asssignment 1 solution 2012

7
1 Solution Assignment 1. A Carte having a mass of 60 kg falls horizontally off the back of a truck which is travelling at 80km/hr. Determine the coefficient of kinetic friction between the road and the crate if the crate slides 45 m on the ground with in no tumbling along the road before coming to rest. Assume that the initial speed of the crate along the road is 80 km/hr. 559 . 0 45 81 . 9 2 ) 22 . 22 ( ) ( 2 ) 22 . 22 ( 0 2 45 / 22 . 22 60 60 1000 80 / 80 2 2 2 2 = × × = - × + = + = - = = - = = = × × = = μ μ μ μ S g aS u V g a ma mg ma F m S s m hr km u

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  • 1

    Solution Assignment

    1. A Carte having a mass of 60 kg falls horizontally off the back of a truck which is travelling at 80km/hr. Determine the coefficient of kinetic friction between the road and the crate if the crate slides 45 m on the ground with in no tumbling along the road before coming to rest. Assume that the initial speed of the crate along the road is 80 km/hr.

    559.04581.92

    )22.22()(2)22.22(0

    2

    45

    /22.226060

    100080/80

    2

    2

    22

    =

    =

    +=

    +=

    =

    =

    =

    =

    =

    ==

    SgaSuV

    gamamg

    maFmS

    smhrkmu

  • 2

    2. If the system is released from rest, determine the speeds of both masses after B has moved 1m. Neglect friction and the masses of the pulleys.

    Alternative solution

  • 3

  • 4

    3. At the given instant member AB has the angular motions shown. Determine the velocity and acceleration of the slider block C at this instant. (Use vector analysis)

    [ ]

    [ ] ( )

    2

    2

    2

    2

    /65.54/00.3

    &

    )(19.15)(33.6)(12)(5)(12)(5)(12)(5)(

    )(53)(

    54

    )(63)(14)(37)(72

    /38.9/13.1

    &125)(12)(5

    21)(73)7(

    )(53)(

    54

    scma

    sradjiEquating

    jiijjijika

    jaiaajijjka

    aaa

    scmVCsrad

    jiequatingijjikV

    iijkV

    jViVVVVV

    C

    BC

    BCBCBCBCBC

    CCC

    B

    BCCB

    CB

    CBCBCBCB

    BAB

    CCC

    CBBC

    =

    =

    =++=

    =

    ==

    +=

    =

    =

    +=+=

    ===

    +=

    +=

  • 5

    4. The wheel rolls without slipping such that at the instant shown it has an angular velocity . Determine the velocity of point B on the rod at this instant.

    [ ]

    [ ]

    aV

    Solvingaa

    aaVjiEquating

    iajajaiakrV

    iajajaiakrV

    iVV

    VVV

    B

    BA

    BAB

    BABABABABABA

    ACA

    BB

    BAAB

    +=

    +=

    +=

    +=+==

    +=+==

    =

    +=

    331

    30

    &)()(3)()(3)(

    )()()()()(

    )(

  • 6

    5. For the mechanism shown in figure, link 2 rotates at constant angular velocity. Construct the velocity polygon and determine the acceleration D.

  • 7