 20
5J J
X : m = 2/5
Y : M = 1
K = 10 J
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