Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A uniform plank of length 2.00 m and mass 30.0 kg is supported by three ropes as indicated by the blue vectors in Figure P12.25. Find the tension in each rope when a 700-N person is $d = 0.500 m$ from the left end.

The second rope has a tension of =672.1N

The third rope has a tension of =382.78N

Anticlockwise torque is considered good, whereas clockwise torque is considered negative.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Conceptualize:

Consider this: For any item to be in equilibrium, the net forces operating on it must be zero, as well as the net torque acting on it.

Step 2: Categorize:

Because the plank must be balanced,

The sum of upward and downward forces equals the sum of downward forces.

$i.e. Σ F_{up} = Σ F_{dimn}$

The torques around a point should add up to zero.

$\begin{array}{l} i.e. Σ τ = 0 \end{array}$

Step 3: Analyze:

The net vertical force is (from the free body diagram)

$\begin{array}{l} T_{2} + T_{1} \sin 40^{°} = M g + w \\ T_{2} + T_{1} \sin 40^{°} = (30 kg) (9.8 m / s^{2}) + 700 N \\ T_{2} + T_{1} \sin 40^{°} = 994 N \end{array}$

The horizontal force is net.

$- T_{3} = T_{1} \cos 40^{°}$

In a counterclockwise route, take torque around the location where the man stood.

$\begin{array}{l} - T_{2} d - Mg (\frac{L}{2} - d) + T_{1} \sin 40^{°} (L - d) = 0 \\ - T_{2} (0.5 m) - 147 N + T_{1} \sin 40^{°} (2 m - 0.5 m) = 0 \\ T_{2} = 3 T_{1} \sin 40^{°} - 294 \end{array}$

Step 4: Determining the tension:

Using the equations above,

$\begin{array}{l} 3 T_{1} \sin 40^{°} - 294 + T_{1} \sin 40^{°} = 994 N \\ T_{1} \sin 40^{°} = 322 N \\ T_{1} = 500.94 N \\ T_{1} = 501 N \end{array}$

The second rope has a tension of

$\begin{array}{l} T_{2} = 3 T_{1} \sin 40^{°} - 294 \\ = 3 (501) \sin 40^{°} - 294 \\ = 672.1 N \end{array}$

The third rope has a tension of

$\begin{array}{l} T_{3} = - T_{1} \cos 40^{°} \\ = - (501 N) \cos 40^{°} \\ = 383.78 N \end{array}$

Step 5: Conclusion:

Anticlockwise torque is considered good, whereas clockwise torque is considered negative.

Find Study Materials for

Create Study Materials

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

A uniform plank of length 2.00 m and mass 30.0 kg is supported by three ropes as indicated by the blue vectors in Figure P12.25. Find the tension in each rope when a 700-N person is $d = 0.500 m$ from the left end.

Step by Step Solution

Step 1: Conceptualize:

Step 2: Categorize:

Step 3: Analyze:

Step 4: Determining the tension:

Step 5: Conclusion:

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

A uniform plank of length 2.00 m and mass 30.0 kg is supported by three ropes as indicated by the blue vectors in Figure P12.25. Find the tension in each rope when a 700-N person is d=0.500m from the left end.

Step by Step Solution

Step 1: Conceptualize:

Step 2: Categorize:

Step 3: Analyze:

Step 4: Determining the tension:

Step 5: Conclusion:

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

A uniform plank of length 2.00 m and mass 30.0 kg is supported by three ropes as indicated by the blue vectors in Figure P12.25. Find the tension in each rope when a 700-N person is $d = 0.500 m$ from the left end.