Thermodynamics

Thermodynamics States About Energy Conversion Thermodynamics is the branch of science that embodies the principles of energy transformation in macroscopic systems. The general restrictions which experience has shown to apply to all such transformations are known as the laws of thermodynamics. These laws are primitive; they cannot be derived from anything more basic. The first law of thermodynamics states that energy is conserved; that, although it can be altered in form and transferred from one place to another, the total quantity remains constant. Thus, the first law of thermodynamics depends on the concept of energy; but, conversely, energy is an essential thermodynamic function because it allows the first law to be formulated. This coupling is characteristic of the primitive concepts of thermodynamics. The words system and surroundings are similarly coupled. A system is taken to be any object, any quantity of matter, any region, and so on, selected for study and set apart (men

Velocity Problem Solving

1.      The velocity of a particle is given by v = 20t2 – 100t + 50, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 6 seconds of motion and evaluate the velocity when a is zero.

Answer: v = -75 m/s.

2.      The displacement of a particle is given by s  = 2t2 -30t2 + 100t -50, where s is in meters and t is in seconds. Plot the displacement, velocity, and acceleration as function of time for the first 12 seconds of motion. Determine the time at which the velocity is zero.

3.      The displacement of a particle is given by s = (-2 + 3t) e-0.5t, where s is in meters and t is in seconds. Plot the displacement, velocity, and acceleration versus time for the first 20 seconds of motion. Determine the time at which the acceleration is zero.

Answer:      v = (4 – 1.5 t) e-0.5t

                        a = (-3.5 + 0.75t) e-0.5t, t = 4.67 s

4.      The velocity of a particle that moves along the s axis is given by v = 2 + 5t3/2, where t is in seconds and v is in meters per second. Evaluate the displacement s, velocity v, and acceleration a when t = 4s. the particle is at the origin s = 0 when t = 0.

5.      the acceleration of a particle is given by a = 4t – 30, where a is in meters per second squared and t is in seconds. Determine the velocity and displacement as functions of time. The initial displacement at t = 0 is s0 = -5 m, and the initial velocity is v0 = 3 m/s.

Answer:      v = 3 – 30t + 2t2

                        s =  -5 + 3t – 15t2 + 2/3 t3

6.      Calculate the constant acceleration a in g’s which the catapult of an aircraft carrier must provide to produce a launch velocity of 290 km/h in a distance of 100 m. Assume that the carrier is at anchor.

7.      In the final stages of a moon landing, the lunar module descends under retrothrust of its descend engine to which h = 5 m of the lunar surface where it has a downward velocity of 2 m/s. If the descent engine is cut off abruptly at this point, compute the impact velocity of the landing gear with the moon. Lunar gravity is ½ of the earth gravity.

Answer: v = 4.51 m/s

8.      A car comes to a complete stop from an initial speed of 80 km/h in a distance of 30 m. with the same constant acceleration, what would be the stopping distance s from an initial speed of 110 km/h?

9.      A projectile is fired vertically with an initial velocity of 200 m/s. Calculate the maximum altitude h reached by the projectile and the time t after firing for it to return to the ground. Neglect air resistance and take the gravitational acceleration to be constant at 9.81 m/s2.

Answer: h = 2040 m, t = 40.8 s

10.  The graph shows the displacement time history for the rectilinear motion of a particle during an S second interval. Determine the average velocity vav during the interval and to within reasonable limits of accuracy, find the instantaneous velocity v when t = 4 s.

11.  During an 8-second interval the velocity of a particle moving in a straight line varies with the time as shown. Within reasonable limits of accuracy, determine the amount Da by which the acceleration at t = 4 s exceed the average acceleration during the interval. What is the displacement Ds during the interval?

Answer: Da = 0.50 m/s2, Ds = 64 m.

12.  Experimental data for the motion of a particle along a straight line yield measured values of the velocity v for various position coordinates s. A smooth curve is drawn through the points as shown in the graph. Determine the acceleration of the particle when s = 20 m.