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Hooke’s Law and Young’s Modulus Worksheet
Necessary knowledge
F
F = kx (Hooke’s Law) OR k = .
x
where k is the spring constant (stiffness or force constant) of the spring
F = applied force
x = extension of the spring.
Strain () is defined as the increase in length of a wire (x) divided by its the original length (L).
x
strain ε =
L
Stress () is defined as the force (F) applied per unit cross-sectional area (A) of the wire.
F
stress ¿
A
The force (F) in this case is the normal force (acts
perpendicular to the cross-sectional area).
σ
Young’s modulus = stress/strain: ¿
ε
F
σ A FL
Thus ¿ = =
ε x xA
L
Thus for a cylindrical wire ¿ ( Fx ) ×( π4 dL )
2
where d is the diameter of the wire.
, 2
Questions
1. The figure shows the extension-force graph for a wire that is
stretched and then released.
1.1 Which point shows the limit of proportionality?
1.2 Which point shows the elastic limit?
2. The figure shows the extension-force graph for 4 springs, A, B, C and D.
2.1 Which spring has the greatest value of force constant?
2.2 Which spring is the least stiff?
2.3 Which of the four springs does not obey Hooke’s Law?
3. List the metals in the Table on page 1 from stiffest to least
stiff.
4. Which of the non-metals in the Table on page 1 is the
stiffest?
5. The figure shows stress–strain graphs for two materials, A and B. Use the graphs to determine
Young’s modulus of each material.
6. A piece of steel wire, 200.0 cm long and having cross-sectional area of 0.50 mm 2, is stretched by a
force of 50 N. Its new length is found to be 200.1 cm. Calculate the stress and strain, and Young’s
modulus of steel.
7. Calculate the extension of a copper wire of length 1.00 m and diameter 1.00 mm when a tensile force
of 10 N is applied to the end of the wire. (Young modulus of copper = 130 GPa.)
Hooke’s Law and Young’s Modulus Worksheet
Necessary knowledge
F
F = kx (Hooke’s Law) OR k = .
x
where k is the spring constant (stiffness or force constant) of the spring
F = applied force
x = extension of the spring.
Strain () is defined as the increase in length of a wire (x) divided by its the original length (L).
x
strain ε =
L
Stress () is defined as the force (F) applied per unit cross-sectional area (A) of the wire.
F
stress ¿
A
The force (F) in this case is the normal force (acts
perpendicular to the cross-sectional area).
σ
Young’s modulus = stress/strain: ¿
ε
F
σ A FL
Thus ¿ = =
ε x xA
L
Thus for a cylindrical wire ¿ ( Fx ) ×( π4 dL )
2
where d is the diameter of the wire.
, 2
Questions
1. The figure shows the extension-force graph for a wire that is
stretched and then released.
1.1 Which point shows the limit of proportionality?
1.2 Which point shows the elastic limit?
2. The figure shows the extension-force graph for 4 springs, A, B, C and D.
2.1 Which spring has the greatest value of force constant?
2.2 Which spring is the least stiff?
2.3 Which of the four springs does not obey Hooke’s Law?
3. List the metals in the Table on page 1 from stiffest to least
stiff.
4. Which of the non-metals in the Table on page 1 is the
stiffest?
5. The figure shows stress–strain graphs for two materials, A and B. Use the graphs to determine
Young’s modulus of each material.
6. A piece of steel wire, 200.0 cm long and having cross-sectional area of 0.50 mm 2, is stretched by a
force of 50 N. Its new length is found to be 200.1 cm. Calculate the stress and strain, and Young’s
modulus of steel.
7. Calculate the extension of a copper wire of length 1.00 m and diameter 1.00 mm when a tensile force
of 10 N is applied to the end of the wire. (Young modulus of copper = 130 GPa.)
