Particle Motion Analysis: Absolute, Dependent, and Relative - Prof. Cahucom, Cheat Sheet of Engineering

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Kinematics Part 3

Mechanics of Rigid Bodies

Absolute-Dependent Motion Analysis of Two Particles

There are some motions where two objects or particles depend on each other for

their movement. These are usually found on two objects connected by a rope or

wrapped around pulleys.

These are used to enhance the output of the pulley, so that any person can lift 20

• 50 times their weight.

Absolute-Dependent Motion Analysis of Two Particles

• Set up a fixed point of reference or datum line
• Establish position “s” coordinate along the direction of motion
• Using geometry or trigonometry, relate the position coordinate to the total length

of the cord

• Take the 1 st

derivative and second derivative of the generated position-

coordinate equation to get the velocity and acceleration equation which will

relate the motion of the particles.

Absolute-Dependent Motion Analysis of Two Particles We have a figure as an example for Analysis. Total Length = Sa + Lcd + Sb Then getting the derivatives in terms of time; This is also called the

“Time Derivative”.

It is assumed that the Total length and the Lcd are assumed to be constant therefore 0 = Va + Vb Therefore: Va = - Vb With this relationship we can say that when Block A goes down then Block B goes up and vice versa.

Absolute-Dependent Motion Analysis of Two Particles Another example: Ans: 2Vb = - Va

Absolute-Dependent Motion Analysis of Two Particles Example: Determine the speed of Block A if Block B goes up by 6ft/s Ans: 18 ft/s

Absolute-Dependent Motion Analysis of Two Particles Example: Block B is pulled downward at 4ft/s and the speed is decreasing at 2𝑓𝑡/𝑠 2 . (a) Determine the velocity of block A at that instant. Ans: 1ft/s (upward) (a) Determine the acceleration of block A at that instant. Ans: 𝟎. 𝟓 𝒇𝒕/𝒔 𝟐

Relative Motion of Particle Using Translating Axes As Einstein said that there is an infinite frame of reference in which where the theory of relativity comes in where it states that in one second there are multiple frames of reference and they can diverge and create whole new universes. It is the same when we are interacting with movements of people. The most common example of this one is when we have a two persons. Let us have Person A and Person B.

Relative Motion of Particle Using Translating Axes A Train travels 60mph due east and car travels at 45mph N 45 E as shown in the figure. Find the magnitude and angle of the velocity of the train relative to the automobile Ans: 𝑽 𝒃/𝒂 = 42.503 mph 𝜽 = 48.433 deg

Relative Motion of Particle Using Translating Axes At the instant shown in the figure, cars A and B are traveling with speeds of 18 m/s and 12 m/s, respectively. Also at this instant, A has a decrease in speed of 2 m/s2, and B has an increase in speed of 3 m/s2. Determine the velocity and acceleration of B with respect to A. Ans: V b/a = 9.689 m/s A b/a = 5.324 m/s^

Relative Motion of Particle Using Translating Axes At the instant shown, the car at A is travelling at 10 m/s around the curve while increasing its speed at 5𝑚/𝑠 2

. The car at B is travelling at 18.5 m/s along the straightaway and increasing its speed at 2𝑚/𝑠 2 . (a) Determine the relative velocity of A with respect to B at this instant. Ans: 13.44 m/s (b) Determine the relative acceleration of A with respect to B at this instant. Ans:𝟒. 𝟑𝟐 𝒎/𝒔 𝟐

References

Engineering Mechanics Dynamics - SI Version Pytel

Hibbler Dynamics 12

th

Edition