Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

Answers without the blur.

Just sign up for free and you're in.

Short Answer

To get up on the roof, a person (mass \(70.0\;{\rm{kg}}\)) places a \(6.00\;{\rm{m}}\)aluminum ladder (mass \(10.0\;{\rm{kg}}\)) against the house on a concrete pad with the base of the ladder \(2.00\;{\rm{m}}\)from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the ladder is \(2\;{\rm{m}}\)from the bottom. The person is standing \(3\;{\rm{m}}\) from the bottom. What are the magnitudes of the forces on the ladder at the top and bottom?

The magnitude of the force at the top is \(133\;{\rm{N}}\) and at the bottom is \(784\;{\rm{N}}\).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Data

Given:

The mass of the person is \({m_1} = 70.0\;{\rm{kg}}\).

The mass of the ladder is \({m_2} = 10.0\;{\rm{kg}}\).

The length of the ladder is \(l = 6\;{\rm{m}}\).

The distance between the ladder and the concrete pad is \(2.0\;{\rm{m}}\).

The distance between the bottom of the ladder and the person is \(3\;{\rm{m}}\).

Step 2: Calculation of the force

The diagram of the ladder can be shown as below,

Applying the condition of equilibrium under forces we get,

\(\begin{align}n - {m_1}g - mg &= 0\\n = {m_1}g + mg\\n &= 70.0 \times 9.8 + 10.0 \times 9.8\\n &= 784\;{\rm{N}}\end{align}\)

Applying the condition of equilibrium under torque, we get,

\(\begin{align}mg{l_1}\cos \theta - mg{l_2}\cos \theta + f\sqrt {{l^2} - {d^2}} - nl\cos \theta &= 0\\f &= \frac{{nl\cos \theta - mg{l_1}\cos \theta + mg{l_2}\cos \theta }}{{\sqrt {{l^2} - {d^2}} }}\\f &= \frac{{784 \times 2 - 10 \times 9.8 \times 4 \times \frac{2}{6} - 70 \times 9.8 \times 3 \times \frac{2}{6}}}{{\sqrt {{6^2} - {2^2}} }}\\ &= 133\;{\rm{N}}\end{align}\)

Find Study Materials for

Create Study Materials

Select your language

College Physics (Urone)

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given Data

Step 2: Calculation of the force

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

College Physics (Urone)

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given Data

Step 2: Calculation of the force

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics