
Concept explainers
yB so that the ball will enter the basket.

Answer to Problem 13.77P
The value of yB=0.488m.
Explanation of Solution
Consider the diagram of the suspended ball by an inextensible cord.
Let us consider at point “A” as position 1 and then the point described by the angle is considered as position 2.
The path of the ball changes from the circular motion to parabolic motion.
So far then the tension in the cord becomes zero.
From the above diagram x-coordinate of the ball at the position 2 is taken as x2.
Then the y-coordinate of the ball at position 2 is takes as y2.
So the free body diagram of the ball at position 2 is calculated by :
Then apply the newton’s second law after that resolve the forces acting on the ball at the position 2
So, here the cord becomes slack at point 2.
And substitute Q=0 in above formula, we get the:
Here applying the conservation of energy at position 1 and 2 for the ball.
To find the angle swept by the ball is
Then formulate the kinetic energy of the ball at position 1 as T1.
Formulate the potential energy of the ball, we get:
Here we have to substitute h=l, we get:
Formulate the kinetic energy of the ball at the position 2 to be considered as T2.
Formulate the potential energy of the ball at point 2 is V2.
Consider equation 1 and substitute required values.
Substitute
Finally from equation (1) we get:
Substitute required values, we get:
Then, find the velocity of the ball at point 2.
After that the velocity of the projectile ball after reaches its point 2 is to be vp.
In this we have horizontal velocity component and vertical velocity component.
Formulate the horizontal velocity component of the projectile ball along with −ve X-axis.
Formulate the horizontal distance between the basket and point of suspension of the ball.
Substitute
Formulate the vertical velocity component of the projectile ball with the negative X-axis.
Vertical distance between the basket and the point of suspension is to be yB..
Substitute
Find the y-coordinate value by substituting all the required values.
Want to see more full solutions like this?
Chapter 13 Solutions
Vector Mechanics For Engineers
- practise questionarrow_forwardCan you provide steps and an explaination on how the height value to calculate the Pressure at point B is (-5-3.5) and the solution is 86.4kPa.arrow_forwardPROBLEM 3.46 The solid cylindrical rod BC of length L = 600 mm is attached to the rigid lever AB of length a = 380 mm and to the support at C. When a 500 N force P is applied at A, design specifications require that the displacement of A not exceed 25 mm when a 500 N force P is applied at A For the material indicated determine the required diameter of the rod. Aluminium: Tall = 65 MPa, G = 27 GPa. Aarrow_forward
- Find the equivalent mass of the rocker arm assembly with respect to the x coordinate. k₁ mi m2 k₁arrow_forward2. Figure below shows a U-tube manometer open at both ends and containing a column of liquid mercury of length l and specific weight y. Considering a small displacement x of the manometer meniscus from its equilibrium position (or datum), determine the equivalent spring constant associated with the restoring force. Datum Area, Aarrow_forward1. The consequences of a head-on collision of two automobiles can be studied by considering the impact of the automobile on a barrier, as shown in figure below. Construct a mathematical model (i.e., draw the diagram) by considering the masses of the automobile body, engine, transmission, and suspension and the elasticity of the bumpers, radiator, sheet metal body, driveline, and engine mounts.arrow_forward
- 3.) 15.40 – Collar B moves up at constant velocity vB = 1.5 m/s. Rod AB has length = 1.2 m. The incline is at angle = 25°. Compute an expression for the angular velocity of rod AB, ė and the velocity of end A of the rod (✓✓) as a function of v₂,1,0,0. Then compute numerical answers for ȧ & y_ with 0 = 50°.arrow_forward2.) 15.12 The assembly shown consists of the straight rod ABC which passes through and is welded to the grectangular plate DEFH. The assembly rotates about the axis AC with a constant angular velocity of 9 rad/s. Knowing that the motion when viewed from C is counterclockwise, determine the velocity and acceleration of corner F.arrow_forward500 Q3: The attachment shown in Fig.3 is made of 1040 HR. The static force is 30 kN. Specify the weldment (give the pattern, electrode number, type of weld, length of weld, and leg size). Fig. 3 All dimension in mm 30 kN 100 (10 Marks)arrow_forward
- (read image) (answer given)arrow_forwardA cylinder and a disk are used as pulleys, as shown in the figure. Using the data given in the figure, if a body of mass m = 3 kg is released from rest after falling a height h 1.5 m, find: a) The velocity of the body. b) The angular velocity of the disk. c) The number of revolutions the cylinder has made. T₁ F Rd = 0.2 m md = 2 kg T T₂1 Rc = 0.4 m mc = 5 kg ☐ m = 3 kgarrow_forward(read image) (answer given)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





