Question

The external force, F_ext, required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring. Thus, the force a spring applies when it is extended a distance ?x = x - x_0 away from its equilibrium length x_0 is given by F_s = -k(x - x_0) = -k?x. This is known as Hooke's law. The proportionality constant k is known as the spring constant, which is a measure of the spring 'stiffness' and has dimensions of force/length and units of N/m. The negative sign is usually included to indicate that the restoring force due to the spring is in the opposite direction to the force which caused the displacement. x_0 F_s F_ext ?x x=x_0+?x Problem 1: (5 points) A scale can be made using a spring and measuring the displacement from equilibrium when masses are hung from the spring. If a spring is displaced a distance ?x from equilibrium when a mass m is hung from the spring on earth, what would be the displacement on the moon when the same mass is hung from the spring? Problem 2: (15 points) Explain how a set of n known (calibrated) test masses {m_1, m_2, m_3, ..., m_n}, with m_1 < m_2 < m_3 < ... < m_n, could be used to determine the spring constant, k, of an uncalibrated spring. You will be doing this in lab this week. Hint: Consider the change in length of the spring when adding additional masses, for example the amount the spring stretches from position x_1 to position x_2 when adding mass m_2 to the spring that already has mass m_1 on it is ?x_21 = x_2 - x_1 = ((m_2+m_1)g)/k - (m_1g)/k = (m_2g)/k.

          The external force, F_ext, required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring. Thus, the force a spring applies when it is extended a distance ?x = x - x_0 away from its equilibrium length x_0 is given by
F_s = -k(x - x_0) = -k?x.
This is known as Hooke's law. The proportionality constant k is known as the spring constant, which is a measure of the spring 'stiffness' and has dimensions of force/length and units of N/m. The negative sign is usually included to indicate that the restoring force due to the spring is in the opposite direction to the force which caused the displacement.
x_0
F_s F_ext
?x
x=x_0+?x
Problem 1: (5 points)
A scale can be made using a spring and measuring the displacement from equilibrium when masses are hung from the spring. If a spring is displaced a distance ?x from equilibrium when a mass m is hung from the spring on earth, what would be the displacement on the moon when the same mass is hung from the spring?
Problem 2: (15 points)
Explain how a set of n known (calibrated) test masses {m_1, m_2, m_3, ..., m_n}, with m_1 < m_2 < m_3 < ... < m_n, could be used to determine the spring constant, k, of an uncalibrated spring. You will be doing this in lab this week.
Hint: Consider the change in length of the spring when adding additional masses, for example the amount the spring stretches from position x_1 to position x_2 when adding mass m_2 to the spring that already has mass m_1 on it is
?x_21 = x_2 - x_1 = ((m_2+m_1)g)/k - (m_1g)/k = (m_2g)/k.

The external force, Fext, required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring. Thus, the force a spring applies when it is extended a distance ?x = x - x0 away from its equilibrium length x0 is given by
Fs = -k(x - x0) = -k?x.
This is known as Hooke's law. The proportionality constant k is known as the spring constant, which is a measure of the spring 'stiffness' and has dimensions of force/length and units of N/m. The negative sign is usually included to indicate that the restoring force due to the spring is in the opposite direction to the force which caused the displacement.
x0
Fs Fext
?x
x=x0+?x
Problem 1: (5 points)
A scale can be made using a spring and measuring the displacement from equilibrium when masses are hung from the spring. If a spring is displaced a distance ?x from equilibrium when a mass m is hung from the spring on earth, what would be the displacement on the moon when the same mass is hung from the spring?
Problem 2: (15 points)
Explain how a set of n known (calibrated) test masses m1, m2, m3, ..., mn, with m1 < m2 < m3 < ... < mn, could be used to determine the spring constant, k, of an uncalibrated spring. You will be doing this in lab this week.
Hint: Consider the change in length of the spring when adding additional masses, for example the amount the spring stretches from position x1 to position x2 when adding mass m2 to the spring that already has mass m1 on it is
?x21 = x2 - x1 = ((m2+m1)g)/k - (m1g)/k = (m2g)/k.

Added by Michelle G.

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