Heating A Metallic Scale

A metallic scale (linear) expands in length when heated. As a result all the paging is displaced from their usual (correct) positions.

Diffrence of length of two rods:

Consider two rods 1 and 2 of length l₁ and l₂   . Lest they be heated through a temperature . If l′₁ and l′₂ are their larger lengths, then:

                l′₂ = l₂ (1+a₂Δt)

                l′₁=l₁ (1+a₁Δt)

Since the difference of size of two rods is constant

   l′₂ -l′₁ = l₂ -l₁       and   l₁a₁=l₂a₂     

Time peried of Pendulum:

Time period (T) of a simple pendulum of length l is given by T= 2π√(l/g)       

If there is a rise in temperature by Δt, length of the pendulum increases and hence the time period increase. As a given result the clock slows down.

If l_o be the length of the pendulum and corresponding time period be T₀ then     

   T_o =  2π√(l_o/g)       

If the pendulum be heated by Δt  (rise in temperature), the new time section T₁ is:

as α is very small ⇒  ΔT/T_o = 1/2αΔt              

The above relation gives the time lost per second by the pendulum clock. If Δt is the fall in temperature, same equation will provide the time gained by the clock per second as its oscillation will become faster due to reduction in its length.

Stress in Objects:

If cross-sectional area of wire is A and F be the tension developed in wire due to stretching. Thus the stress created in the wire due to this tension F is given as

                Stress = Force/Area=  F / A                                                                                ... (i)

Strain given in wire due to its elastic properties is Strain = ΔL/L = αΔT      ... (ii)

If young's modulus of the material of wire is Y, we require

                          Υ = Stress/strain       or         Υ = (F/A)/αΔT         or  F = ΥAαΔT                        ... (iii)

Equation - (iii) gives the expression for tension in the wire due to decrease in its temperature by ΔT. This result gives the tension in wire if initially wire is just taught between rods. If it already has some force in it then this expression will give the increment in tension in the wire.

Email based Physics assignment help - homework help at Expertsmind

Are you searching physics expert for help with Error in measurement due to Thermal expansion  questions?  Error in measurement due to Thermal expansion  topic is not easier to learn without external help?  We at www.expertsmind.com offer finest service of Physics assignment help and physics homework help. Live tutors are available for 24x7 hours helping students in their Error in measurement due to Thermal expansion  related problems. We provide step by step Error in measurement due to Thermal expansion  question's answers with 100% plagiarism free content. We prepare quality content and notes for Error in measurement due to Thermal expansion  topic under physics theory and study material. These are avail for subscribed users and they can get advantages anytime.

Why Expertsmind for assignment help

1. Higher degree holder and experienced experts network
2. Punctuality and responsibility of work
3. Quality solution with 100% plagiarism free answers
4. Time on Delivery
5. Privacy of information and details
6. Excellence in solving physics queries in excels and word format.
7. Best tutoring assistance 24x7 hours