Physics: Springs and Hooke's Law

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Questions and Answers

What is required to shape a spring or wire?

A single force acting at the center

Only compressive forces

A pair of equal and opposite forces (correct)

Only tensile forces

What does Hooke's law state about the relationship between force and extension within the elastic limit?

Force is independent of extension

Force is exponentially related to extension

Force is directly proportional to extension (correct)

Force is inversely proportional to extension

What happens to a material once it exceeds its elastic limit according to Hooke's law?

It becomes permanently elastic

It will exhibit only elastic deformation

It will undergo plastic deformation (correct)

It returns to its original shape

Which of the following is true about the force constant 'k' in Hooke's law?

It is a measure of stiffness of the material Signup and view all the answers

In a force-extension graph, what does the gradient of the line up until point A represent?

The force constant of the material Signup and view all the answers

What characterizes a material that shows plastic deformation?

It will experience permanent deformation Signup and view all the answers

What is the relationship between the loading and unloading curves for a metal wire within its elastic limit?

They are the same in this region Signup and view all the answers

What type of forces act on a spring when it is being stretched?

Tensile forces acting away from the center Signup and view all the answers

What does the area between the loading and unloading curves on a force-extension graph represent?

Energy required to stretch the material Signup and view all the answers

Which material is described as undergoing plastic deformation when a force is applied?

Polythene Signup and view all the answers

What technique can reduce error in measuring extension in the experiment?

Reading values at eye-level Signup and view all the answers

When calculating the total spring constant for springs in series, which formula applies?

$\frac{1}{k} = \frac{1}{k_1} + \frac{1}{k_2} + \frac{1}{k_3}$ Signup and view all the answers

In a force-extension graph for elastic materials, what does the gradient of the straight section represent?

Force constant of the material Signup and view all the answers

What happens to the energy used to deform an elastic material when the force is removed?

It transfers to thermal energy Signup and view all the answers

Which of the following is NOT a characteristic of rubber described?

Experiences plastic deformation Signup and view all the answers

Which method helps in accurately determining the force-extension characteristics?

Using varying masses and recording extensions Signup and view all the answers

What occurs at the limit of proportionality, point P, on a stress-strain graph for a wire?

Hooke's law is obeyed up to this point. Signup and view all the answers

Which of the following statements is true about the ultimate tensile strength (UTS) of materials?

UTS represents the maximum breaking stress that can be applied. Signup and view all the answers

What distinguishes the unloading curve of rubber from its loading curve?

Some energy is lost as thermal energy. Signup and view all the answers

Which statement best describes the behavior of a brittle material like glass under stress?

It shows elastic behavior until a breakpoint and then snaps. Signup and view all the answers

What is a characteristic of ductile materials in terms of deformation?

They typically undergo elastic deformation followed by plastic deformation. Signup and view all the answers

What is the formula used to calculate elastic potential energy stored in a material?

$E = rac{1}{2} F x$ Signup and view all the answers

What happens to the energy when plastic deformation occurs in a material?

It is used to rearrange the atoms into new positions. Signup and view all the answers

How is tensile stress calculated?

$ ext{Stress} ( au) = rac{F}{A}$ Signup and view all the answers

What does the Young modulus measure?

The ratio of stress to strain in a material. Signup and view all the answers

What is the unit for tensile strain?

It has no unit. Signup and view all the answers

What is the purpose of measuring the diameter of a wire before calculating its Young modulus?

To find the cross-sectional area of the wire. Signup and view all the answers

Which of the following techniques is used to determine the Young modulus of a wire?

Applying various forces and measuring the wire's extension. Signup and view all the answers

What does the area under a force-extension graph represent?

The total work done on the material. Signup and view all the answers

Study Notes

Springs

Springs can experience tensile or compressive forces.
- Tensile forces stretch the spring.
- Compressive forces shorten the spring.

Hooke's Law

Within the elastic limit, the force applied to a spring is directly proportional to the extension.
F ∝ x
F = kx
- k is the force constant of the material, measured in Nm-1.
- A larger force constant indicates a stiffer material.

Force-Extension Graph

The force-extension graph shows the relationship between force and extension for a spring.
Elastic deformation occurs up to the elastic limit, where the spring returns to its original shape after the force is removed.
- The gradient of the straight line portion of the graph represents the force constant.
Plastic deformation occurs beyond the elastic limit, where the spring permanently deforms.

Force-Extension Graphs for Different Materials

Metal Wire: Shows a linear elastic region followed by a plastic deformation region.
Rubber: Does not obey Hooke's Law and exhibits a hysteresis loop.
- This represents energy lost as thermal energy during stretching and release.
Polyethene: Exhibits plastic deformation with minimal elastic behaviour.
- Easily stretched into new shapes.

Techniques to Investigate Force-Extension Characteristics

Experimental Setup:
- Material is suspended vertically.
- A fiducial marker on the ruler is used to measure the original length.
- Standard masses are attached to the material to apply a force.
Error Reduction:
- Read the values for extension at eye-level.
- Use a set square to ensure the ruler is straight.
Determining Force Constant:
- Plot a graph of force against extension.
- Find the gradient of the straight section within the elastic limit.

Springs in Series and Parallel

Series:
- 1/k = 1/k1 + 1/k2 + 1/k3
Parallel:
- k = k1 + k2 + k3

Mechanical Properties of Materials

Work Done: Elastic deformation results in work done, which is stored as elastic potential energy.
Elastic Potential Energy (E):
- E = (1/2)Fx
- E = (1/2)kx^2

Stress, Strain, and Young Modulus

Tensile Stress (σ):
- Force applied per unit cross-sectional area.
- σ = F/A
- Measured in Nm-2 (Pa).
Tensile Strain (ε):
- Extension or compression per unit original length.
- ε = x/L
- Unitless.
Young Modulus (E):
- Ratio of stress to strain.
- E = σ/ε
- Measure of material stiffness, independent of shape and size.
- Gradient of the stress-strain graph within the linear region.

Techniques to Determine Young Modulus

Experimental Procedure:
- Measure the diameter of the wire using a micrometer to calculate its cross-sectional area.
- Suspend the wire vertically with a weight attached.
- Measure extension for different forces applied.
Calculation:
- Calculate stress and strain using recorded data.
- Plot a graph of stress against strain and determine the gradient for the Young modulus.

Ultimate Tensile Strength (UTS)

The maximum breaking stress a material can withstand before failing.
A material with a high UTS is considered strong.
On a stress-strain graph:
- P: Limit of proportionality (Hooke's Law is obeyed)
- E: Elastic limit
- Y1, Y2: Yield points (rapid extension)
- UTS: Ultimate tensile strength (maximum breaking stress)

Stress-Strain Graphs for Other Materials

Brittle Materials (e.g., glass): Exhibit linear elastic behaviour until the breakpoint, where they snap.
Elastic Materials (e.g., rubber): Endure high tensile stress before breaking, but exhibit hysteresis with some energy loss.
Ductile Materials (e.g., metals): Undergo elastic deformation, followed by plastic deformation before reaching UTS and breakpoint.

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Description

This quiz explores the principles of springs, including the concepts of tensile and compressive forces, as well as Hooke's Law. Understand the force-extension relationship through different materials and the implications of elastic and plastic deformation. Test your knowledge on the force-constant and graphical representations.