VECTOR MECH. FOR EGR: STATS & DYNAM (LL
12th Edition
ISBN: 9781260663778
Author: BEER
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 12.1, Problem 12.26P
A constant force P is applied to a piston and rod of total mass m to make them move in a cylinder filled with oil. As the piston moves, the oil is forced through orifices in the piston and exerts on the piston a force of magnitude kv in a direction opposite to the motion of the piston. Knowing that the piston starts from rest at t = 0 and x = 0, show that the equation relating x, v, and t, where x is the distance traveled by the piston and v is the speed of the piston, is linear in each of these variables.
Fig. P12.26
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Q2.
Show that the distance from the top of the cylinder to the piston surface
in a conventional engine is given by:
R²
x=r(1-cos)+
-(1-cos 20)
4L
where is the crankshaft angle, R is the length between the main
bearing and the big end bearing and L is the distance between the
centres of the connecting rod.
Comment upon the accuracy of the equation stated in part (a).
Discuss how the piston motion can be employed to determine the slider
crank piston force.
A body Diagram of
A nonconducting container filled with 25 kg of water at 20°C is fitted with a stirrer,which is made to turn by gravity acting on a weight of mass 35 kg. The weight fallsslowly through a distance of 5 m in driving the stirrer. Assuming that all work doneon the weight is transferred to the water and that the local acceleration of gravity is9.8 m·s−2, determine:(a) The amount of work done on the water.(b) The internal energy change of the water.(c) The final temperature of the water, for which CP = 4.18 kJ·kg−1·°C−1.(d) The amount of heat that must be removed from the water to return it to its initialtemperature.(e) The total energy change of the universe because of (1) the process of loweringthe weight, (2) the process of cooling the water back to its initial temperature, and(3) both processes together.
Develop the mathematical model of the system below, knowing that f is an action force on the mass M2, Z2 and Z1 are the respective displacements of the masses from the equilibrium position, and between the two masses there is an oil film with a coefficient of friction viscous given by b. The answer must contain the differential equation.
Chapter 12 Solutions
VECTOR MECH. FOR EGR: STATS & DYNAM (LL
Ch. 12.1 - A 1000-lb boulder B is resting on a 200-lb...Ch. 12.1 - Marble A is placed in a hollow tube, and the tube...Ch. 12.1 - The two systems shown start from rest. On the...Ch. 12.1 - Blocks A and B are released from rest in the...Ch. 12.1 - People sit on a Ferris wheel at points A, B, C,...Ch. 12.1 - Crate A is gently placed with zero initial...Ch. 12.1 - Two blocks weighing WA and WB are at rest on a...Ch. 12.1 - Objects A, B, and C have masses mA, mB, and mC,...Ch. 12.1 - Prob. 12.4FBPCh. 12.1 - Blocks A and B have masses mA and mB,...
Ch. 12.1 - A pilot of mass m flies a jet in a half-vertical...Ch. 12.1 - Wires AC and BC are attached to a sphere that...Ch. 12.1 - A collar of mass m is attached to a spring and...Ch. 12.1 - Prob. 12.9FBPCh. 12.1 - At the instant shown, the length of the boom AB is...Ch. 12.1 - Disk A rotates in a horizontal plane about a...Ch. 12.1 - Pin B has a mass m and slides along the slot in...Ch. 12.1 - The acceleration due to gravity on Mars is 3.75...Ch. 12.1 - The value of g at any latitude may be obtained...Ch. 12.1 - A Global Positioning System (GPS) satellite is in...Ch. 12.1 - Prob. 12.4PCh. 12.1 - A loading car is at rest on a track forming an...Ch. 12.1 - A 0.5-oz model rocket is launched vertically from...Ch. 12.1 - Determine the maximum theoretical speed that may...Ch. 12.1 - A tugboat pulls a small barge through a harbor....Ch. 12.1 - Prob. 12.9PCh. 12.1 - A 4-kg package is released from rest at point A...Ch. 12.1 - The coefficients of friction between the load and...Ch. 12.1 - A light train made up of two cars is traveling at...Ch. 12.1 - The two blocks shown are originally at rest....Ch. 12.1 - The two blocks shown are originally at rest....Ch. 12.1 - Prob. 12.15PCh. 12.1 - Prob. 12.16PCh. 12.1 - A 5000-lb truck is being used to lift a 1000-lb...Ch. 12.1 - Block A has a mass of 40 kg, and block B has a...Ch. 12.1 - Block A has a mass of 40 kg, and block B has a...Ch. 12.1 - The flat-bed trailer carries two 1500-kg beams...Ch. 12.1 - Prob. 12.21PCh. 12.1 - To unload a bound stack of plywood from a truck,...Ch. 12.1 - To transport a series of bundles of shingles A to...Ch. 12.1 - An airplane has a mass of 25 Mg and its engines...Ch. 12.1 - Determine the maximum theoretical speed that a...Ch. 12.1 - A constant force P is applied to a piston and rod...Ch. 12.1 - A spring AB of constant k is attached to a support...Ch. 12.1 - Block A has a mass of 10 kg, and blocks B and C...Ch. 12.1 - Prob. 12.29PCh. 12.1 - Prob. 12.30PCh. 12.1 - A 10-lb block B rests as shown on a 20-lb bracket...Ch. 12.1 - Knowing that k = 0.30, determine the acceleration...Ch. 12.1 - Knowing that k = 0.30, determine the acceleration...Ch. 12.1 - The 30-lb block B is supported by the 55-lb block...Ch. 12.1 - Block B of mass 10 kg rests as shown on the upper...Ch. 12.1 - Knowing that the swings of an amusement park ride...Ch. 12.1 - During a hammer throwers practice swings, the...Ch. 12.1 - Human centrifuges are often used to simulate...Ch. 12.1 - A single wire ACB passes through a ring at C...Ch. 12.1 - Prob. 12.41PCh. 12.1 - The 0.5-kg flyballs of a centrifugal governor...Ch. 12.1 - As part of an outdoor display, a 5-kg model C of...Ch. 12.1 - Prob. 12.44PCh. 12.1 - During a high-speed chase, a 2400-lb sports car...Ch. 12.1 - An airline pilot climbs to a new flight level...Ch. 12.1 - The roller-coaster track shown is contained in a...Ch. 12.1 - A spherical-cap governor is fixed to a vertical...Ch. 12.1 - A series of small packages, each with a mass of...Ch. 12.1 - A 55-kg pilot flies a jet trainer in a half...Ch. 12.1 - Prob. 12.51PCh. 12.1 - A curve in a speed track has a radius of 1000 ft...Ch. 12.1 - Tilting trains, such as the Acela Express that...Ch. 12.1 - Prob. 12.54PCh. 12.1 - A 3-kg block is at rest relative to a parabolic...Ch. 12.1 - Prob. 12.56PCh. 12.1 - A turntable A is built into a stage for use in a...Ch. 12.1 - The carnival ride from Prob. 12.51 is modified so...Ch. 12.1 - Prob. 12.59PCh. 12.1 - A small 8-oz collar D can slide on portion AB of a...Ch. 12.1 - A small block B fits inside a slot cut in arm OA...Ch. 12.1 - The parallel-link mechanism ABCD is used to...Ch. 12.1 - Prob. 12.63PCh. 12.1 - A small 250-g collar C can slide on a semicircular...Ch. 12.1 - A small 250-g collar C can slide on a semicircular...Ch. 12.1 - An advanced spatial disorientation trainer is...Ch. 12.1 - The 3-kg collar B slides on the frictionless arm...Ch. 12.1 - A 0.5-kg block B slides without friction inside a...Ch. 12.1 - Pin B weighs 4 oz and is free to slide in a...Ch. 12.1 - The parasailing system shown uses a winch to let...Ch. 12.1 - A 700-kg horse A lifts a 50-kg hay bale B as...Ch. 12.2 - A particle of mass m is projected from point A...Ch. 12.2 - A particle of mass m is projected from point A...Ch. 12.2 - Determine the mass of the earth knowing that the...Ch. 12.2 - Show that the radius r of the moons orbit can be...Ch. 12.2 - Communication satellites are placed in a...Ch. 12.2 - Prob. 12.81PCh. 12.2 - The orbit of the planet Venus is nearly circular...Ch. 12.2 - A satellite is placed into a circular orbit about...Ch. 12.2 - The periodic time (see Prob. 12.83) of an earth...Ch. 12.2 - A 500-kg spacecraft first is placed into a...Ch. 12.2 - A space vehicle is in a circular orbit of 2200-km...Ch. 12.2 - Prob. 12.87PCh. 12.2 - Prob. 12.88PCh. 12.2 - Prob. 12.89PCh. 12.2 - A 1-kg collar can slide on a horizontal rod that...Ch. 12.2 - Two 2.6-lb collars A and B can slide without...Ch. 12.2 - A small ball swings in a horizontal circle at the...Ch. 12.3 - A uniform crate C with mass mC is being...Ch. 12.3 - A uniform crate C with mass m is being transported...Ch. 12.3 - Prob. 12.94PCh. 12.3 - Prob. 12.95PCh. 12.3 - A particle with a mass m describes the path...Ch. 12.3 - A particle of mass m describes the parabola y =...Ch. 12.3 - Prob. 12.98PCh. 12.3 - Prob. 12.99PCh. 12.3 - Prob. 12.100PCh. 12.3 - Prob. 12.101PCh. 12.3 - A satellite describes an elliptic orbit about a...Ch. 12.3 - Prob. 12.103PCh. 12.3 - Prob. 12.104PCh. 12.3 - Prob. 12.105PCh. 12.3 - Halleys comet travels in an elongated elliptic...Ch. 12.3 - Prob. 12.109PCh. 12.3 - A space probe is to be placed in a circular orbit...Ch. 12.3 - The Clementine spacecraft described an elliptic...Ch. 12.3 - A space probe is describing a circular orbit of...Ch. 12.3 - Prob. 12.115PCh. 12.3 - A space shuttle is describing a circular orbit at...Ch. 12.3 - Prob. 12.117PCh. 12.3 - A satellite describes an elliptic orbit about a...Ch. 12.3 - Prob. 12.119PCh. 12.3 - Prob. 12.120PCh. 12.3 - Show that the angular momentum per unit mass h of...Ch. 12 - In the braking test of a sports car, its velocity...Ch. 12 - A bucket is attached to a rope of length L = 1.2 m...Ch. 12 - A 500-lb crate B is suspended from a cable...Ch. 12 - The parasailing system shown uses a winch to pull...Ch. 12 - A robot arm moves in the vertical plane so that...Ch. 12 - Telemetry technology is used to quantify kinematic...Ch. 12 - The radius of the orbit of a moon of a given...Ch. 12 - Prob. 12.131RPCh. 12 - Prob. 12.132RPCh. 12 - Disk A rotates in a horizontal plane about a...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- I hope that you kan write the answer by using a paper ,but not acomputerarrow_forward-- Q3. The boundary of a system is fixed or movable and has mass but has no thickness and no volume. fixed or movable with zero thickness, no mass, and no volume. fixed and has mass, thickness, and no volume. movable and has thickness, no volume, and no mass.arrow_forwardA 10-kg mass is attached to a spring having a spring constant of 140 N/m. The mass is started in motion from the equilibrium position with an initial velocity of 1 m/sec in the upward direc-tion and with an applied external force given by ƒ(t) = 5 sin t (in newtons). The mass is in a viscous medium with a coefficient of resistance equal to 90 N-sec/m. Formulate an initial value prob-lem that models the given system; solve the model and interpret the results.arrow_forward
- A 36.0-g projectile is launched by the expansion of hot gas in an arrangement shown in figure a. The cross-sectional area of the launch tube is 1.0 cm2, and the length that the projectile travels down the tube after starting from rest is 32 cm. As the gas expands, the pressure varies as shown in figure b. The values for the initial pressure and volume are Pi = 12 ✕ 105 Pa and Vi = 8.0 cm3 while the final values are Pf = 1.1 ✕ 105 Pa and Vf = 40.0 cm3. Friction between the projectile and the launch tube is negligible. (a) If the projectile is launched into a vacuum, what is the speed of the projectile as it leaves the launch tube? In m/s. (b) If instead the projectile is launched into air at a pressure of 1.1 ✕ 105 Pa, what fraction of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down the tube? w(spent)/w(env)=arrow_forwardQ4. The 9-kg ball is connected to a spring with spring constant k = 100 N/m and unstretched length of 0.8 m. Initially the spring is compressed and has length 0.5 m. Then under the constant applied force F = 340 N (in the direction shown in the image) acting on the ball, the spring is stretched to a new length 1.4 m. Determine the work done by the spring to the ball during this process. Please pay attention: the numbers may change since they are randomized. Negative sign must be included if the work done is negative. Your answer must include 1 place after the decimal point, and proper SI unit. F |15° 40°arrow_forwardA 39.0-g projectile is launched by the expansion of hot gas in an arrangement shown in figure a. The cross-sectional area of the launch tube is 1.0 cm2, and the length that the projectile travels down the tube after starting from rest is 32 cm. As the gas expands, the pressure varies as shown in figure b. The values for the initial pressure and volume are P, = 15 x 105 Pa and V, = 8.0 cm3 while the final values are P; = 1.5 x 105 Pa and V; = 40.0 cm³. Friction between the projectile and the launch tube is negligible. P P; 32 cm Gas Pf - 8 cm - V V; (a) If the projectile is launched into a vacuum, what is the speed of the projectile as it leaves the launch tube? m/s (b) If instead the projectile is launched into air at a pressure of 1.5 x 105 Pa, what fraction of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down the tube? spent = envarrow_forward
- An object of mass M is attached to a string. The length of the string is r and has no mass. The objects moves in a vertical circle counterclockwise as shown. When the ball is at point F, the string is horizontal. Point E is at the bottom of the circle and point D is at the top of the circle. Air resistance is negligible. Express all algebraic answers in terms of the given quantities and fundamental constants. Suppose that the string breaks at the instant the ball is at point F. Describe the motion of the ball immediately after the string breaks.arrow_forwardB8arrow_forwardAn object of mass m=2kg is part of a system and it is subject only to conservative forces and constrained to move along a horizontal line such that the potential energy of the system is given by the function U(x)=(−10)/(x2+1), where x is in meters and U is in joules. The graph of the function is shown in the image. (e) Another object is subject only to a different set of conservative forces and constrained to move along a horizontal line such that its potential energy is given by a different function U(x). Explain how the new function U(x) could be used to locate a point of stable equilibrium.arrow_forward
- es Channel AB is fixed in space, and its centerline lies in the xy plane. The plane containing edges AC and AD of the channel is parallel to the xz plane. The surfaces of the channel are frictionless and the sphere E has 1.8 kg mass. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 4.552 N D 30° T 4.552 N A 30° E X 20° B 30° Determine the force supported by cord EF, and the reactions RC and Rp between the sphere and sides C and D, respectively, of the channel. (Round the final answers to four decimal places.) The force supported by cord EF is 11.5253 N. The reactions RC and RD between the sphere and sides Cand D, respectively, of the channel are as follows: RC= RD=arrow_forwardQ4. The 3-kg ball is connected to a spring with spring constant k = 100 N/m and unstretched length of 0.8 m. Initially the spring is compressed and has length 0.6 m. Then under the constant applied force F = 300 N (in the direction shown in the image) acting on the ball, the spring is stretched to a new length 1.3 m. Determine the work done by the spring to the ball during this process. Please pay attention: the numbers may change since they are randomized. Negative sign must be included if the work done is negative. Your answer must include 1 place after the decimal point, and proper SI unit. WM Your Answer: Answer 40° units F 15°arrow_forward2. The 200 gram toy car will be compressed against the spring and released to send it around the loop which has diameter of 60 cm. Determine minimum required spring compression to maintain contact with the track for the entire loop. First use kinetics to determine minimum velocity at the top of the track, and then apply conservation of energy. Spring constant is 400 N/m. -------arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- 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
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
First Law of Thermodynamics, Basic Introduction - Internal Energy, Heat and Work - Chemistry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=NyOYW07-L5g;License: Standard youtube license