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Equilibrium with Multiple Supports quiz

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  • What must the sum of all torques about any point on an object in equilibrium equal?
    The sum of all torques about any point must equal zero for an object in equilibrium.
  • Why is it helpful to choose a point where a force acts as the axis of rotation when writing torque equations?
    Forces acting at the axis produce no torque, simplifying the equation by reducing the number of terms.
  • In the example with a board and two ropes, where does the weight of the board act?
    The weight of the board acts at its center, which is the midpoint of the board.
  • How do you determine the direction (sign) of torque produced by a force?
    Clockwise torques are usually considered negative, and counterclockwise torques are positive.
  • What equation relates the upward tensions and downward weights for the board in equilibrium?
    The sum of the tensions equals the sum of the weights: T1 + T2 = mg + Mg.
  • If you know one tension in a two-rope system, how can you find the other?
    You can substitute the known tension into the force equilibrium equation to solve for the other tension.
  • What is the advantage of writing the torque equation about the point where T1 acts?
    Writing the equation about point T1 eliminates T1 from the torque equation, making it easier to solve for T2.
  • How do you calculate the torque produced by a force?
    Torque is calculated as the force multiplied by the distance from the axis, times the sine of the angle between them (τ = F·r·sinθ).
  • Why do all the sine terms become 1 in the example problem?
    Because all forces are vertical and all distances are horizontal, making the angle between them 90°, and sin(90°) = 1.
  • What is the calculated value of T2 in the example problem?
    T2 is calculated to be 88 newtons.
  • What is the calculated value of T1 in the example problem?
    T1 is calculated to be 112 newtons.
  • Why is T1 greater than T2 in the example?
    T1 is greater because the additional mass is closer to the left rope, increasing the force needed there.
  • What happens if you choose a point with no forces acting on it as your axis for torque calculations?
    Choosing such a point does not simplify the equation, as no terms are eliminated.
  • What does the equilibrium condition for forces state for the board?
    The sum of all vertical forces must be zero for the board to remain in equilibrium.
  • How can you check if your answers for tensions make physical sense?
    You can reason that the tension should be greater in the rope closer to the added mass, matching the calculated results.