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

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles

i think the answer is tomato juice? not entirely sure though