Concept explainers
A stepladder of negligible weight is constructed as shown in Figure P12.40, with AC = BC = ℓ = 4.00 m. A painter of mass m = 70.0 kg stands on the ladder d = 3.00 m from the bottom. Assuming the floor is frictionless, find (a) the tension in the horizontal bar DE connecting the two halves of the ladder, (b) the normal forces at A and B, and (c) the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half. Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately.
Figure P12.40 Problems 40 and 41.
(a)
The tension in the horizontal bar
Answer to Problem 12.56AP
The tension in the horizontal bar
Explanation of Solution
The length of the each ladder is
The following figure shows the force diagram of the ladder
Figure-(I)
Formula to calculate the angle made by the ladder with horizontal is,
Here,
Substitute
Formula to calculate the torque about the point
Here,
Substitute
Formula to calculate the net torque about the point
Here,
Substitute
Substitute
Conclusion:
Therefore, the tension in the horizontal bar
(b)
The normal force at
Answer to Problem 12.56AP
The normal force at
Explanation of Solution
Formula to calculate the net torque about the point
Here,
Substitute
Substitute
Conclusion:
Therefore, the normal force at
(c)
The components of the force acting on the hinge point
Answer to Problem 12.56AP
The horizontal component of the force at hinge point
Explanation of Solution
Formula to calculate the net horizontal forces acting on the right half of the ladder is,
Here,
Substitute
Formula to calculate the net vertical forces acting on the right half of the ladder is,
Here,
Substitute
Conclusion:
Therefore, the vertical component of the force acting on the hinge point in right half of the ladder is
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Chapter 12 Solutions
Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
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