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

Ch. 3 - The motor in Figure P3.11 lifts the mass mL by...Ch. 3 - Instead of using the system shown in Figure 3.2.6a...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Derive the expression for the equivalent inertia...Ch. 3 - Prob. 3.18PCh. 3 - The geared system shown in Figure P3.19 represents...Ch. 3 - Prob. 3.20PCh. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - For the geared system shown in Figure P3.23,...Ch. 3 - For the geared system discussed in Problem 3.23,...Ch. 3 - The geared system shown in Figure P3.25 is similar...Ch. 3 - Consider the rack-and-pinion gear shown in Figure...Ch. 3 - The lead screw (also called a power screw or a...Ch. 3 - Prob. 3.29PCh. 3 - Derive the equation of motion of the block of mass...Ch. 3 - Assume the cylinder in Figure P3.31 rolls without...Ch. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - A slender rod 1.4 m long and of mass 20 kg is...Ch. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - The pendulum shown in Figure P3.38 consists of a...Ch. 3 - Prob. 3.39PCh. 3 - A single link of a robot arm is shown in Figure...Ch. 3 - 3.41 It is required to determine the maximum...Ch. 3 - Figure P3.42 illustrates a pendulum with a base...Ch. 3 - Figure P3.43 illustrates a pendulum with a base...Ch. 3 - 3.44 The overhead trolley shown in Figure P3.44 is...Ch. 3 - Prob. 3.45PCh. 3 - The “sky crane” shown on the text cover was a...
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