Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
Question
Book Icon
Chapter 2, Problem 2.1P

(a)

To determine

Check whether the given function is integrable.

(a)

Expert Solution
Check Mark

Answer to Problem 2.1P

The given function is not integrable.

Explanation of Solution

The basic equation is

    F=mix¨i

The given equation is

    F(xi,t)=f(xi)g(t)=mix¨i

This is not integrable.

Conclusion:

The given function is not integrable.

(b)

To determine

Check whether the given function is integrable.

(b)

Expert Solution
Check Mark

Answer to Problem 2.1P

The given function is integrable.

Explanation of Solution

The given function is

    F(x˙i,t)=f(x˙i)g(t)=mix¨if(x˙i)g(t)=midx˙idtdx˙if(x˙i)=g(t)mi

This is integrable.

Conclusion:

The given function is integrable.

(c)

To determine

Check whether the given function is integrable.

(c)

Expert Solution
Check Mark

Answer to Problem 2.1P

The given function is not integrable.

Explanation of Solution

The basic equation is

    F=mix¨i

The given equation is

    F(xi,x˙i)=f(xi)g(x˙i)=mix¨i

This is not integrable.

Conclusion:

The given function is not integrable.

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Chapter 2 Solutions

Classical Dynamics of Particles and Systems

Ch. 2 - A particle is projected vertically upward in a...Ch. 2 - A particle moves in a medium under the influence...Ch. 2 - A projectile is fired with initial speed 0 at an...Ch. 2 - A particle of mass m slides down an inclined...Ch. 2 - A particle is projected with an initial velocity 0...Ch. 2 - A strong softball player smacks the ball at a...Ch. 2 - Prob. 2.19PCh. 2 - A gun fires a projectile of mass 10 kg of the type...Ch. 2 - Prob. 2.21PCh. 2 - Prob. 2.22PCh. 2 - A skier weighing 90 kg starts from rest down a...Ch. 2 - A block of mass m = 1.62 kg slides down a...Ch. 2 - A child slides a block of mass 2 kg along a slick...Ch. 2 - A rope having a total mass of 0.4 kg and total...Ch. 2 - A superball of mass M and a marble of mass m are...Ch. 2 - An automobile driver traveling down an 8% grade...Ch. 2 - A student drops a water-filled balloon from the...Ch. 2 - Prob. 2.31PCh. 2 - Two blocks of unequal mass are connected by a...Ch. 2 - A particle is released from rest (y = 0) and falls...Ch. 2 - Perform the numerical calculations of Example 2.7...Ch. 2 - Prob. 2.36PCh. 2 - A particle of mass m has speed υ = α/x, where x is...Ch. 2 - The speed of a particle of mass m varies with the...Ch. 2 - A boat with initial speed υ0 is launched on a...Ch. 2 - A train moves along the tracks at a constant speed...Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Consider a particle moving in the region x > 0...Ch. 2 - Prob. 2.48PCh. 2 - Prob. 2.49PCh. 2 - According to special relativity, a particle of...Ch. 2 - Let us make the (unrealistic) assumption that a...Ch. 2 - A particle of mass m moving in one dimension has...Ch. 2 - A potato of mass 0.5 kg moves under Earth’s...Ch. 2 - Prob. 2.55P
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