#### Problem Statement**Determine the maximum angle a uniform ladder can make with a wall without slipping if its coefficients of static friction with the ground and the wall are 0.4 and 0.3, respectively (see Figure 4).**### ExplanationThis problem involves calculating the maximum angle at which a ladder can be positioned against a wall without slipping, based on the given coefficients of static friction. The static friction coefficients provided are essential for determining the point at which the ladder will begin to slip due to the forces acting on it.- **Coefficient of static friction with the ground (μ_ground):** 0.4- **Coefficient of static friction with the wall (μ_wall):** 0.3### Figure 4(Description of Figure 4, if necessary)Figure 4 would typically illustrate a ladder leaning against a wall, depicting the forces acting on the ladder, including the normal force, gravitational force, and frictional forces. This diagram helps visualize the angles and relationships between different forces that are vital in solving for the maximum allowable angle.### Steps for Solution1. **Identify Forces Acting on the Ladder** - Gravitational force (weight) acting downwards. - Normal force from the ground acting perpendicular to the ground. - Normal force from the wall acting perpendicular to the wall. - Frictional force at the base of the ladder counteracting slipping. - Frictional force at the top of the ladder counteracting slipping.2. **Equations of Equilibrium** - Sum of horizontal forces must equal zero. - Sum of vertical forces must equal zero. - Sum of moments about any point (typically the base of the ladder) must equal zero.3. **Calculate the Maximum Angle** - Derive the expressions involving these forces and solve for the maximum angle at which the ladder does not slip.### ConclusionBy following these steps and using the provided coefficients of static friction, you can determine the maximum angle at which the ladder can safely lean against the wall without the risk of slipping. **Fig 4: Understanding Frictional Forces in an Inclined Plane**The diagram represents an inclined plane with an angle \( \theta \). The plane's surface has two different coefficients of static friction (\( \mu_s \)) at different points:- \( \mu_s = 0.4 \): The coefficient of static friction at the base of the inclined plane.- \( \mu_s' = 0.3 \): The coefficient of static friction along the inclined face.These coefficients indicate the resistance to the initiation of sliding motion between the surfaces in contact. The frictional force is dependent on these coefficients and the normal force. The angle \( \theta \) represents the incline's angle with the horizontal surface.This figure illustrates how varying frictional forces can affect the behavior of objects on inclined planes, crucial for understanding mechanics in physics.

When a system is in equilibrium then there will be two simultaneous conditions to be satisfied.…

Answered: 4) Determine the maximum angle a…

4) Determine the maximum angle a uniform ladder can make with a wall without slipping if its coefficients of static friction with the ground and the wall are 0.4 and 0.3, respectively (see Figure 4).

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)...

See similar textbooks

Related questions

Q: 53° 5 m A uniform 8ON beam that is 5 m long is attached to a wall by a cable as shown in the figure.…

Q: 11. In the image below, the uniform ladder has a length of 5 m and sits with an angle of 30.0° with…

A: As per our guidelines, we are supposed to answer only first three subparts in case of multiple…

Q: 4. Two identical uniform beams weighing 260 N each are connected at the bottom end with a…

Q: a G 6 mm b

A: Radius R=6mmlocation of center of gravity G(x,y)=(0,0)

Q: a uniform thin pole has a weight of 50 N and a length of 26 m If it is placed against the rough wall…

A: We know that for the equilibrium of any system the resultant of all horizontal forces must be zero,…

Q: Physics 12 Equilibrium Problems 1. A 79kg person is standing at the edge of a 22kg diving board.…

A: Step 1:Step 2:

Q: In the figure, a uniform rod of mass m is hinged to a building at its lower end, while its upper end…

Q: One end of a uniform 2.0-m-long rod of weight o is supported by a cable at an angle of 0 = 37 with…

A: From the above figure, the equilibrium condition of force in the horizontal direction Tcosθ=N…

Q: A tow truck is pulling a car out of a ditch by means of a steel cable (Y = 2.0 x 1011 N/m2) that is…

Q: 10. One end of a 1.5 kg uniform stick that is 2.0 m long is placed against a vertical wall as shown.…

A: The objective of the question is to find the maximum value of the angle theta for the stick to…

Q: Compression member AB is used to hold up the 250 x 340-mm rectangular plate. If the compressive…

Q: A tow truck is pulling a car out of a ditch by means of a steel cable (Y = 2.0 x 1011 N/m²) that is…

A: The objective of the question is to find out how much the steel cable has stretched when the car…

Q: Homework (05 January 2021) 1. A ladder of 5 m long and weighing 260 N, is placed against a vertical…

A: Draw the Free Body Diagram of the ladder placed against a vertical wall and determine the given…

Q: 2. A uniform ladder 10.0 m long and weighing 50.0 N rests against a smooth vertical wal1. (a) If the…

Q: end of a uniform meterstick is placed against a vertical wall. The other end is held by a…

A: Net Torque and coefficient friction Torque is way of describing the force that is working to cause…

Q: A uniform ladder whose length is 4.5 m and whose weight is 490 N leans against a frictionless…

Q: A 20.0-m-long uniform beam weighing 700 N rests on walls A and B, as shown in the figure below. с…

Q: 4. A uniform ladder of mass (m) and length (L) leans against a frictionless wall, see figure. If the…

A: Static friction is noted to as the force-create in the middle of paired objects when single object…

Q: A lightweight diving board is supported by two pillars. One is at the end of the board and the other…

A: Given data: Distance between the pillars, d=3.80 m Mass of the person, m=75 kg Force, F=760 N

Q: 8-10. The uniform 20-lb ladder rests on the rough floor for which the coefficient of static friction…

A: To calculate the horizontal force required to move the ladder. Given:Weight of the ladder: W=20…

Q: Determine the magnitude P of the vertical force required to lift the wheelbarrow free of the ground…

A: Balance torque about point O would give us the value of P required to lift the cart from point B

Q: 3. A 130 kg uniform beam is attached to a vertical wall at one end and is supported by a cable at…

Q: 4. A uniform ladder of mass (m = 12.5 kg) and length (L) leans against a frictionless wall, see…

A: Given that:- Mass of ladder=12.5kg

Q: A uniform ladder of mass m and length , leans at an angle against a wall, see the figure (Figure 1)…

A: Percentage deviationD can be given as:D=true value of θmin-approximate value of θmintrue value of…

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

#### Problem Statement

**Determine the maximum angle a uniform ladder can make with a wall without slipping if its coefficients of static friction with the ground and the wall are 0.4 and 0.3, respectively (see Figure 4).**

### Explanation

This problem involves calculating the maximum angle at which a ladder can be positioned against a wall without slipping, based on the given coefficients of static friction. The static friction coefficients provided are essential for determining the point at which the ladder will begin to slip due to the forces acting on it.

- **Coefficient of static friction with the ground (μ_ground):** 0.4
- **Coefficient of static friction with the wall (μ_wall):** 0.3

### Figure 4

(Description of Figure 4, if necessary)

Figure 4 would typically illustrate a ladder leaning against a wall, depicting the forces acting on the ladder, including the normal force, gravitational force, and frictional forces. This diagram helps visualize the angles and relationships between different forces that are vital in solving for the maximum allowable angle.

### Steps for Solution

1. **Identify Forces Acting on the Ladder**
- Gravitational force (weight) acting downwards.
- Normal force from the ground acting perpendicular to the ground.
- Normal force from the wall acting perpendicular to the wall.
- Frictional force at the base of the ladder counteracting slipping.
- Frictional force at the top of the ladder counteracting slipping.

2. **Equations of Equilibrium**
- Sum of horizontal forces must equal zero.
- Sum of vertical forces must equal zero.
- Sum of moments about any point (typically the base of the ladder) must equal zero.

3. **Calculate the Maximum Angle**
- Derive the expressions involving these forces and solve for the maximum angle at which the ladder does not slip.

### Conclusion

By following these steps and using the provided coefficients of static friction, you can determine the maximum angle at which the ladder can safely lean against the wall without the risk of slipping.

**Fig 4: Understanding Frictional Forces in an Inclined Plane**

The diagram represents an inclined plane with an angle \( \theta \). The plane's surface has two different coefficients of static friction (\( \mu_s \)) at different points:

- \( \mu_s = 0.4 \): The coefficient of static friction at the base of the inclined plane.
- \( \mu_s' = 0.3 \): The coefficient of static friction along the inclined face.

These coefficients indicate the resistance to the initiation of sliding motion between the surfaces in contact. The frictional force is dependent on these coefficients and the normal force. The angle \( \theta \) represents the incline's angle with the horizontal surface.

This figure illustrates how varying frictional forces can affect the behavior of objects on inclined planes, crucial for understanding mechanics in physics.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Introduction

VIEW

Solution

VIEW

Step by step

Solved in 2 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

9
10. One end of a 1.5 kg uniform stick that is 2.0 m long is placed against a vertical wall as shown. A light cord making an angle 0 with the stick holds the other end. The coefficient of static friction between the end of the stick and the wall is 0.500. a) What is the maximum value the angle 0 can have if the stick is to remain in equilibrium? Ө b) When 0 = 15° a body of the same weight as the stick is suspended from the stick a distance x from the wall. What is the minimum value of x for which the stick will remain in equilibrium?
3. A uniform beam of mass 20 kg is suspended horizontally by a wall at one end and a cable that makes an angle of 0= 30° with the beam at the other end. The cable can sustain a maximum tension of 300 N before it breaks. a) What is the farthest distance from the wall (x) that a 10 kg mass can be suspended without the upper cable breaking? b) When x has this value what is the force exerted by the wall onto the beam? Wall 10 kg 10 m
5-
A uniform horizontal shelf of width L and mass m is held to a wall by a frictonless hinge and by a string at an angle of , measured from the shelf. The string is connected by the shelf at a distance of x from the wall. What is the tension in the string and what are the horizontal and vertical components of the hinge's force?
11. The diagram below shows a ladder that is 6.0 m long and has a mass of 20.0 kg. The ladder rests on a level floor and against a wall at an angle of 15° to the wall. The coefficient of static friction between the ladder and the floor is 0.232. A person with a mass of 60.0 kg begins to climb the ladder. The base of the ladder will begin to slide away from the wall when the person reaches which distance interval from the base of the ladder? A. 0 m–1.5 mB. 1.5 m–3.0 mC. 3.0 m–4.5 mD. 4.5 m–6.0 m
A cargo ship is loading using a boom crane, which is a 15 m long pole with a cable for lifting cargo which is suspended from the end of the pole. The boom is raised via a cable attached at a point that is 2/3 of the distance to the end of the pole. At one point the crane is lifting an 900 kg crate with the pole making a 30 degree angle with the horizontal, while the cable makes a 40 degree angle with the horizontal. Estimate the tension on the cable.
5) Consider a rigid steel beam of length L = 14.5 m and mass mb = 375 kg resting on two supports, one at each end. A worker of mass mw = 76 kg sits on the beam at a distance x from support A. Refer to the figure, though note that it is not drawn to scale. a) Enter an expression for the force support B must exert on the beam in order for it to remain at rest, in terms of defined quantities, x, and g. b) When the worker sits at a distance x = 7.5 m from support A, calculate the force, in newtons, that support B must exert on the beam in order for it to remain at rest. Use g with three significant figures. c) The force exerted on the beam by support A is measured and found to be FA = 2390 N. At what distance x, in meters, from support A is the worker sitting now?
Ladder Slip? A 3.0-m-long ladder leans against a frictionless wall at an angle of 60°. What is the minimum value of the coefficient of static friction with the ground, that prevents the ladder from slipping? \L=3.0 m dz Center of mass • net = 0 about this point. 60° Gravity acts at di the center of mass. ***** Static friction prevents slipping.
A television set rests on four rubber pads, each one having a height of 1.0 cm and a radius of 0.60 cm. If a 200-N horizontal force is applied to the television set, what is the shear stress on each of the pads assuming they do not slide on the floor? O A) 177 N/m2 B) 4.42x105 N/m² O C) 1.77x106 N/m2 D) 44.2 N/m2 acer Pauso Prisc Scrik F12 F11 F10 Home Ins SREATH End UGG Del KEFFECT WAVE# P Enter
1. A 1260 N uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. A W = 1940 N crate hangs from the far end of the beam. a) Calculate the magnitude of the horizontal component of the force that the wall exerts on the left end of the beam if the angle between the cable and horizontal is 0 = 36°. N Вeam 30.0° W
A horizontal 4.0 m long 5.0 N uniform bar at one end is attached to a wall by a frictionless hinge; and at the middle of the bar there is a vertical cable pulling down 7.0 N, and at the middle of the bar there is also a cable that is at 45 ° to the horizontal pulling up as shown. ii) What is the magnitude of the horizontal component of the force on the bar due to the hinge?