Deformation of Solids

Define the Young modulus.

Determine the cross-sectional area of the wire.

area = ______ $\text{m}^2$

The extension of the wire is initially $2.0 \times 10^{-3}\text{ m}$.

Determine the work done to increase the extension of the wire to $3.0 \times 10^{-3}\text{ m}$.

work done = ______ $\text{J}$

Use Fig. 3.2 to calculate the force exerted on the wire by the model planet.

force = ______ $\text{N}$

The elastic potential energy of X is $0.31\ \text{J}$.

Calculate the original length of the wire before the model planet was attached.

original length = ______ $\text{m}$

Wire X is replaced by a new wire, Y, with the same original length and diameter but double the Young modulus of X. Wire Y also obeys Hooke’s law.

On Fig. 3.2, draw a line representing the variation with strain of the stress for Y.

Define strain.

Calculate the Young modulus of the wire.

$\text{Young modulus}$ = ______ $\text{Pa}$

On Fig. 4.1, draw a line to show how the stress varies with the strain for the wire up to its limit of proportionality.

A second copper wire has the same length as the wire in (b) but a larger diameter. Both wires are subjected to a tensile force of $18\text{ N}$.

By placing a tick (✓) in each row, complete Table 4.1 to compare the stress and strain of the two wires.

Table 4.1

State Hooke’s law.

On the line in Fig. 3.1, draw a cross ($\times$) to show the limit of proportionality. Label this cross with the letter P.

On the line in Fig. 3.1, draw a cross ($\times$) to show the elastic limit. Label this cross with the letter E.

the spring constant of the sample

spring constant = ______ $\text{N m}^{-1}$

the Young modulus of the material from which the sample is made.

Young modulus = ______ $\text{Pa}$

Determine an estimate of the work done on the sample as it is extended from zero extension to its breaking point. Explain your reasoning.

work done = ______ $\text{J}$

A second sample of the same material has a larger cross-sectional area than the original sample but the same initial length. The two samples are each deformed with the limit of proportionality.

State and explain qualitatively how the spring constant of the second sample compares with that of the original sample.

Define the Young modulus of a material.

On Fig. 4.1, sketch the variation of tensile force $F$ in the wire with its extension $x$.

State the name of the quantity represented by the gradient of the line in Fig. 4.1.

State the name of the quantity represented by the area under the line in Fig. 4.1.

Another wire Q is made from a metal that has twice the Young modulus of the metal of wire P in (b). Wire Q has the same volume as wire P but has double the cross-sectional area of wire P.

The two wires are extended by equal tensile forces within their limits of proportionality.

State and explain how the extension of wire Q compares with the extension of wire P.

stress

strain.

Determine the cross-sectional area of wire X.

cross-sectional area = ______ $\text{m}^2$

Wire Y has a greater diameter than wire X.

Explain, without calculation, whether the Young modulus of the metal from which wire Y is made is less than, the same as or greater than $1.9 \times 10^9\ \text{Pa}$.

state the name of the law that gives the relationship between the force and the extension

determine the spring constant, in $\text{N m}^{-1}$

spring constant = ______ $\text{N m}^{-1}$

determine the elastic potential energy when $F = 6.0\ \text{N}$.

elastic potential energy = ______ $\text{J}$

Define the Young modulus.

Determine the unstretched length of the wire.

unstretched length = ______ $\text{m}$

For an applied force $F$ of $30\text{ N}$, determine:

● the stress in the wire

stress = ______ $\text{Pa}$

● the strain of the wire.

strain = ______

state what is represented by the gradient

explain why the area under the line represents the elastic potential energy of the wire.

Use Fig. 4.1 to determine:

● the extension $x_G$ of wire G

$x_G$ = ______ $\text{mm}$

● the extension $x_H$ of wire H.

$x_H$ = ______ $\text{mm}$

Calculate the total elastic potential energy $E_P$ of the composite wire due to the weight of the block.

$E_P$ = ______ $\text{J}$

The original length of wire G is $L$ and the original length of wire H is $1.5L$.

Calculate the ratio

ratio = ______

Determine the spring constant $k$ of the spring.

$k$ = ______ $\text{N m}^{-1}$

Determine the elastic potential energy in the spring when the applied force $F$ is $15\text{ N}$.

elastic potential energy = ______ $\text{J}$