A single self-energizing long shoe drum shoe uses a molded lining of friction coefficient 0.45 and maximum allowable pressure of 150 psi as the friction material. If the angle subtended by the shoe is 120°, with θ1 = 0, find the face width required for the shoe to stop a torque of 3800 lb. in. The drum diameter is 12-in.

A = 10.83 in² ,  w = 3.29 in

Explanation:

For this exercise we must use the rotational equilibrium condition

        Σ τ = 0

in this case they give us the external torque τ = 3800 lb in.

        τ - τ’= 0

        τ = τ'

where τ‘ is the torque exerted by the brake shoe that is given by the friction force

      τ’ = fr r sin θ

indicates that θ= 120º and the radius is half the diameter of the drum

      r = 6 in

the friction force is given by the expression

       fr = μ N

substitute

        τ = μ N r sin θ         (1)

to find the normal let's use Newton's second law on the perpendicular pressure axis

        Σ F = 0

        N - f = 0

        N = f

The applied force can be found using the definition of pressure

         P = f / A

where A is the area of the footing

         f = P A

let's substitute

          N = P A

let's substitute in 1

         τ = μ P A r sin θ

let's calculate

          A = 3800 / (0.45 150 6 sin 120)

          A = 10.83 in²

to find the size of the shoe we must assume a specific shape, suppose the shoe is square

          A =w²

          w = √A

          w = 3.29 in

specific latent heat of fusion, lf, of a substance is defined as the amount of heat required to change a unit mass of the substance from solid to liquid state, without any change in the temperature.

explanation:

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.