Concept explainers
Disk A rotates in a horizontal plane about a vertical axis at the
(a)
Find the position of the slider and horizontal force exerted on the slider by disk at
Answer to Problem 12.133RP
The position of the slider at
The horizontal force exerted on the slider by disk at
Explanation of Solution
Given information:
The polar coordinate
The mass
The distance
The spring constant (k) is 100 N/m.
Calculation:
Consider the Position of the slider is in point O
Find the displacement of spring when
Consider distance of the slider (r) from the point O is 500 mm.
Find the displacement of spring when
Substitute 500 mm for r.
Find the restoring force (F) of spring when
Substitute 100 N/m for k and 500 mm for
Sketch the free body diagram and kinetic diagram of forces on disk A and spring as shown in in Figure (1).
Refer Figure (1).
Write the equation of radial component of acceleration
Apply Newton’s law of equation along radial direction.
The radial force is equal to the restoring force.
Find the equation of restoring force (F).
Substitute
Substitute
Write the equation of
Integrate Equation (1) to find
Use Equation (1) to substitute for
Slider B is at initial position when
Write
Integrate Equation (4) to find
Use Equation (3) to substitute for
Find the position of the slider at
Use Equation (4) to substitute for
Thus, the position of the slider at
Refer Figure 1.
Apply Newton’s law of Equation along transverse direction.
Write the transverse component of acceleration
Here,
The transverse force is the horizontal force exerted on the slider by disk.
The disk is rotating at constant rate. Therefore, the polar coordinate of transverse acceleration,
Find the horizontal force exerted on the slider by disk at
Write the equation of transverse force
Substitute
Substitute 0 for
Substitute Equation (3) in Equation (7).
Thus, the horizontal force exerted on the slider by disk at
(b)
Find the position of the slider and horizontal force exerted on the slider by disk at
Answer to Problem 12.133RP
The position of the slider at
The horizontal force exerted on the slider by disk at
Explanation of Solution
Calculation:
Consider the Position of the slider is in point O
Find the displacement of spring when
Consider distance of the slider (r) from the point O is 500 mm.
Find the displacement of spring when
Substitute 500 mm for r.
Find the restoring force (F) of spring when
Substitute 200 N/m for k and 500 mm for
Refer Figure (1).
Write the equation of radial component of acceleration
Apply Newton’s law of equation along radial direction.
The radial force is equal to the restoring force.
Find the equation of restoring force (F).
Substitute
Substitute
Write the equation of radial velocity of the slider in terms of r.
Here,
Write equation of the rate of change of position coordinate in terms of differential equation.
Apply differentiation to Equation (8)
Rewrite Equation (10) by multiplying and dividing the right-hand side by dr.
Substitute Equation (10) to rewrite Equation (11).
Substitute Equation (8) to rewrite Equation (12).
Substitute
Apply the limits to integrate the Equation (14).
At the time of instant
Substitute Equation (8) in Equation (15).
Integrate Equation (16).
Use spherical polar coordinates and choose,
Differentiate Equation (18).
Rewrite Equation (18).
Rewrite Equation (20) for
Use Equation (20) and (21) to change the values of limit in Equation (17).
Apply the trigonometric formula of
Use Equation (23) to rewrite Equation (22).
Substitute 0.5m for
Thus, the position of the slider at
Find the radial polar coordinate of velocity using Equation (24).
Differentiate Equation (24) with respect to t.
Substitute 500 mm for
Find the horizontal force exerted on the slider by disk at
Substitute
Substitute 0.1 s for t and
Thus, the horizontal force exerted on the slider by disk at
Want to see more full solutions like this?
Chapter 12 Solutions
VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
Additional Engineering Textbook Solutions
Vector Mechanics For Engineers
BASIC BIOMECHANICS
Database Concepts (8th Edition)
Thermodynamics: An Engineering Approach
Mechanics of Materials (10th Edition)
Modern Database Management
- 4. G A micarta pinion rotating at 1200 r.p.m. is to transmit 1 kW to a cast iron gear at a speed of 192 r.p.m. Assuming a starting overload of 20% and using 20° full depth involute teeth, determine the module, number of teeth on the pinion and gear and face width. Take allowable static strength for micarta as 40 MPa and for cast iron as 53 MPa. Check the pair in wear.arrow_forwardI want to solve these choicesarrow_forward2. A spur gear made of bronze drives a mid steel pinion with angular velocity ratio of 32: 1. The pressure angle is 14½. It transmits 5 kW at 1800 r.p.m. of pinion. Considering only strength, design the smallest diameter gears and find also necessary face width. The number of teeth should not be less than 15 teeth on either gear. The elastic strength of bronze may be taken as 84 MPa and of steel as 105 MPa. Lewis factor for 14½½ pressure angle may be taken 0.684 0.124 y = No. of teeth as [Ans. m 3 mm; b= 35 mm; Dp = 48 mm; D= 168 mm]arrow_forward
- Q2. Determine the safety factors for the bracket rod shown in Figure 2 based on both the distortion-energy theory and the maximum shear theory and compare them. Given: The material is 2024-T4 aluminum with a yield strength of 47 000 psi. The rod length /= 6 in. and arm a = 8 in. The rod outside diameter od 1.5 in., id = 1 in, h=2 in., t=0.5 in., Load F= 1000 lb. Assumptions: The load is static and the assembly is at room temperature. Consider shear due to transverse loading as well as other stresses. (Note: solve in SI units) wall tube Figure 2 armarrow_forwardThe question has been set up with all the cuts needed to accurately derive expressions for V(x) and M(x). Using the cuts free body diagrams set up below, derive expressions for V(x) and M(x). If you use the method of cuts then validate your answers using calculus or vice versa.arrow_forwardIt is required to treat 130 kmol/hr of chloroform-air feed gas mixture that contains 12% chloroform. It is required to remove 93% of chloroform using 150 kmol/hr of solvent that contains 99.6% water and 0.4% chloroform. The cross sectional area of the column is 0.8 m². Calculate the column height using the following data; kx'.a = 1.35 (kmol/m³.s (Ax)), and ky'.a = 0.06 (kmol/m³.s (Ay)), kx/ky = 1.35, and the equilibrium data are: X 0 0.0133 0.033 y 0 0.01 0.0266 0.049 0.064 0.0747 0.0933 0.1053 0.0433 0.06 0.0733 0.111 0.1 0.12 0.14arrow_forward
- ४ B: Find the numerical solution for the 2D equation below and calculate the temperature values for each grid point shown in Fig. 2 (show all steps). (Do only one trail using following initial values and show the final matrix) [T1] T₂ T3 [T] 1 = [0] 0 0 d dx dx) (ka)+4(ka) = dy -20xy, k = 1 + 0.3 T ge L=3cm, 4x= Ay B.Cs.: at x=0=LT=0°C at y=0-L T=10°C Fig. (2)arrow_forward: +0 العنوان use only Two rods fins) having same dimensions, one made orass (k = 85 Wm K) and the mer of copper (k = 375 W/m K), having of their ends inserted into a furna. At a section 10.5 cm a way from furnace, the temperature of brass rod 120 Find the distance at which the ame temperature would be reached in the per rod ? both ends are ex osed to the same environment. ns 2.05 ۲/۱ ostrararrow_forwardFor the beam show below, draw A.F.D, S.F.D, B.M.D 6 kN/m 1 M B. 3 M Marrow_forward
- 1. Two long rods of the same diameter-one made of brass (k=85w/m.k) and the other made of copper (k=375 w/m.k) have one of their ends inserted into a furnace (as shown in the following figure). Both rods are exposed to the same environment. At a distance of 105 mm from the furnace, the temperature of the brass rod is 120°C. At what distance from the furnace will the same temperature be reached in the copper rod? Furnace 105 mm T₁ Brass rod ⑪ h Too- x2- Ti Copper rodarrow_forward: +0 العنوان use only Two rods fins) having same dimensions, one made orass (k = 85 Wm K) and the mer of copper (k = 375 W/m K), having of their ends inserted into a furna. At a section 10.5 cm a way from furnace, the temperature of brass rod 120 Find the distance at which the ame temperature would be reached in the per rod ? both ends are ex osed to the same environment. ns 2.05 ۲/۱ ostrararrow_forwardمشر on ۲/۱ Two rods (fins) having same dimensions, one made of brass(k=85 m K) and the other of copper (k = 375 W/m K), having one of their ends inserted into a furnace. At a section 10.5 cm a way from the furnace, the temperature brass rod 120°C. Find the distance at which the same temperature would be reached in the copper rod ? both ends are exposed to the same environment. 22.05 ofthearrow_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