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Math Help - string and curve, find angle

  1. #1
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    string and curve, find angle

    A block is hung by a string from the inside roof of a van.

    When the van goes straight ahead at a speed of 24 m/s, the block hangs vertically down.
    But when the van maintains this same speed around an unbanked curve (radius = 180 m),
    the block swings toward the outside of the curve.
    Then the string makes an angle with the vertical.

    Find the angle theta.

    not sure if this has to do with a lifting force or not. and if there is an equation for this problem.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    A block is hung by a string from the inside roof of a van.

    When the van goes straight ahead at a speed of 24 m/s, the block hangs vertically down.
    But when the van maintains this same speed around an unbanked curve (radius = 180 m),
    the block swings toward the outside of the curve.
    Then the string makes an angle with the vertical.
    Find the angle theta.
    ...
    Hello,

    I assume that the mentioned curve is a circle.

    Then a centrifugal force can be observed and a centripetal force is necessary to pull the block in the direction of the center of the circle. Both forces have the same value but opposite directions. Together with the weight of the block you'll get a parallelogramm of forces (see attachment)

    \overrightarrow{F_W}=9.81 \cdot m

    \overrightarrow{F_c}=\frac{m \cdot v^2}{r}= \frac{m \cdot 24^2}{180}=3.2 \cdot m

    then \tan(\theta)=\frac{3.2}{9.81}~\implies~\theta \approx 18.066^\circ
    Attached Thumbnails Attached Thumbnails string and curve, find angle-block_in_car.gif  
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