LIST UNITS - Physics 1 Rotational A stepladder of negligible weight is construct
ID: 1520044 • Letter: L
Question
LIST UNITS - Physics 1 Rotational
A stepladder of negligible weight is constructed as shown in Figure P12.57 where x = 2.20 m. A painter of mass 65.0 kg stands on the ladder 3.00 m from the bottom.
Assuming the floor is frictionless, find the following. (Suggestion: Treat the ladder as a single object, but also each half of the ladder separately.)
(a) the tension in the horizontal bar connecting the two halves of the ladder
(b) the normal forces at A and B
(at A)
(at B)
(c) the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half
(rightward component)
(upward component)
Explanation / Answer
Since there is no friction at the floor, the reactions at A and B are vertical. Furthermore, since the ladder is of "negligible weight," the vertical reactions sum to the painters weight:
Fa + Fb = 65.0kg * 9.8m/s² = 637 N
Summing the moments about B, we get
M = 0 = 65.0kg * 9.8m/s² * (5/8)*2.20m - Fa*2.20m
Fa = 398.125 N (b)
so Fb = 725N - Fa = 238.8 N (b)
Cut the ladder vertically in half and consider the right side.
Sum the moments about the midpoint of the bar -- any forces in the bar create no moment about that point.
M = 0 = Fb*1.1m - Fch*2.00m*sin
where Fch is the horizontal force at C (any vertical component has no moment action)
and = arccos(1.1/2.00) = 56.6º. So
0 = 272N * 1.1m - Fch*2.00m*sin56.6º
Fch = 157.3 N part of (c) -- leftward component of right half on left = rightward component of left half on right (by Newton III)
Since there is no horizontal force at the floor, the tension in the rod must be
Frod = 157.3 N (a)
I'm not sure how to get the vertical force at C except to assume that the bar carries no shear (vertical force). Then analyzing the vertical forces (still on the right side of the ladder) gives
Fcy = -Fb = 218.8 N vertical part of (c), upward
Hope this helps!
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.