Unit 04 REVIEW OF PARTICLE DYNAMICS in Engineering Mechanics

Unit 04 of Engineering Mechanics covers the topic “Review of Particle Dynamics,” which involves the study of particle motion and forces acting on them. This section introduces the fundamental concepts of particle dynamics, including as Newton’s equations of motion, energy and momentum conservation, and the idea of work and energy.

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Important Questions For Engineering Mechanics:
*Unit-01     *Unit-02    
*Unit-03    *Unit-04 
*Unit-05    *Short-Q/Ans
*Question-Paper with solution 21-22 

Q1. Define the following terms: 

• i. Displacement. 
• ii. Velocity. 
• iii. Acceleration.  

Ans. Following are the parameters used for defining the rectilinear motion:

i. Displacement : It is described as the change in the particle’s location over a predetermined period of time. The particle’s beginning and ending positions are the only factors that affect the displacement, which is a vector quantity. 

ii. Velocity : The rate at which a particle’s displacement changes over time is referred to as its velocity. 

iii. Acceleration : The rate at which a particle’s velocity changes over time is referred to as acceleration.

Q2. Acceleration of a ship moving along a straight curve varies directly as the square of its speed. If the speed drops from 3 m/sec to 1.5 m/sec in one minute, find the dist ance moved in this period.

Ans. 

1. Acceleration is given by,

2. On integrating both sides,

3. From eq. (4.3.1.), we get

4.On integrating both sides, 

Q3. A stone is dropped into a well and is heard to strike the water after 4 seconds. Find the depth of the well if the velocity of sound is 350 m/sec. 

Ans. Given: t =4 sec, velocity of sound 350 m/sec 

To Find: Depth of the well.

3. Considering downward motion of stone and using the relation  

4. The time it takes for a sound to travel from the water’s surface to the well’s top, given the motion of the sound, is given by, 

5. From eq. (4.6.1), we have 

6. Solution of the quadratic equation given as,

Q4. Define the following terms: 

• i. Angular displacement. 
• ii. Angular velocity. 
• iii. Angular acceleration. 

Ans. Following are the parameters required for defining the curvilinear motion of the body: 

i. Angular Displacement: The angle through which a body moves from its starting condition is used to measure the displacement of a body in rotation, which is known as the angular displacement.

ii. Angular Velocity: Angular velocity is the rate at which a body’s angular displacement changes with respect to time. If the body traverses angular distance dθ over a time interval dt, then the average angular velocity ω is given by,

iii. Angular Acceleration: Angular acceleration is the rate at which the angular velocity of a body changes in relation to time. 

Q5. Write a short note on power.  

Ans. 1. The rate at which work is completed is referred to as power. A machine’s capacity to perform work is typically stated as its rated power. 

2. If W is the total work done in a time interval t, then average power is given by, 

3. The instantaneous power, i.e., power at a particular instant of time is given by,

4. The force can be assumed to be constant over this infinitesimally small time interval dt. Hence, we can write the above expression as: 

5. In SI system of units, the unit of power is Joule per second (J/sec), also called watt (W). 

Q6. Acceleration of particle is defined by a = 21-21s², where a is acceleration in m/sec² and s is in meters. The particle starts with rest at s = 0, Determine (a) velocity when s = 1.5 m, (b) the position where velocity is again zero, (c) the position where the velocity is maximum. 

Ans. Given:  a = 21-21s² , u = 0

To Find: i. Velocity when s = 1.5 m. 

ii. The position where velocity is again zero.

iii The position where the velocity is maximum.

1. Velocity when s = 1.5 m,

2. Position where velocity is again zero, 

Here C is integration constant. 

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