**Problem 3: Ladder Against a Frictionless Wall**Consider a 3-meter-long uniform ladder of mass \(m = 10 \, \text{kg}\) that leans against a frictionless wall. The ladder is resting on the floor, where it experiences a coefficient of static friction, \(\mu_s = 0.4\). The angle that the ladder makes with the horizontal is \(\theta\).**A. Minimum Angle \(\theta\) Without Slipping:**What is the minimum angle, \(\theta\), greater than zero, that the ladder can make with the horizontal without slipping?**B. Frictional Force at \(\theta = 60^\circ\):**If the ladder is placed at an angle \(\theta = 60^\circ\), what is the magnitude and direction of the frictional force on the ladder?**C. Maximum Height for a 70 kg Man:**With the ladder still at a \(60^\circ\) angle, how high off the ground can a 70 kg man climb without the ladder slipping?**D. Tension in the Rope:**Suppose the man wants to climb to the top of the ladder while it remains at the \(60^\circ\) angle. He attaches a massless rope to the middle of the ladder and extends it horizontally to the wall where he attaches it. What will the tension in the rope be when he reaches the top of the ladder?**Diagram Explanation:**The illustration shows a ladder leaning against a vertical wall, with the angle \(\theta\) marked between the ladder and the horizontal ground.

Given: length of ladder l = 3 m mass of ladder m =10kg friction coefficient μ=0.4A: angle that ladder makes with Horizontal and not slip: in equilibrium N2=μN1 ... (1)andW=N1 ....(2) now taking moment about lower end of ladder; we get N2 *lsinθ-W*l2cosθ = 0μmgl sinθ-mgl2cosθ = 0tanθ = 12μθ=tan-112μ = tan-112*0.4θ=51.3°

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3. A 3m long uniform ladder of mass m = 10 kg leans up against a frictionless wall as shown. The ladder resting on the floor experiences a coefficient of friction, µs = 0.4. The angle the ladder makes with the horizontal is 0. А. What is the minimum angle, 0, (non-zero!) the ladder can make with the horizontal and not slip? В. If you now place the ladder at an angle 0 = 60°, what is the magnitude and direction of the frictional force on the ladder? С. 70kg man get without the ladder slipping? With the ladder at that same 60° angle, how high off the ground could a

3. A 3m long uniform ladder of mass m = 10 kg leans up against a frictionless wall as shown. The ladder resting on the floor experiences a coefficient of friction, µs = 0.4. The angle the ladder makes with the horizontal is 0. А. What is the minimum angle, 0, (non-zero!) the ladder can make with the horizontal and not slip? В. If you now place the ladder at an angle 0 = 60°, what is the magnitude and direction of the frictional force on the ladder? С. 70kg man get without the ladder slipping? With the ladder at that same 60° angle, how high off the ground could a

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

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

**Problem 3: Ladder Against a Frictionless Wall**

Consider a 3-meter-long uniform ladder of mass \(m = 10 \, \text{kg}\) that leans against a frictionless wall. The ladder is resting on the floor, where it experiences a coefficient of static friction, \(\mu_s = 0.4\). The angle that the ladder makes with the horizontal is \(\theta\).

**A. Minimum Angle \(\theta\) Without Slipping:**

What is the minimum angle, \(\theta\), greater than zero, that the ladder can make with the horizontal without slipping?

**B. Frictional Force at \(\theta = 60^\circ\):**

If the ladder is placed at an angle \(\theta = 60^\circ\), what is the magnitude and direction of the frictional force on the ladder?

**C. Maximum Height for a 70 kg Man:**

With the ladder still at a \(60^\circ\) angle, how high off the ground can a 70 kg man climb without the ladder slipping?

**D. Tension in the Rope:**

Suppose the man wants to climb to the top of the ladder while it remains at the \(60^\circ\) angle. He attaches a massless rope to the middle of the ladder and extends it horizontally to the wall where he attaches it. What will the tension in the rope be when he reaches the top of the ladder?

**Diagram Explanation:**

The illustration shows a ladder leaning against a vertical wall, with the angle \(\theta\) marked between the ladder and the horizontal ground.

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