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Work By Springs quiz

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  • What equation describes the force exerted by a spring according to Hooke's Law?
    Hooke's Law is described by F = -kx, where k is the spring constant and x is the displacement from equilibrium.
  • What does the negative sign in Hooke's Law indicate about the direction of the spring force?
    The negative sign means the spring force acts in the opposite direction to the displacement.
  • How are the spring force and applied force related in magnitude and direction?
    They are equal in magnitude but opposite in direction, forming an action-reaction pair.
  • What is the spring constant 'k' and what are its units?
    The spring constant 'k' measures the stiffness of the spring and is expressed in newtons per meter (N/m).
  • How do you calculate the deformation 'x' of a spring when given the force and spring constant?
    Deformation x is calculated by rearranging Hooke's Law: x = F/k.
  • What is the equilibrium position of a spring?
    The equilibrium position is where the spring is relaxed and x equals 0.
  • How do you determine the deformation when a spring is stretched from its original length?
    Deformation x is the difference between the final and initial lengths of the spring.
  • What happens to the force required to deform a spring if the spring constant is doubled?
    Doubling the spring constant doubles the force required to achieve the same deformation.
  • What is a restoring force in the context of springs?
    A restoring force is the spring force that always acts to return the system to equilibrium, opposing deformation.
  • Why can't you use the standard work formula (Fd cos θ) for springs without modification?
    Because the spring force is variable, not constant, so you must use the average force over the displacement.
  • How do you find the average force exerted by a spring during compression or extension?
    The average force is 1/2 kx, where k is the spring constant and x is the total deformation.
  • What is the formula for the work done by an applied force when compressing or stretching a spring?
    The work done is W = 1/2 kx^2, where k is the spring constant and x is the deformation.
  • What is the formula for the work done by the spring force during compression or extension?
    The work done by the spring is W = -1/2 kx^2, which is negative because the force opposes the displacement.
  • What is the angle between the applied force and displacement when compressing a spring, and how does it affect the work calculation?
    The angle is 0 degrees, so cos(0) = 1, making the work positive for the applied force.
  • What is the angle between the spring force and displacement, and what is the result for the work done by the spring?
    The angle is 180 degrees, so cos(180) = -1, making the work done by the spring negative.