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

In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is h. The mug slides off the counter and strikes the floor at distance d from the base of the counter.
(a) With what velocity did the mug leave the counter?
(b) What was the direction of the mug's velocity just before it hit the floor?

The velocity of the mug when it leaves the counter is $d \cdot \sqrt{\frac{g}{2 \cdot h}}$ .
The direction of the mug’s velocity just before it hit the floor is $\frac{2 \cdot h}{d}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Data

The height of the counter is h.
The mug slides off the counter and strikes the floor at distance d from the base of the counter.

Step 2: Definition of velocity

The rate of change of an object's location with regard to a frame of reference is its velocity, which is a function of time. A statement of an object's speed and direction of motion is referred to as velocity.

Step3: Find the velocity of the mug when it leaves the counter.

(a)

The initial angle is $θ_{0} = 0$ and the initial height is $y_{0} = h$ .

Therefore,

$x = v_{0} \cdot t y = h - \frac{1}{2} \cdot g \cdot t^{2}$

The maximum distance is $x_{\max} = d$ and the final height is $y = 0$ :

$d = v_{0} \cdot t_{\max} 0 = h - \frac{1}{2} \cdot g \cdot t_{\max^{2}}$

Rewrite the equations above:

$v_{0} = \frac{d}{t_{\max}} t_{\max} = \sqrt{\frac{2 \cdot h}{g}}$

Substitute the second equation into first and calculate the result:

$v_{0} = \frac{d}{\sqrt{\frac{2 \cdot h}{g}}} = d \cdot \sqrt{\frac{g}{2 \cdot h}}$

Step 4: Find the direction of the mug’s velocity just before it hit the floor.

(b)

The $v_{x}$ component of motion is constant in horizontal projectile motion, but the $v_{y}$ component rises in magnitude:

width="94" style="max-width: none; vertical-align: -41px;" $v_{x} = v_{0} v_{y} = \sqrt{2 \cdot g \cdot y}$

The mug's velocity components at the instant of collision with the ground are:

$v_{x} = v_{0} = d \cdot \sqrt{\frac{g}{2 \cdot h}} v_{y} = \sqrt{2 \cdot g \cdot h}$

The velocity angle $θ$ at the instant of contact may be computed as follows:

Find Study Materials for

Create Study Materials

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given Data

Step 2: Definition of velocity

Step3: Find the velocity of the mug when it leaves the counter.

Step 4: Find the direction of the mug’s velocity just before it hit the floor.

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

Step by Step Solution

Step 1: Given Data

Step 2: Definition of velocity

Step3: Find the velocity of the mug when it leaves the counter.

Step 4: Find the direction of the mug’s velocity just before it hit the floor.

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

Famous Physicists

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