Concept explainers
5.137 and 5.138 Locate the centroid of the plane area shown.
Fig. P5.137
The centroid of the plane shown.
Answer to Problem 5.137RP
The centroid of the plane area
Explanation of Solution
Refer Figure 1.
The plane is considered as two separate sections as in figure 1. Section 1 is a perpendicular triangle and section 2 is a rectangle.
Write an expression to calculate the area of section 1.
Here,
Write an expression to calculate the area of section 2.
Here,
Write an expression to calculate the area of the plane.
Here,
Write an expression to calculate the x component of the centroid of the plane.
Here,
There are two sections in the plane. Rewrite equation (IV) according to the plane.
Here,
Write an expression to calculate the y component of the centroid of the plane.
Here,
There are two sections in the plane. Rewrite equation (VI) according to the plane.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the centroid of the plane area
Want to see more full solutions like this?
Chapter 5 Solutions
Vector Mechanics for Engineers: Statics
- For hot rolling processes, show that the average strain rate can be given as: = (1+5)√RdIn(+1)arrow_forward: +0 usão العنوان on to A vertical true centrifugal casting process is used to produce bushings that are 250 mm long and 200 mm in outside diameter. If the rotational speed during solidification is 500 rev/min, determine the inside radii at the top and bottom of the bushing if R-2R. Take: -9.81 mis ۲/۱ ostrararrow_forward: +0 العنوان use only In conventional drawing of a stainless steel wire, the original diameter D.-3mm, the area reduction at each die stand r-40%, and the proposed final diameter D.-0.5mm, how many die stands are required to complete this process. онarrow_forward
- In non-continuous dieless drawing process for copper tube as shown in Fig. (1), take the following data: Do-20mm, to=3mm, D=12mm, ti/to=0.6 and vo-15mm/s. Calculate: (1) area reduction RA, (2) drawing velocity v. Knowing that: t₁: final thickness D₁ V. Fig. (1) Darrow_forwardA vertical true centrifugal casting process is used to produce bushings that are 250 mm long and 200 mm in outside diameter. If the rotational speed during solidification is 500 rev/min, determine the inside radii at the top and bottom of the bushing if R-2Rb. Take: 8-9.81 m/sarrow_forwardIn conventional drawing of a stainless steel wire, the original diameter D.-3mm, the area reduction at each die stand r-40%, and the proposed final diameter D₁-0.5mm, how many die stands are required to complete this process.arrow_forward
- A vertical true centrifugal casting process is used to produce bushings that are 250 mm long and 200 mm in outside diameter. If the rotational speed during solidification is 500 rev/min, determine the inside radii at the top and bottom of the bushing if R-2Rb. Take: 8-9.81 m/sarrow_forwardIn non-continuous dieless drawing process for copper tube as shown in Fig. (1), take the following data: Do-20mm, to=3mm, D=12mm, ti/to=0.6 and vo-15mm/s. Calculate: (1) area reduction RA, (2) drawing velocity v. Knowing that: t₁: final thickness D₁ V. Fig. (1) Darrow_forward-6- 8 من 8 Mechanical vibration HW-prob-1 lecture 8 By: Lecturer Mohammed O. attea The 8-lb body is released from rest a distance xo to the right of the equilibrium position. Determine the displacement x as a function of time t, where t = 0 is the time of release. c=2.5 lb-sec/ft wwwww k-3 lb/in. 8 lb Prob. -2 Find the value of (c) if the system is critically damping. Prob-3 Find Meq and Ceq at point B, Drive eq. of motion for the system below. Ш H -7~ + 目 T T & T тт +arrow_forward
- Q For the following plan of building foundation, Determine immediate settlement at points (A) and (B) knowing that: E,-25MPa, u=0.3, Depth of foundation (D) =1m, Depth of layer below base level of foundation (H)=10m. 3m 2m 100kPa A 2m 150kPa 5m 200kPa Barrow_forwardW PE 2 43 R² 80 + 10 + kr³ Ø8=0 +0 R²+J+ kr200 R² + J-) + k r² = 0 kr20 kr20 8+ W₁ = = 0 R²+1) R²+J+) 4 lec 8.pdf Mechanical vibration lecture 6 By: Lecturer Mohammed C. Attea HW1 (Energy method) Find equation of motion and natural frequency for the system shown in fig. by energy method. m. Jo 000 HW2// For the system Fig below find 1-F.B.D 2Eq.of motion 8 wn 4-0 (1) -5- marrow_forwardThe hose supplying the cylinder operating the bucket of a large excavator has fluid at 1000 psi flowing at 5 gpm. What is theavailable power in the line?arrow_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