Forces & Elasticity Flashcards

All 28 cards in this deck

Why does stretching a spring require more than one force?

One force alone would make it accelerate; two opposing forces are needed to change its shape.
e.g. pulling one end while the other end is held.

Name the three ways an elastic object can be distorted by forces.

Stretching, bending and compressing.

What is elastic distortion?

The object returns to its original shape and length when the forces are removed.

What is inelastic distortion?

The object does not return to its original shape and length when the forces are removed; it stays permanently deformed.

True or false? A single force applied to a spring is enough to compress it.

False. At least two forces (a pair of opposing forces) are needed, otherwise the spring would simply accelerate.

True or false? A spring that has been stretched beyond its elastic limit no longer returns to its original length.

True. Past the elastic limit the distortion is inelastic and some deformation is permanent.

State Hooke's law in words.

The extension of a spring is directly proportional to the force applied, provided the limit of proportionality is not exceeded.

What is the equation linking force, spring constant and extension, with units?

$F = k \times x$
force (N) = spring constant (N/m) $\times$ extension (m)

What does the spring constant tell you about a spring?

How stiff it is — the force needed per metre of extension (N/m). A larger $k$ means a stiffer spring.

What are the steps to calculate a spring constant from force and extension?
e.g. a force of $6$ N gives an extension of $4$ cm

1. Convert extension to metres: $4$ cm $= 0.04$ m
2. Rearrange $F = k \times x$ to $k = F \div x$
3. $k = 6 \div 0.04 = 150$ N/m

How do you find the spring constant from a force–extension graph?
e.g. the line passes through $(0.02$ m$, 5$ N$)$

Find the gradient of the straight-line part: $k =$ force $\div$ extension.
$k = 5 \div 0.02 = 250$ N/m

What is the difference between a linear and a non-linear force–extension relationship?

Linear: the graph is a straight line through the origin (extension proportional to force). Non-linear: the graph is curved, so extension is not proportional to force.

True or false? Extension is the same as the stretched length of the spring.

False. Extension = stretched length $-$ original (unstretched) length.

What is the name of the point on a force–extension graph beyond which the line stops being straight?

The limit of proportionality (beyond it, Hooke's law no longer applies).

What is the equation for the energy transferred (work done) in stretching a spring?

$E = \frac{1}{2} \times k \times x^2$
energy (J) = $\frac{1}{2} \times$ spring constant (N/m) $\times$ (extension (m))$^2$

What energy store does the work done in stretching a spring elastically go into?

The elastic potential (elastic strain) energy store of the spring.

What are the steps to calculate the energy transferred in stretching a spring?
e.g. $k = 24$ N/m, extension $= 12$ cm

1. Convert extension to metres: $12$ cm $= 0.12$ m
2. Substitute into $E = \frac{1}{2} \times k \times x^2$: $\frac{1}{2} \times 24 \times 0.12^2$
3. $E = 0.17$ J

What are the steps to find the extension of a spring from the work done on it?
e.g. $E = 45$ J, $k = 140$ N/m

1. Substitute into $E = \frac{1}{2} \times k \times x^2$: $45 = \frac{1}{2} \times 140 \times x^2$
2. Rearrange: $x = \sqrt{\dfrac{2E}{k}} = \sqrt{\dfrac{2 \times 45}{140}}$
3. $x = 0.80$ m

What does the area between the line of a force–extension graph and the extension axis represent?

The work done on the spring / the energy transferred to its elastic potential energy store.

True or false? Doubling the extension of a spring doubles the energy stored in it.

False. Energy depends on $x^2$, so doubling the extension gives four times the energy.

True or false? Extension must be converted to metres before using $E = \frac{1}{2} \times k \times x^2$.

True. Using centimetres gives an answer that is wrong by a power of ten (a POT error).

In the core practical, how is the extension of the spring found at each load?

Subtract the original (unloaded) length from the new length measured with a metre rule: extension = difference between the two positions.

What are the steps of the core practical to investigate force and extension for a spring?
e.g. adding $1$ N weights up to $5$ N

1. Clamp the spring vertically and measure its original length with a metre rule.
2. Add a known weight, then measure the new length and calculate extension = new $-$ original.
3. Repeat for increasing weights and plot force against extension.

In the force–extension core practical, which variable is plotted on which axis (Edexcel convention)?

Force (N) on the vertical axis, extension (m) on the horizontal axis.

Give two ways to reduce measurement error when finding the extension of a spring.

Read the rule at eye level to avoid parallax and use a fixed pointer/marker on the spring; take repeat readings.

How does the shape of a force–extension graph for rubber differ from that for a spring?

Rubber gives a non-linear (curved) graph, and its loading and unloading curves do not pass through the same points; a spring gives a straight line with one line only.

What does the area enclosed between the loading and unloading curves for a stretched rubber band represent?

The difference in energy transferred when loading and unloading — energy transferred to the thermal energy store (dissipated to the surroundings).

True or false? In the force–extension practical you should keep adding weights until the spring no longer returns to its original length.

False. Overloading permanently deforms the spring and ruins the results; stay within the elastic limit.