Chapter 12: Q. 58 (page 333)

3.0-m-long ladder, as shown in Figure 12.35, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.40. What is the minimum angle the
ladder can make with the floor without slipping?

Short Answer

Expert verified

The minimum angle the ladder can make with the floor without slipping is 51.34^o

Step by step solution

Given information

3.0-m-long ladder, leans against a frictionless wall.

The coefficient of static friction between the ladder and the floor is 0.40.

Explanation

Lets first draw the diagram to understand the and solve the problem

First find the force due to friction is

f_s=f_smax=μ_sN_{2...................................................}(1)

For the ladder to be in equilibrium the net resultant horizontal and vertical forces must zero and Torque about origin should be zero

$\sum F_{x} = 0 N_{1} - f_{s_{\max}} = 0 f_{s_{\max}} = N_{1} \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots (2)$

And

$\sum F_{y} = 0 N_{2} - W = 0 N_{2} = W \dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)$

Equate Torque

$\sum τ_{O} = 0 N_{1} (3 m Sin θ) + W (1.5 m Cos θ) - N_{2} (3 m Cos θ) = 0$

Solve for angle we get

$θ = \tan^{- 1} (\frac{5}{4}) = 51.34 °$

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3.0-m-long ladder, as shown in Figure 12.35, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.40. What is the minimum angle the
ladder can make with the floor without slipping?

Short Answer

Step by step solution

Given information

Explanation

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3.0-m-long ladder, as shown in Figure 12.35, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.40. What is the minimum angle theladder can make with the floor without slipping?

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Quantum Physics

Conservation of Energy and Momentum

Space Physics

Linear Momentum

Engineering Physics

Magnetism

Study anywhere. Anytime. Across all devices.

3.0-m-long ladder, as shown in Figure 12.35, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.40. What is the minimum angle the
ladder can make with the floor without slipping?