
Concept explainers
(a)
The position, velocity, and acceleration of the particle at
(a)

Answer to Problem 11.93P
The position (r), velocity (v), and acceleration of the particle (a) at
Explanation of Solution
Given information:
The given position
The value of
The value of
Calculation:
Determine the position vector of the particle using the relation.
Substitute 30 mm for
Determine the velocity value
Differentiate the Equation (1) with respect to t.
Determine the acceleration value (a).
Differentiate the Equation (2) with respect to t.
Determine the position of the particle at
Substitute 0 for t in Equation (1).
Determine the velocity of the particle at
Substitute 0 for t in Equation (2).
Determine the magnitude of velocity of the particle at
Substitute 30 mm/s for
Determine the direction of the velocity using the relation.
Substitute 31.42 mm/s for
Determine the acceleration of the particle at
Substitute 0 for t in Equation (3).
Determine the magnitude of acceleration of the particle at
Substitute
Determine the direction of the velocity using the relation.
Substitute
Therefore, the position (r), velocity (v), and acceleration of the particle (a) at
(b)
The position, velocity, and acceleration of the particle at
(b)

Answer to Problem 11.93P
The position (r), velocity (v), and acceleration of the particle (a) at
Explanation of Solution
Given information:
The given position vector of vibrating particle (r) is
The value of
The value of
Calculation:
Determine the position of the particle at
Substitute 1.5 s for t in Equation (1).
Determine the magnitude of position of the particle at
Substitute 18 mm for
Determine the direction of the position using the relation.
Substitute 1.87 mm for
Determine the velocity of the particle at
Substitute 0 for t in Equation (2).
Determine the magnitude of velocity of the particle at
Substitute 4.8 mm/s for
Determine the direction of the velocity using the relation.
Substitute 2.94 mm/s for
Determine the acceleration of the particle at
Substitute 1.5 s for t in Equation (3).
Determine the magnitude of acceleration of the particle at
Substitute
Determine the direction of the velocity using the relation.
Substitute
Therefore, the position (r), velocity (v), and acceleration of the particle (a) at
Want to see more full solutions like this?
Chapter 11 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- To save fuel during the heating season it is suggested that glass windows be covered at night with a 1.2 cm layer of polystyrene. Estimate the percent savings in energy and discuss the feasibility of this idea. Show the thermal circuit with and without the insulation panel. Consider a typical case of 0.2 cm thick window glass with inside and outside heat transfer coefficients of 6 and 32 W/m²-ºC. Lg←←Lp h T₁ T。 g kp insulation panelarrow_forwardA plate of thickness L and thermal conductivity k is exposed to a fluid at temperature T1 with a heat transfer coefficient h, on one side and T2 and h₂ on the other side. Determine the one-dimensional temperature distribution in the plate. Assume steady state and constant conductivity. L h h T%2 k Tx1 0xarrow_forwardDetermine the heater capacity needed to maintain the inside temperature of a laboratory chamber at 38°C when placed in a room at 21°C. The chamber is cubical with each side measuring 35 cm. The walls are 1.2 cm thick and are made of polystyrene. The inside and outside heat transfer coefficients are 5 and 22 W/m²-°C.arrow_forward
- (a) Refer to the above figure .What kind of controller is it ? (b) simplify the block diagramto derive the closed loop transfer function of the system. (C) What are the assumptions thatare needed to make to findthe controller gain ? What arethe value of Kp , Ti and Td ?arrow_forwardLonsider a regenerative gas turbine power plant with two stages of compression and two stages of expansion. The compressor pressure ratio of the compressor is 3. Air enters each stage of compressor at 290 K and esch stage of turbine at 1400 K. The regetierator has an effectiveness of 100%, Determine (a) The enthalpy at stage#2 in KJ/kg (b) The enthalpy at stage in KJ/kg" (c) The cathalpy at stager in KJ/kg* (d) The enthalpy at stage#10 in KJ/kg (c) The mass flow rate of air needed to develop a net power output of 50 MW *For all final answers please enter the integer part only, (ie 1234) and do not include the decimal part and the decimal point No rounding in your calculationarrow_forwardConsider a regenerative gas turbine power plant with two stages of compression and two stages of expansion. The compressor pressure ratio of the compressor is 3. Air enters each stage of compressor at 290 K and each stage of turbine at 1400 K. The regenerator has an effectiveness of 100%. Determine (a) The enthalpy at stage#2 in KJ/kg⭑ (b) The enthalpy at stage#6 in KJ/kg* (c) The enthalpy at stage#9 in KJ/kg (d) The enthalpy at stage#10 in KJ/kg (e)The mass flow rate of air needed to develop a net power output of 50 MW* *For all final answers please enter the integer part only, (ie 1234) and do not include the decimal part and the decimal point No rounding in your calculation. Compressor stage 1 Regenerator www HX ww 9 Combustor Reheat Intercooler ww Compressor stage 2 Turbine 1 combustor Turbine 2arrow_forward
- Design a proportional derivitivecontroller for a plant orsystemthat satisfies the following specifications : 1. is steady-state error is less than 2 % for a ramp input. 2.) Damping ratio (zeta) is greater than 0.7have determined the 3. Once youvalue of kp and kd, then plotthe response of the compensated(with controller) and uncompensated( without the controller, only the plantsystem using MATLAB.arrow_forwardExample 2 The particle has a mass of 0.5 kg and is confined to move along the smooth horizontal slot due to the rotation of the arm OA. Determine the force of the rod on the particle and the normal force of the slot on the particle when 0 = 30°. The rod is rotating with a constant angular velocity 2 rad/s. Assume the particle contacts only one side of the slot at any instant. B =2 rad/s 0.5 m 0.5(9.81)N r F 30° Narrow_forwardA gas turbine cycle has two stages of compression, with an intercooler between the stages. Air enters the first stage at 100 kPa, 300 K. The pressure efficiency of 82%. Air exits the intercooler at 330 K. Calculate the temperature at the exit of each compressor stage and the total specific work required.arrow_forward
- For problem 13, your answer should be the same as problem 12. Calculate the flow velocity and the heat transfer/area of the outer surfaces for both duct geometries to see the performance difference of the two designs.arrow_forwardOne end of a thin uniform rod of mass m and length 31 rests against a smooth vertical wall. The other end of the rod is attached by a string of length 1 to a fixed point O which is located a distance 21 from the wall. A horizontal force of magnitude F₁ is applied to the lower end of the rod as shown. Assuming the rod and the string remain in the same vertical plane perpendicular to the wall, find the angle 0 between the rod and the wall at the position of static equilibrium. Notes: This quiz is going to walk you through a sequence of steps to do this. It won't give you the answers, but it will hopefully get you to see how to approach problems like this so that you have a working reference/template in the future. This is actually a modified version of a problem from the textbook (6.3). Note that in that problem, is not actually given. It has been introduced for convenience as we move through solving the problem, and should not show up in the final answer. DO NOT DO PROBLEM 6.3. It is…arrow_forwardvarrow_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





