When the rope is at an angle of
(a)
The velocities of A and B just after the impact.
Answer to Problem 13.188P
Explanation of Solution
Given information:
Mass of sphere is
Mass of wedge is
Concept used:
The total linear momentum of two particles is conserved. Therefore:
The co-efficient of restitution is defined as.
The principle of conservation of energy is defined as.
“When a particle moves under the action of conservation of forces. the sum of kinetic energy and potential energy of that particle remains constant.”
Calculation:
At initial stage:
Find the Kinetic and potential energies.
Just before the impact:
Therefore.
Substitute and solve:
Draw impulse momentum diagram.
Apply conservation of momentum in t direction.
Therefore:
For both A and B :
Apply conservation of momentum in x direction.
Substitute:
Therefore:
Apply co-efficient of restitution equation.
Substitute:
Solve.
Solve equation 1 and 2.
Find the magnitude of
Find the angle.
Conclusion:
The velocities of A and B just after the impact is equal to:
(b)
The maximum deflection of the spring.
Answer to Problem 13.188P
Maximum deflection of the spring is
Explanation of Solution
Given information:
Mass of sphere is
Mass of wedge is
Concept used:
The principle of conservation of energy is defined as:
“When a particle moves under the action of conservation of forces. the sum of kinetic energy and potential energy of that particle remains constant”
Calculation:
According to the conservation of energy:
Just after the impact.
Rearrange:
According to sub part a.:
Substitute and solve:
Therefore.
Conclusion:
The maximum deflection is equal to
Want to see more full solutions like this?
Chapter 13 Solutions
Vector Mechanics For Engineers
- During a pregame warmup period, two basketballs collide above the hoop when in the positions shown. Just before impact, ball 1 has a velocity v1 which makes a 32° angle with the horizontal. If the velocity v2 of ball 2 just before impact has the same magnitude as v1, determine the two possible values of the angle θ (θ1 < θ2) measured from the horizontal, which will cause ball 1 to go directly through the center of the basket. The coefficient of restitution is e = 0.64arrow_forwardThe 12-lb box slides on the surface for which μk = 0.3. The box has a velocity v = 15 ft/s when it is 2 ft from the plate. a) If the box strikes the smooth plate, which has a weight of 22 lb and is held in position by an unstretched spring of stiffness k = 440 lb/ft, determine the maximum compression imparted to the spring. Take e = 0.8 between the box and the plate. Assume that the plate slides smoothly. x = ?arrow_forwardDirect central impact occurs between a 100lbs body moving to the right at 5 ft per second and a body of weight W moving to the left at 3 ft per sec. The coefficient of restitution e = 0.5. After impact the 100lb body rebounds to the left at 2ft/s. Determine the weight W of the other body. (lbs)arrow_forward
- The two disks AA and BB have a mass of 4 kgkg and 6 kgkg , respectively. They collide with the initial velocities shown. The coefficient of restitution is eee = 0.75. Suppose that (vA)1(vA)1va = 6 m/sm/s , (vB)1(vB)1vb = 8 m/sm/s Determine the magnitude of the velocity of AA just after impact. Determine the angle between the xx axis and the velocity of AA just after impact, measured clockwise from the negative xx axis.arrow_forwardThe 9.0 kg sphere A is held at an angle of 60° as shown, and then is released from rest and hits the B sphere which has a mass of 4.5 kg. In this crash the coefficient of restitution is e = 0.75. The sphere B is attached to the end of a rod lightweight rotating around the O point. The spring is initially non elongated and it is known that the maximum angle θ that the rod turned after the crash measured from the initial position was of 21.4º. Calculate: a) The speed with which sphere A impacts with sphere B. b) The magnitude and direction of the velocities of each sphere A and B after impact. c) The mechanical energy dissipated on impact. d) The spring stiffness constant k.arrow_forwardThe van is traveling at 20 km/h when the coupling of the trailer at A fails. If the trailer has a mass of 250 kg and coasts 45 m before coming to rest, determine the constant horizontal force F created by rolling friction which causes the trailer to stop. Note: 3 decimal points in every answer.arrow_forward
- The two disks AA and BB have a mass of 4 kgkg and 6 kgkg , respectively. They collide with the initial velocities shown. The coefficient of restitution is eee = 0.75. Suppose that (vA)1(vA)1va = 6 m/sm/s , (vB)1(vB)1vb = 8 m/sm/s Determine the magnitude of the velocity of BB just after impact. Determine the angle between the xx axis and the velocity of BB just after impact, measured clockwise from the positive xx axis.arrow_forwardA 8.7-Mg truck is resting on the deck of a barge which displaces 235 Mg and is at rest in still water. If the truck starts and drives toward the bow at a speed relative to the barge vrel = 7.5 km/h, calculate the speed v of the barge. The resistance to the motion of the barge through the water is negligible at low speeds.arrow_forwardA smooth can C, having a mass of 5 kg, is lifted from a feed at A to a ramp at B by a rotating rod. The rod maintains a constant angular velocity of θ˙ = 0.5 rad/s, Neglect the effects of friction in the calculation and the size of the can so that r=(1.2cosθ)m. The ramp from A to B is circular, having a radius of 600 mm. (a) Determine the magnitude of the force which the rod exerts on the can at the instant θθ = 30∘∘. Express your answer to three significant figures and include the appropriate units.arrow_forward
- The collar of mass m is released from rest while in position A and subsequently travels with negligible friction along the vertical-plane circular guide. Determine the magnitude of the normal force exerted by the guide on the collar (a) just before the collar passes point B, (b) just after the collar passes point B (i.e., the collar is now on the curved portion of the guide), (c) as the collar passes point C, and (d) just before the collar passes point D. Use the values m = 0.5 kg, R = 1.0 m, and k = 290 N/m. The unstretched length of the spring is 0.70R.arrow_forwardThe van is traveling at 20 km/h when the coupling of the trailer at A fails. If the trailer has a mass of 300 kg and coasts 50 m before coming to rest, determine the constant horizontal force F created by rolling friction which causes the trailer to stop.arrow_forwardThe 12-Mg truck drives onto the 366-Mg barge from the dock at 27 km/h and brakes to stop on the deck. The barge is free to move in the water, which offers negligible resistance to motion at low speeds. Calculate the speed of the barge after the truck has come to rest on it.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