System Dynamics
System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 3, Problem 3.1P
To determine

The speed and distance traveled of the mass as the functions of time. And the time taken by the mass to reach the platform and ground.

Expert Solution & Answer
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Answer to Problem 3.1P

The speed and height of the mass are as:

v(t)=gt2h(t)=12gt2

The time taken by the mass to reach the platform and ground is 1 second and 1.36 second respectively.

Explanation of Solution

Given:

m=2,a=g, s=h and u=0

The height of the platform from the ground is 10 feet.

The height of the point from where the mass falls is 30 feet.

Concept Used:

Following kinematics equations are employed for evaluating the speed and height as the functions of time:

v=u+ats=ut+12at2

The latter equation is used for calculating the time taken by the mass to reach the platform and ground.

Calculation:

Since,

v=u+at

Therefore, on keeping the values for u and a.

v(t)=gt2

Similarly, for the height, that is

Since,

s=ut+12at2

On substituting the values

h(t)=12gt2

The time taken to reach the platform:

h(t)=ut+12gt26.097=0t+129.8t2t2=12.1959.81=1t=1sec

Similarly, The time taken to reach the ground:

h(t)=ut+12gt29.146=0t+129.8t2t2=18.299.81=1.86t=1.36sec.

Conclusion:

The speed and height of the mass are as:

v(t)=gt2h(t)=12gt2

The time taken by the mass to reach the platform and ground is 1 second and 1.36 second respectively.

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Chapter 3 Solutions

System Dynamics

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