university physics

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A mass m1 = 7.65 kg, is at rest on a frictionless horizontal surface and connected to a wall by a spring with k = 67.9 N/m, as shown in the figure. A second mass, m2 = 5.29 kg, is moving to the right at v0 = 15.3 m/s. The two masses collide and stick together.
the figure is
htt p://s2.dosya.tc/server22/DIDqtx/P043figure.png. html

a) What is the maximum compression of the spring?
(in m) 2.731 m

b) How long will it take after the collision to reach this maximum compression?
(in s) 0.6857 s


i tried everything ,just found out the second one but still have a problem about the first one.

  • university physics -

    First find the speed after collision from conservation of momentum
    initial momentum:
    m v = 5.29 * 15.3 = 80.9 which will be momentum after crash

    after crash
    m = 5.29+7.65 = 12.94 kg
    so for v after crash:
    12.94 v = 80.9
    v = 6.25 m/s after crash
    v at end is zero and energy after crash is conserved so
    (1/2)(12.94)(6.25)^2 = (1/2) (67.9) x^2
    x^2 = 7.45
    and
    x = 2.73 meters I agree

    time = 1/4 of period T
    T = 2 pi sqrt(m/k)
    = 2 pi sqrt (12.94/67.9)
    = 2.74 seconds
    1/4 T = .6857 seconds sure enough

  • university physics -

    thank you!

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