Week 10 – SS1 Third Term Physics Notes

WEEK 10
TOPIC : ENERGY STORED IN AN ELASTIC MATERIAL
CONTENT : Force in a bar
Energy stored in a wire
Energy stored per unit area
Force in a bar
When a bar is heated and then prevented from contracting as it cools, a considerable force is exerted at the end of the bar. Given a bar of a young modulus E, a cross sectional area A, a linear expansivity of magnitude α and a decrease in temperature of Ө,then
E = stress/strain = F/A/e/L
=F/A х L/e
E = FL/Ae
F = EAe/L ………………………….1
Recall, Linear expansivity α = change in length/original length х temperature change
α = e/L х Ө
e = αLӨ
F = EAαeLӨ/eL
F = EAαӨ ……………………………2

 
 
 
 EVALUATION
1. Show that F = EAαӨ when a bar is heated and then prevented from contracting as it cools
2. A steel rod of cross sectional area 2cm² is heated to 100˚C and then prevented from contracting when it cooled to 10˚C. find the force exerted on the steel = 12 х 10^-6/K and young modulus is 2 х10¹¹N/m²
ENERGY STORED IN A WIRE
The application of force on any wire provided the elasticity limit is not exceeded is proportional to the extension provided.
Consequently, the force in the wire has increase from zero to F
Average force = f + O/2 = f/2
Recall work done = Average force х distance
W = f/2 x e = ½ fe ………………………….3
Substitute eqn 1 into 3
W = EAe²/2L……………………………….4
ENERGY STORED PER UNIT VOLUME
W_V =
½ X Stress X Strain…………………..5
This implies that Wv = Ee²/2L²

 Substance which lengthens considerable and undergo plastic deforemation until they break are known as ductile substance. E.g lead, coper, wrought iron.
Substance which break after the elastic limit is reached are known as brittle substance e.g glass and high carbon steel. It should be noted that brass, bronze and many alloys appears to have no yield point. By this we mean that this material increase in length beyond the elastic limit as the lead is increased without the sudden appearance of a plastic stage.
EVALUATION
1. A uniform steel wire of length 4m and are of cross section 3×10^-6m² is extended by 1mm. Calculate the energy stored in the wire if the elastic limit is not exceeded (young modulus = 2×10¹¹n/m²)
2. A spiral spring is compressed by 0.02m. Calculate the energy stored in the spring if the force constant is 400n/m²
Reading Assignment : Read more on elasticity – New school physics (pg96-98)

WEEKEND ASSIGNMENT
1. A steel rod of cross sectional area 2cm² is heated to 100˚C and then prevented from contracting when it cooled to 10˚C. find the force exerted on the steel = 12 х 10^-6/K and young modulus is 2 х10¹¹N/m²
2. A uniform steel wire of length 4m and are of cross section 3×10^-6m² is extended by 1mm. Calculate the energy stored in the wire if the elastic limit is not exceeded (young modulus = 2×10¹¹n/m²)