Question

The brass strip AB has been attached to a fixed support at A and rests on a rough support at B. Knowing that the coefficient of friction Is 0.60 between the strip and the support at B, determine the decrease In temperature for which slipping will Impend. Brass strip: E = 105 CPa alpha = 20 times 10-6 pc

Answer 1

Answer:

Decrease in temperature = 4.6714°C

Step-by-step explanation:

We know that the formula fro deflection is:

δ = PL/AE + LαΔT

As deflection is equal to zero in this case, the formula becomes

ΔT = -P/αAE   -------------- equation (1)

Now,

we see that only vertical force acting is weight

W = mg = 100*9.81

W = 981N = ∑$F_{y}$                                  where 1N = 1kgm/s²

Now,

for horizontal forces

As we know that, Sum of all horizontal forces = 0

P - μN = 0

P - μW = 0

P = μW

P = 0.6 * 981

P = 588.8N or 589N

Now we need to calculate the area

area = width * thickness = 20 * 3

area = 60 mm²

Now by substituting all these values in equation 1, wee get

ΔT = -P/αAE = - 588.6/(20*10⁻⁶*60*10⁻⁶*105*10⁹)

ΔT = - 4.6714°C (negative sign indicates decrease)