Question

Required information Problem 16.048 - DEPENDENT MULTI-PART PROBLEM - ASSIGN ALL PARTS NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A uniform slender rod AB rests on a frictionless horizontal surface, and a force P of magnitude 0.25 lb is applied at A in a direction perpendicular to the rod. Assume that the rod weighs 2.2 lb. Problem 16.048.a - Acceleration A of slender rod on frictionless surface Determine the acceleration of Point A. (You must provide an answer before moving on to the next part.) The acceleration of Point A is 14.6 14.6 Correct ft/s2 →.

Answer 1

NOTE: The diagram is attached to this solution

Answer:

The acceleration of point A = 14.64 ft/s²

Step-by-step explanation:

By proper analysis of the diagram, acceleration of point A will be: (Check the free body diagram attached)

`a_(A) = \bar{a} + (\alpha L)/(2)`

Weight, W = mg

g = 32.2 ft/s²

m = W/g

`p = m \bar{a}\\p = w \bar{a} /g`

`\bar{a} = pg/w\\\bar{a} = 0.25g/2.2\\\bar{a} =3.66`

`(pL)/(2) = I \alpha`

but
`I = (wL^(2) )/(12g)`

`(pL)/(2) = (\alpha wL^(2) )/(12g)\\\alpha = (6 g p)/(wL)\\\alpha = (6*g*0.25)/(2.2L) \\\alpha = 21.96/L`

`a_(A) = 3.66 + ((21.96/L ) * L)/(2)\\a_(A) = 3.66 + 10.98\\a_(A) = 14. 64 ft/s^(2)`