A stepladder of negligible weight is constructed as shown in the figure below, with \( AC = BC = \ell = 3.20\, \text{m} \). A painter of mass \( m = 65.0\, \text{kg} \) stands on the ladder \( d = 3.00\, \text{m} \) from the bottom. *[Illustration of a stepladder with points labeled: A, B, C, D, E; a person of mass \( m \) stands on the ladder at point C. The ladder legs make a vertex at point C and are joined by a horizontal bar at D and E.]* Assuming the floor is frictionless, find the following. (*Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately.*) (a) the tension in the horizontal bar \( DE \) connecting the two halves of the ladder \[ \boxed{\phantom{N}} \] N (b) the normal forces at \( A \) and \( B \) at \( A \) \[ \boxed{\phantom{N}} \] N at \( B \) \[ \boxed{\phantom{N}} \] N (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 \[ \boxed{\phantom{N}} \] N upward component \[ \boxed{\phantom{N}} \] N

A stepladder of negligible weight is constructed as shown in the figure below, with \( AC = BC = \ell = 3.20\, \text{m} \). A painter of mass \( m = 65.0\, \text{kg} \) stands on the ladder \( d = 3.00\, \text{m} \) from the bottom. [Illustration of a stepladder with points labeled: A, B, C, D, E; a person of mass \( m \) stands on the ladder at point C. The ladder legs make a vertex at point C and are joined by a horizontal bar at D and E.] Assuming the floor is frictionless, find the following. (Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately.) (a) the tension in the horizontal bar \( DE \) connecting the two halves of the ladder \[ \boxed{\phantom{N}} \] N (b) the normal forces at \( A \) and \( B \) at \( A \) \[ \boxed{\phantom{N}} \] N at \( B \) \[ \boxed{\phantom{N}} \] N (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 \[ \boxed{\phantom{N}} \] N upward component \[ \boxed{\phantom{N}} \] N

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Rotational Equilibrium And Rotational Dynamics

In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.

Equilibrium of Forces

The tension created on one body during push or pull is known as force.

Question

A stepladder of negligible weight is constructed as shown in the figure below, with \( AC = BC = \ell = 3.20\, \text{m} \). A painter of mass \( m = 65.0\, \text{kg} \) stands on the ladder \( d = 3.00\, \text{m} \) from the bottom.

*[Illustration of a stepladder with points labeled: A, B, C, D, E; a person of mass \( m \) stands on the ladder at point C. The ladder legs make a vertex at point C and are joined by a horizontal bar at D and E.]*

Assuming the floor is frictionless, find the following. (*Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately.*)

(a) the tension in the horizontal bar \( DE \) connecting the two halves of the ladder
\[ \boxed{\phantom{N}} \] N

(b) the normal forces at \( A \) and \( B \)
at \( A \) \[ \boxed{\phantom{N}} \] N
at \( B \) \[ \boxed{\phantom{N}} \] N

(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 \[ \boxed{\phantom{N}} \] N
upward component \[ \boxed{\phantom{N}} \] N

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