Forces and Elasticity

How many forces have to be applied to a stationary object to change their shape?

more than 1

How can stationary objects change their shape by? (name the 3 ways)

• stretching (forces in opposite directions away from the object)

• bending (forces that distort the object)

• compressing (forces in opposite directions towards the object)

BTW, a combination of all 3 can occur

What is placing a mass on top of a spring placed on a flat surface an example of?

What are the two forces?

What direction are they working?

• Compression

  • weight of the mass

  • reaction force from the surface to the spring

• towards each other

What is placing a mas on the bottom of a vertically hanging spring an example of?

What are the 2 forces involved?

What direction are they working?

• stretching

  • weight of the mass

  • tension in the spring

• away from each other

What is a diving board bending when a swimmer stands at the far end an example of?

What are the two forces involved?

What direction do they act in in the example and what other direction can cause this type of change of shape?

• bending

  • weight of swimmer

  • reaction force from the block to the dividing board

• 2 forces act towards each other, but at different points on the object

• can also be cause by 2 forces at an angle to each other

What do some materials do when stretched and other such as plastic do?

• return to their original shape (springs, rubber bands)

• remain permanently distorted

What is the name for a change of shape and what two types are there?

• deformation

• elastic and inelastic

When does elastic deformation occur?

give 3 examples

• When objects return to their original shape when the stretching force is removed

  • rubber bands

  • fabrics

  • steel springs

When does inelastic deformation occur?

give 3 examples

• When objects remain stretched and do not return completely to their original shape even when the stretching force is removed

  • plastic

  • clay

  • glass

What 2 things does hooke’s law concern the relationship between?

• extension of an elastic object

• the applied force

What does hooke’s law state?

The extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality

What does directly proportional mean here?

If force is increased, extension increases.

What is the limit of proportionality?

How does it vary?

• The point beyond which the relationship between force and extension is no longer directly proportional

• varies according to the material

What can you use to test hooke’s law?

The hooke’s law experiment

What is the equation that defines hooke’s law?

What are the units?

• force = spring constant x extension

• F = k x e

•   (N)  =       (N/m)          x       (m)

What can the symbol e in the equation F = k x e represent (2 options)

extension or compression of an elastic object

What does the spring constant represent?

How stiff a spring is (higher, stiffer)

How do we calculate extension of an object?

final length - original length

In an experiment how would we find extension of the spring?

• mark position of bottom unstretched spring on ruler

• mark position (from bottom of spring) of stretched spring

What type of relationship is hooke’s law between force and extension?

How is it represented on a force-extension graph therefore?

What type of relationship do materials that do not obey hooke’s law, i.e force and extension are no longer directly proportional, have?

How is it represented on a force-extension graph therefore?

• linear

• straight line

• non-linear

• curve

equation for calculating spring constant?

what does this equation show in regards with what the spring constant is equal to?

• k = F/e

• Force per unit extension needed to extend the spring, assuming its limit of proportionality is not reached

When force-extension graph is straight line or a part of it is?

How can we find spring constant from this line? (2 different ways depending on what’s on what axis)

• The material obeys hooke’s law up to the limit of proportionality

• Find gradient (if force is on y-axis and extension is on x-axis)

• Find 1 / gradient (if force is on x-axis and extension is on y-axis

What does the symbol ‘∝’ mean?

Proportional to

When a spring is stretched or compressed, what does work?

Work is done by the spring

What is work done?

In the context of springs being stretched an compressed, where is energy transferred to in the spring?

• the transfer of energy

• to its elastic potential energy store

What is elastic potential energy defined as?

The energy stored in an elastic object when work is done on the object

At what point would a spring be inelastically deformed?

Up until this point what is the relationship between work done and elastic potential energy?

• It exceeded its limit of proportionality

• Work done on string and elastic potential energy are equal

What would the equation be for finding the work done, or the elastic potential energy stored, while stretching or compressing a spring?

• E_e  = ½ x k x e²

• E_e = elastic potential energy in joules (J)

• k = spring constant in newtons per metre (N/m)

• e = extension in metres (m)

What is the equation only for?

Since e² is used, what happens if the extension is doubled to the work done?

• Springs that have not been stretched beyond their limit of proportionality

• It is quadrupled

In the required practical: investigating force and extension, what is the independent, dependent and control variable?

• Force, F

• Extension

• Spring constant, k

Devise a method for the practical, in 8 steps

1. Set up the apparatus as shown in the diagram, initially without any masses hanging from the spring

2. Align the marker to a value on the ruler, record this initial length of the spring

3. Add the 100 mass hanger onto the spring

4. Record the mass (in kg) and position (in cm) from the ruler now that the spring has extended

5. Add another 100 g to the mass hanger

6. Record the new mass and position from the ruler now that the spring has extended further

7. Repeat this process until all masses have been added

8. The masses are then removed and the entire process repeated again, until it has been carried out a total of three times, and an average length is calculated

How would we find the force from the different masses?

Use w = mg, we know mass and gravitational field strength so multiply them

When making the graph, what should you put on each axis despite it going against what yopu normally do in an experiment but for this occasion it makes it easier?

Put extension on x - axis and force on y axis so that it is easier to find the spring constant because you only need the gradient and further more, it link nicer to y = mx + c, F = ke

What could a systematic error be and how to avoid it?

Incorrect measurements so make sure the measurements on the ruler are taken at eye level to avoid parallax error

Name 3 ways we could improve random errors

• With the use of a pointer (a fiducial marker) to measure extension more accurately

• Wait a few seconds for the spring to fully extend when a mass is added before taking the reading for its new length

• Make sure to check whether the spring has not gone past its limit of proportionality

What are systematic errors?

What are random errors?

• Faults in the apparatus or experimental method which consistently affect every measurement, for example, a zero error. This affects accuracy.

• Unpredictable changes in an experiment causing one measurement to differ slightly from the next. Affects precision.