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1

M&K Problem 4/4

mA = 10 kg

mB = 15 kg

mC = 8 kg⇀aA = 2

⇀ı m/s

2

⇀aB =

⇀

0 m/s2

⇀aC = −1.5

⇀ı m/s

2∑ ⇀

F = m⇀̈rG (4/1)

m⇀rG =

∑mi

⇀r i

.. . m

⇀̈rG =

∑mi

⇀̈r i

(M&K Fig.P4/4)

= [(10)(2) + (15)(0) + (8)(−1.5)]⇀ı kg ·m/s

2= 8

⇀ı N

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2

M&K Problem 4/4

∑ ⇀

F = [(10)(9.81) + (15)(9.81) + (8)(9.81)− T ]⇀ı

= [323.73− T ]⇀ı N

But/Maar ∑ ⇀

F = m⇀̈rG (4/1)

.. . [323.73− T ]

⇀ı = 8

⇀ı

.. . T = 315.73 N

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1

M&K Edition 5 Problem 4/4

The two small spheres, each of massm, are connected by a chord of length2b (measured from the centers of thespheres) and are initially at rest on asmooth horizontal surface in the posi-tion shown. If a vertical force of con-stant magnitude F is applied to thecenter A of the chord, determine thevelocity v of each sphere when theycollide as θ approaches 90◦. What isthe maximum value of F for whichthe spheres do not lose contact withthe surface? (Analyze the systemwithout dismembering it.)

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2

M&K Edition 5 Problem 4/4

Assume / Neem aan:

Spheres stay in contact with the hor-izontal surface.

Sfere bly in kontak met horisontaleoppervlakte.

Principle / Beginsel:

U1−2 = ∆T (4/2)

U1−2 = F (b− b sin θ)

T =1

2mv2

G +∑ 1

2mi|

⇀

ρ̇i|2 (4/4)

T1 = 0

T2 = 0 +∑ 1

2miv

2 = mv2

.. . ∆T = T2 − T1 = mv2

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3

M&K Edition 5 Problem 4/4

U1−2 = ∆T (4/2)

.. . F (b− b sin θ) = mv2

.. . v =

√Fb

m(1− sin θ)

For spheres to stay in contact with horizontal surface:Vir sfere om in kontak met horisontale oppervlakte te bly:

F < 2mg