Concept explainers
(a)
Angular momentum per unit mass and energy per unit mass.
Answer to Problem 13.118P
We got
Angular momentum per unit mass
Energy per unit mass
Explanation of Solution
Given information:
Radius
Speed
Planet mass
Concept used:
Following formulae will be used.
Calculation:
Angular momentum per unit mass,
Energy per unit mass,
Conclusion:
We got
Angular momentum per unit mass
Energy per unit mass
(b)
Formula derivation.
Answer to Problem 13.118P
We got required formula as
Explanation of Solution
Given information:
Radius
Speed
Planet mass
Concept used:
Following formulae will be used.
Calculation:
Angular momentum per unit mass,
Energy per unit mass,
By solving of quadratic equation and rearranging,
Conclusion:
We got required formula as
(c)
The eccentricity of the trajectory.
Answer to Problem 13.118P
We got eccentricity as
Explanation of Solution
Given information:
Radius
Speed
Planet mass
Concept used:
Following formulae will be used.
Calculation:
We know when,
Also,
By comparing,
Conclusion:
We got eccentricity as
(d)
To show:
the trajectory shape depending on the energy type.
Answer to Problem 13.118P
Conditions have been shown below for different shape of trajectory at different eccentricity.
Explanation of Solution
Given information:
Radius
Speed
Planet mass
Concept used:
Following formulae will be used.
Calculation:
We know when,
For circular orbit
Conclusion:
Conditions have been shown above for different shape of trajectory at different eccentricity.
Want to see more full solutions like this?
Chapter 13 Solutions
Vector Mechanics For Engineers
- The 1st law of thermodynamics is ΔU = Q –W. Use this statement of the 1st law to show (mathematically) its equivalent statement: “Total energy of the universe is constant”. Here, the universe can be defined as: system + surroundings (everything but the system –everything outside the system). (Hint: this can be shown by two ways-you may either treat system and surroundings as two systems next to each other, or you may treat system + surroundings (universe) as one system.)arrow_forwardPDF 2222222.pdf X A fluid system undergoes a non-flow frictionless process following the pressure-volume relation as p = 10/V + 3 where p is in bar and V is in m3. During the process the volume changes from 0.3 m3 to 0.1 m3 and the system rejects 90 kJ of heat. Determine :(i) Change in internal 大 energy :(ii) Change in enthalpy 1 Add Filearrow_forwardProblem 1. An object with a mass of 200 kg is attached to a rope wound around a pulley which is attached to a horizontal rotating shaft. The radius of the pulley is 25 cm. Power is transmitted through the shaft, causing the object to be lifted at a constant velocity of 2 m/s. Assume a gravitational acceleration g = 9.81 m/s?. Pulley R = 25 cm a) Determine the kinetic energy of the object, in Joules. V = 2 m/s b) Calculate the power transmitted through the shaft, in Watts. c) Calculate the rotational speed of the shaft, in RPM. m = 200 kg %3Darrow_forward
- An engineer wants to design a pendulum which consists of a uniform slender rod and a disk with a mass of m, (kg) and m2 (kg), respectively as shown in Figure 3.2. If the angular velocity w of the pendulum is 18.2 rad/s when it is released at rest from t= 0 s to t =4 s, suggest the mass of m, kg and m, kg of the slender rod and disk that he should use in his design. Noted that this pendulum will be subjected to a torque at M = (10t²)N. m and a constant force of F= 40 N (which is always normal to the rod) and the motion of the pendulum is in the horizontal plane. F = 40 N 0.84 m 1 m 0.35 m G M = (10t²)N. m kg = 0.5 m Figure 3.2 A pendulumarrow_forwardAn object of mass 5 units travels rightward along the parabola y = x2 %3D with a constant speed of 10 units/s. What force does the object experience at the point (O,0)? Select one: a. 200j b. 1000 j c. 100 i d. 500 i e. 200 i + 200 jarrow_forward1. A block with a mass of 1kg is initially at rest while held in contact with a compressed spring. The spring has a stiffness constant of 1000 N/m and is initially compressed by a length of 0.3 meters. Once the mass leaves the spring it will slide 1 meter across the surface of a table where u, = 0.2 is the coefficient of kinetic friction. There are no frictional losses while the mass is in contact with the spring, and there are no losses due to air resistance. Only losses are due to the interaction with the table during the 1-meter slide. The surface of the table is 2 meters above the floor. What is the speed of the mass just before it hits the floor? mass leaves spring 1 meterarrow_forward
- Nhand,A 75 N ma = 3 kg %D VA = 8 m/s Block Block Block Block B A Hx = 0.4 %3D 2 m Ax Note: Diagram is not drawn to scale A hand pushes block A (m,= 3 kg) with a constant force Nand. A= 75 N for a distance Ax 2 m along a (mostly) frictionless table such that it speeds up from rest and is traveling at a speed of 8 m/s after it slides over a rough section of the table (H = 0.4). Block A then collides with a more massive block B (mg = 6 kg) that is initially at rest. Find the speed of block A after it has been released by the hand and just before the rough section of the table. A) 10 m/s B) 20 m/s C) 30 m/s D) 40 m/s E) 50 m/s O A O B O D O Earrow_forwardIn the 1970s cartoon The Super Friends, the Wonder Twins helped Superman and others fight crime. One of the Wonder Twins was Zan, who was able to take on the form of H2O in its various phases (ice, liquid water, water vapor). After taking a physics class, he decides to conduct a little experiment by turning into an ice igloo in the park on a hot day. (a) If his total mass as an igloo is 64.50 kg and he starts with a temperature of −13.50°C, how much heat must flow into him to completely melt his body? J(b) He continues absorbing energy up to the point where he would start to vaporize (100.0°C). How much more heat is required to raise his temperature to the vaporization point? J(c) How much more heat is required to turn him into water vapor at 100.0°C? J(d) If we model the water vapor molecules making up his body as having only six degrees of freedom, what is the average kinetic energy of one of the water vapor molecules that make up Zan? (Consider the case when Zan is water vapor at…arrow_forwardQ2/ During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier women’s match, reaching a speed of 58 m/s. What is the average force exerted on the 0.057 kg tennis ball by Venus Williams’ racquet, assuming that the ball’s speed just after impact is 58 m/s, that the initial horizontal component of the velocity before impact is negligible, and that the ball remained in contact with the racquet for 5 ms?arrow_forward
- 196B/s.110. The coefficint of friction is 0.43 A 3.0 kilogram block is sliding down a 25° incline at a constant speed. 1 0.44 0.38 0.33 0.47 The moment reaction at B is 800N 0.16m + 203 Nm - 175 Nm + 185 Nm 17 Ma 60 deg 0.20m O if A ۱۰:۰۱ ص Marrow_forwardMorning glories close their petals at night and reopen each morning. The motion of one petal can be represented as mass attached to a simple spring. At 12am the petals are most condensed. At 6am and 6pm they are halfway opened. At 12pm they are fully expanded. The stiffness of the petal (its K equivalent) is 1.5x10^-11N/m and each petal has a Mass of 0.002kg A. What is the period of a petal's motion? B. For a petal 6cm longer when fully expanded compared to when it is most condensed, what is its total mechanical energy at 3pm? (Assume t=0 at 12:00am) C. Suppose somebody forgot to add fertilizer and the amplitudes for the oscillation of the petals are decreasing over time. The motion of the petals are now represented by equation: ma + cv + kx=0. The damping factor c=5x10^-8. Give an equation that represents the petal's displacement as a function of time.arrow_forward1. An object of mass 150 kg is dropped from a height of 400 m with no initial velocity. The body encounters an air resistance proportional to its velocity. If the limiting velocity is known to be 100 m/s, find an expression for the velocity v (in m/s) of the body at any time t (in seconds). Use g = 9.8 m/s². v = 100( 1– e -0.047t B) v = 100[ 1- e -0.085: -0.0231 C) v = 100| 1-e D) v = 100 -0.0981 -earrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY