Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
10th Edition
ISBN: 9781337699266
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
Question
Book Icon
Chapter 15, Problem 21P

(a)

To determine

The maximum speed of the bob.

(a)

Expert Solution
Check Mark

Answer to Problem 21P

The maximum speed of the bob is 0.820m/s.

Explanation of Solution

The formula to calculate amplitude is,

    A=Lθ

Here, L is the length of pendulum and θ is the displaced angle.

Substitute 1.00m for L and 15.0° for θ in above equation to find A.

    A=(1.00m)(15.0°(π180°))=0.262m

The formula to calculate angular frequency is,

    ω=gL

Here, g is the acceleration due to gravity.

Substitute 1.00m for L and 9.8m/s2 for g in above equation to find ω.

    ω=9.8m/s21.00m=3.13rad/s

The formula to calculate maximum speed is,

    vmax=Aω

Substitute 0.262m for A and 3.13rad/s for ω in above equation to find vmax.

    vmax=(0.262m)(3.13rad/s)=0.820m/s

Conclusion:

Therefore, the maximum speed of the bob is 0.820m/s.

(b)

To determine

The maximum acceleration of the bob.

(b)

Expert Solution
Check Mark

Answer to Problem 21P

The maximum acceleration of the bob is 2.57rad/s2.

Explanation of Solution

The formula to calculate maximum acceleration of the bob is,

    amax=Aω2

Substitute 0.262m for A and 3.13rad/s for ω in above equation to find amax.

    amax=(0.262 m)(3.13rad/s)2=2.57rad/s2

Conclusion:

Therefore, the maximum acceleration of the bob is 2.57rad/s2.

(c)

To determine

The maximum restoring force of the bob.

(c)

Expert Solution
Check Mark

Answer to Problem 21P

The maximum restoring force of the bob is 0.641N.

Explanation of Solution

The formula to calculate maximum restoring force of the bob is,

    F=mamax

Here, m is the mass of the pendulum.

Substitute Aω2 for amax in above equation.

    F=mAω2

Substitute 0.250kg for m, 0.262 m for A and 3.13rad/s for ω in above equation to find F.

    F=(0.250kg)(0.262m)(3.13rad/s)2=0.641N

Conclusion:

Therefore, the maximum restoring force of the bob is 0.641N.

(d)

To determine

The maximum speed, angular acceleration and restoring force of the bob using the model introduced earlier chapter.

(d)

Expert Solution
Check Mark

Answer to Problem 21P

The maximum speed of the bob is 0.817m/s, the angular acceleration of the bob is 2.54rad/s2 and the restoring force of the bob is 0.634N.

Explanation of Solution

Consider the figure given below.

Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term, Chapter 15, Problem 21P

In triangle ABC,

    cosθ=ACABAC=ABcosθ=Lcosθ

The height of the bob is,

    h=ADAC=LLcosθ=L(1cosθ)

The law of conservation of energy is,

    mgh=12mvmax2

Substitute L(1cosθ) for h in above expression.

    mgL(1cosθ)=12mvmax2gL(1cosθ)=12vmax2

Substitute 15.0° for θ, 1.00m for L and 9.8m/s2 for g in above equation to find vmax.

    (9.8m/s2)(1.00m)(1cos(15.0°))=12vmax2vmax2=2(0.333)m2/s2vmax=2(0.333)m2/s2=0.817m/s

The formula for the moment of inertia of the pendulum is,

    I=mL2

The equation for the conservation of energy is,

    Iα=mgLsinθ

Here, α is the angular acceleration.

Substitute mL2 for I in above expression and rearrange for α.

    mL2α=mgLsinθα=mgLsinθmL2=gsinθL

Substitute 9.8m/s2 for g, 1.00m for L and 15.0° for θ in above equation to find α.

    α=(9.8m/s2)sin(15.0°)1.00m=2.54rad/s2

The force is maximum, when the angle is maximum.

The restoring force is calculated as,

    F=mgsinθ

Substitute 15.0° for θ, 0.250kg for m and 9.8m/s2 for g in above equation to find F.

    F=(0.250kg)(9.8m/s2)sin(15.0°)=0.634N

Conclusion:

Therefore, the maximum speed of the bob is 0.817m/s, the angular acceleration of the bob is 2.54rad/s2 and the restoring force of the bob is 0.634N.

(e)

To determine

The answers of part (a), part (c) and part (d).

(e)

Expert Solution
Check Mark

Explanation of Solution

The restoring force is defined as the force or torque that tends to restore a system to equilibrium after displacement.

The answers are closest but not exactly the same. The angular amplitude of 15.0° is not small, so the simple harmonic oscillation is not accurate. The answers computed from conservation of the energy and from Newton’s second law are more accurate.

Conclusion:

Therefore, the answers are closest but not exactly the same.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
19:39 · C Chegg 1 69% ✓ The compound beam is fixed at Ę and supported by rollers at A and B. There are pins at C and D. Take F=1700 lb. (Figure 1) Figure 800 lb ||-5- F 600 lb بتا D E C BO 10 ft 5 ft 4 ft-—— 6 ft — 5 ft- Solved Part A The compound beam is fixed at E and... Hình ảnh có thể có bản quyền. Tìm hiểu thêm Problem A-12 % Chia sẻ kip 800 lb Truy cập ) D Lưu of C 600 lb |-sa+ 10ft 5ft 4ft6ft D E 5 ft- Trying Cheaa Những kết quả này có hữu ích không? There are pins at C and D To F-1200 Egue!) Chegg Solved The compound b... Có Không ☑ ||| Chegg 10 וח
No chatgpt pls will upvote
No chatgpt pls will upvote

Chapter 15 Solutions

Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term

Ch. 15 - Review. A particle moves along the x axis. It is...Ch. 15 - A ball dropped from a height of 4.00 m makes an...Ch. 15 - A particle moving along the x axis in simple...Ch. 15 - The initial position, velocity, and acceleration...Ch. 15 - You attach an object to the bottom end of a...Ch. 15 - To test the resiliency of its bumper during...Ch. 15 - A particle executes simple harmonic motion with an...Ch. 15 - The amplitude of a system moving in simple...Ch. 15 - A simple harmonic oscillator of amplitude A has a...Ch. 15 - Review. A 65.0-kg bungee jumper steps off a bridge...Ch. 15 - Review. A 0.250-kg block resting on a...Ch. 15 - While driving behind a car traveling at 3.00 m/s,...Ch. 15 - A simple pendulum makes 120 complete oscillations...Ch. 15 - A particle of mass m slides without friction...Ch. 15 - A physical pendulum in the form of a planar object...Ch. 15 - A physical pendulum in the form of a planar object...Ch. 15 - Prob. 21PCh. 15 - Consider the physical pendulum of Figure 15.16....Ch. 15 - A watch balance wheel (Fig. P15.25) has a period...Ch. 15 - Show that the time rate of change of mechanical...Ch. 15 - Show that Equation 15.32 is a solution of Equation...Ch. 15 - As you enter a fine restaurant, you realize that...Ch. 15 - A 2.00-kg object attached to a spring moves...Ch. 15 - Considering an undamped, forced oscillator (b =...Ch. 15 - Prob. 29PCh. 15 - Prob. 30PCh. 15 - An object of mass m moves in simple harmonic...Ch. 15 - Review. This problem extends the reasoning of...Ch. 15 - An object attached to a spring vibrates with...Ch. 15 - Review. A rock rests on a concrete sidewalk. An...Ch. 15 - A pendulum of length L and mass M has a spring of...Ch. 15 - To account for the walking speed of a bipedal or...Ch. 15 - Review. A particle of mass 4.00 kg is attached to...Ch. 15 - People who ride motorcycles and bicycles learn to...Ch. 15 - A ball of mass m is connected to two rubber bands...Ch. 15 - Consider the damped oscillator illustrated in...Ch. 15 - Review. A lobstermans buoy is a solid wooden...Ch. 15 - Your thumb squeaks on a plate you have just...Ch. 15 - Prob. 43APCh. 15 - Prob. 44APCh. 15 - A block of mass m is connected to two springs of...Ch. 15 - Review. A light balloon filled with helium of...Ch. 15 - A particle with a mass of 0.500 kg is attached to...Ch. 15 - A smaller disk of radius r and mass m is attached...Ch. 15 - Review. A system consists of a spring with force...Ch. 15 - Review. Why is the following situation impassible?...Ch. 15 - A light, cubical container of volume a3 is...
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Text book image
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
An Introduction to Physical Science
Physics
ISBN:9781305079137
Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher:Cengage Learning