A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is

Question

A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 m/s2 Find the value of (a) the spring stiffness constant and (b) the mass.

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Latifah 6 months 2021-07-21T01:40:18+00:00 1 Answers 11 views 0

Answers ( )

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    2021-07-21T01:41:48+00:00

    Given Information:  

    Work done = W = 3.0 J

    compressed length = x = 0.12 m

    acceleration = α = 15 m/s²

    Required Information:  

    (a) spring constant = k = ?

    (b) mass = m = ?  

    Answer:  

    (a) spring constant = 416.67

    (b) mass = 3.33 kg

    Explanation:  

    (a)

    We are given a mass spring system,

    We know that work done is given by

    W = ½kx²

    Where W is the work done, k is the spring constant and x is the compressed length of the spring.

    Re-arranging the equation for spring constant k yields,

    k = 2W/x²

    k = 2*3/0.12²

    k = 416.67

    (b)

    We know that force is given by

    F = kx

    We also know from the Newton’s second law that

    F = mα

    equating both equations yields,

    mα = kx

    m = kx/α

    m = (416.67*0.12)/15

    m = 3.33 kg

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