### Problem Statement**4.** A uniform ladder of mass (m = 12.5 kg) and length (L) leans against a frictionless wall, see figure. If the angle θ = 60.0°, find the static friction force between the ladder and the floor when a 90.0-kg person stands half way up the ladder?\[\boxed{\text{Answer:} \ \ \underline{\hspace{1cm}} \ \text{N}}\]### Diagram ExplanationThe provided diagram illustrates a ladder leaning against a frictionless wall. The points of reference and measurements are as follows:- The ladder forms an angle θ = 60.0° with the horizontal ground.- \( L \) represents the length of the ladder.- The weight of the ladder is uniformly distributed, meaning the center of mass is at its midpoint.- A person of mass 90.0 kg stands halfway up the ladder.### Key Variables- \( m \) = mass of the ladder = 12.5 kg- \( θ \) = angle with the horizontal = 60.0°- \( M \) = mass of the person standing halfway up the ladder = 90.0 kg- \( g \) = acceleration due to gravity (assumed to be 9.8 m/s² for calculation purposes)This setup helps one to calculate the static friction force between the ladder and the floor, given other specified parameters.### Calculation Steps (to be provided to the students)1. Calculate the gravitational forces acting on the ladder and the person.2. Determine the torques about the point where the ladder touches the floor.3. Use equilibrium conditions (sum of forces and sum of torques equal to zero) to solve for the static friction force.

Given that:- Mass of ladder=12.5kg

4. A uniform ladder of mass (m = 12.5 kg) and length (L) leans against a frictionless wall, see figure. If the angle 0 = 60.0°, find the static friction force between the ladder and the floor when a 90.0-kg person stands half way up the ladder? p136 k131 N sp136 skp136 skp136 skp136 p136 skp136 skp136 skp136 skp136 skp136 13 skp136 skp136 skr L 136 skp136 skp13/ skp136 skp36 skp136 s zo skp136 skp136 skp136 skp136 skp 16 skp136 skp136 skp136 skp skp136 sk

4. A uniform ladder of mass (m = 12.5 kg) and length (L) leans against a frictionless wall, see figure. If the angle 0 = 60.0°, find the static friction force between the ladder and the floor when a 90.0-kg person stands half way up the ladder? p136 k131 N sp136 skp136 skp136 skp136 p136 skp136 skp136 skp136 skp136 skp136 13 skp136 skp136 skr L 136 skp136 skp13/ skp136 skp36 skp136 s zo skp136 skp136 skp136 skp136 skp 16 skp136 skp136 skp136 skp skp136 sk

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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Center of Gravity of a system

The centre of gravity is a property that is based on the geometry of a rigid body or any particle. It is described as an equilibrium point or a hypothetical location where the total weight of the body is concentrated.

Question

### Problem Statement

**4.** A uniform ladder of mass (m = 12.5 kg) and length (L) leans against a frictionless wall, see figure. If the angle θ = 60.0°, find the static friction force between the ladder and the floor when a 90.0-kg person stands half way up the ladder?

\[
\boxed{\text{Answer:} \ \ \underline{\hspace{1cm}} \ \text{N}}
\]

### Diagram Explanation

The provided diagram illustrates a ladder leaning against a frictionless wall. The points of reference and measurements are as follows:

- The ladder forms an angle θ = 60.0° with the horizontal ground.
- \( L \) represents the length of the ladder.
- The weight of the ladder is uniformly distributed, meaning the center of mass is at its midpoint.
- A person of mass 90.0 kg stands halfway up the ladder.

### Key Variables

- \( m \) = mass of the ladder = 12.5 kg
- \( θ \) = angle with the horizontal = 60.0°
- \( M \) = mass of the person standing halfway up the ladder = 90.0 kg
- \( g \) = acceleration due to gravity (assumed to be 9.8 m/s² for calculation purposes)

This setup helps one to calculate the static friction force between the ladder and the floor, given other specified parameters.

### Calculation Steps (to be provided to the students)

1. Calculate the gravitational forces acting on the ladder and the person.
2. Determine the torques about the point where the ladder touches the floor.
3. Use equilibrium conditions (sum of forces and sum of torques equal to zero) to solve for the static friction force.

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