Physics

The spring shown in the image below has an unstretched length of 3.00m, and a spring constant of 75.0N/m. The mass of m=7.50kg is attached to the end of the spring, and the mass is pulled down to stretch the spring to 4.50m in length. This began the mass moving up and down with simple harmonic motion (SHM). In this simple harmonic motion;
a) What is the spring length;
i) At the locations where the velocity of the mass is zero (2)
ii) At the location where its speed is maximized (1)
iii) when its elastic energy is “0J” (1)
b) Determine the acceleration of the mass when the spring is 4.20m long.
c) Determine the speed of the mass when the spring length is 4.30m long.
d) Determine the time it will take the mass to bounce up to the maximum
height and back to its lowest height eight times.

  1. 👍
  2. 👎
  3. 👁
  1. F = k x
    omega = w = 2 pi f = 2 pi/T = sqrt (k/m) = sqrt 10
    say g = 10 m/s^2
    then for x of center of sinusoidal motion = m g/k = 7.5 * 10 / 75 = 1 meter of stretch due purely to gravity
    so
    answer to first part of first question is 4 meters plus or minus 0.5meters
    answer to second part of first question is 3 + 1 = 4 meters spring length of center of sinusoidal motion where speed is max
    then
    say x = 4.0 + 0.5 sin w t = 4.0 + 0.5 sin [ (sqrt 10 )* t]
    then v = 0.5 sqrt 10 * cos [ (sqrt 10 )* t]
    and a = - 5 sin [ (sqrt 10 )* t]

    f = omega/2 pi = sqrt 10/ 2pi
    so
    T = 1/f = 2 pi / sqrt 10

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    A single mass (m1 = 3.1 kg) hangs from a spring in a motionless elevator. The spring constant is k = 338 N/m. 1. What is the distance the spring is stretched from its unstretched length? 2. Now, three masses (m1 = 3.1 kg, m2 = 9.3

  2. physics

    A spring of stiffness 127 N/m, and with relaxed length 0.19 m, stands vertically on a table, as shown in the figure. Instead of compressing the spring with a heavy block, with your hand you push straight down on the spring until

  3. physics

    A block with mass m = 17 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 4201 N/m after being compressed a distance x1 = 0.556 m from the spring’s unstretched length. The floor is

  4. physics

    A block with mass m = 17 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 4201 N/m after being compressed a distance x1 = 0.556 m from the spring’s unstretched length. The floor is

  1. PHYSICS

    A spring is hung from a ceiling, and an object attached to its lower end stretches the spring by a distance d = 7.70 cm from its unstretched position when the system is in equilibrium as in the figure below. If the spring constant

  2. physics

    An unstretched ideal spring hangs vertically from a fixed support. A 0.4 kg object is then attached to the lower end of the spring. The object is pulled down to a distance of 35cm below the unstretched position and released from

  3. physics

    A block with mass m = 17 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 4201 N/m after being compressed a distance x1 = 0.556 m from the spring’s unstretched length. The floor is

  4. physics

    When a 2.60-kg object is hung vertically on a certain light spring described by Hooke's law, the spring stretches 2.30 cm. (a) What is the force constant of the spring? (b) If the 2.60-kg object is removed, how far will the spring

  1. Physics

    A single mass (m1 = 3.2 kg) hangs from a spring in a motionless elevator. The spring constant is k = 253 N/m. 1) What is the distance the spring is stretched from its unstretched length? This first answer is equal to 12.4 cm but I

  2. Physics

    3 kg object is fastened to a light spring with the intervening cord passing over a pulley. The pulley is frictionless and it's inertia may been neglected. The object is released from rest when the spring is unstretched. If the

  3. College Physics 121

    A spring with a spring constant k = 50N/m has an unstretched length of 20cm. Find the work required to stretch the spring to a length of 30 cm. W = J ?? any help guys?

  4. Science

    Can someone help me with this question? A spring has a spring constant of 300 N/m. Find the magnitude of the force needed to compress the spring by 0.03 m. Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx,

You can view more similar questions or ask a new question.