Concept explainers
(a)
Boulder will land on the road or beyond if
Answer to Problem 13.173P
The horizontal distance travelled by the rock is
Explanation of Solution
Given information:
Rock A falls from a distance of
The total linear momentum of two particles is conserved. Therefore
The co-efficient of restitution is defined as
For a uniformly accelerated motion
In above equation
Calculation:
Assume
Apply conservation of linear momentum in direction t.
Substitute
Apply co-efficient of restitution equation in direction n.
Substitute
Velocity
Velocity in y direction
Assume t as the time that takes for the rod to reach the ground.
Substitute
Solve
Find the horizontal distance
Substitute
Conclusion:
The horizontal distance travelled by the rock is
(b)
Boulder will land on the road or beyond if
Answer to Problem 13.173P
The horizontal distance travelled by the rock is
Explanation of Solution
Given information:
Rock A falls from a distance of
The total linear momentum of two particles is conserved. Therefore
The co-efficient of restitution is defined as
For a uniformly accelerated motion
In above equation
Calculation:
Assume
Apply conservation of linear momentum in direction t.
Substitute
Apply co-efficient of restitution equation in direction n.
Substitute
Velocity
Velocity in y direction
Assume t as the time that takes for the rod to reach the ground.
Substitute
Solve
Find the horizontal distance
Substitute
Conclusion:
The horizontal distance travelled by the rock is
Want to see more full solutions like this?
Chapter 13 Solutions
Vector Mechanics for Engineers: Dynamics
- 1. Two discs sliding on a frictionless horizontal plane with opposite speeds of the same magnitude Vo collide with each other head-on. Disk A is known to have a mass of 3 kg and its velocity is observed to be zero after impact. Determine a) the mass of disk B if the coefficient of restitution between the two disks is known to be 0.5, b) the range of possible values of the mass of disk B if the coefficient of restitution between the two disks is unknown.arrow_forward1. A particle P with mass 0.5 kg is released from rest and slides down a smooth, curved road and sticks to block A (with mass 0.25 kg). Determine the maximum deflection of the spring attached to A, if the spring has a stiffness of 1 kN/m. 4 m k Parrow_forwardIf Block A is 1.6 kg and sphere B is 1.3 kg , L= 1.7 m , and K=332 N/m, Please submit your answer for the problem below in 3 decimal places in meters. 13.200 block A is pushed up against a spring compressing it a dis- tance x. The block is then released from rest and slides down the 20° incline until it strikes sphere B that is suspended from inextensible rope. The spring constant k = K N/m, the coefficient of friction between A and the ground is 0.2, the distance A slides from the unstretched length of the spring d= 1.5 m, and the coefficient of restitution between A and B is 0.8. Knowing the tension in the rope is 20 N when a= 30°, determine the initial compression x of the spring. k 20°f B. Fig. P13.200 137 CC étv LGarrow_forward
- Two types of energy-absorbing fenders designed to be used on a pier are statically loaded. The force-deflection curve for each type of fender is given in the graph. Determine the maximum deflection of each fender when a 90-ton ship moving at 1 mi/h strikes the fender and is brought to rest.arrow_forwardKnowing that, ignoring air resistance, an apple falling from a height h hits the ground when 2h t = If you include air resistance, then vs 0 willappear and the equation of motion becomes: dv m = -mg + kv² v(0) = 0 dt With k> 0. Show that mg gk v(t) = - tanh m and also show that the apple takes time to touch the ground is kh 2kh e m kg Check that this matches the answer when we don't consider the air resistance with k → 0. Tip: for very small x values ex 1+x and In1 + x )= xarrow_forwardA 70-g ball B dropped from a height h0 = 1.5 m reaches a height h2 = 0.25 m after bouncing twice from identical 210-g plates. Plate A rests directly on hard ground, while plate C rests on a foam-rubber mat. Determine (a) the coefficient of restitution between the ball and the plates, (b) the height h1 of the ball’s first bounce.arrow_forward
- Rock falls can cause major damage to roads and infrastructure. To design mitigation bridges and barriers, engineers use the coefficient of restitution to model the behavior of the rocks. Rock A falls a distance of 20 m before striking an incline with a slope of α = 40o. Knowing that the coefficient of restitution between rock A and the incline is 0.2, determine the velocity of the rock right after the impact, both magnitude and angle with respect to the horizontal.arrow_forward2. At a racing event a dirt bike rider jumps off of a ramp angled at = 30 deg and a height d = 1 m off the ground. She remains in the air for a total of T = 1.5 seconds. What was the maximum height, h, that she attained? h A. 3.8 m B. 3.5 m C. 3.3 m D. 2.5 m E. 2.3 m darrow_forwardTwo steel blocks slide without friction on a horizontal surface. Their velocities before the impact are shown. Knowing that e = 0.75, determine their velocities after impact.arrow_forward
- The 3.9-lb rod AB is hanging in the vertical position. A 2.2-lb block, sliding on a smooth horizontal surface with a velocity of 12 ft/s, strikes the rod at its end B. (Figure 1) 3.98 12 ft/s PA ft S A Determine the velocity of the block immediately after the collision. The coefficient of restitution between the block and the rod at B is e = 0.84. Express your answer to three significant figures and include the appropriate units. ? B C 3 ft form Cyc HEALT wayarrow_forward... Two blocks A and B of the same mass 0.93 kg are released from rest on a 26.3° incline when they are S = 10.8 m apart, as shown. The coefficient of friction under the upper block A is 0.16, and that under the lower block B is 0.33. Compute the distanced travelled by block B (in m) until the blocks touch each other. Round off only on the final answer expressed in 3 decimal places. blocks.png B A 8. E'arrow_forward1 2 2 blocks of ice are sliding on frictionless ice in opposite directions collide. The 1st block's mass is 3kg. It is moving to the right at 3 m/s. The 2nd block's mass is 2kg. It is moving to the left at 2 m/s. After the impact, the 2nd block moves to the right with a speed of 2 m/s What is the coefficient of restitution? m1 = 3 vla= 3 m2 = 2 v2a= -1 After collision: v2b=2 Momentum_a= m1*vla + m2*v2a v1b = (Momentum_a - m2*v2b) / m1 % Restitution equation e = (v2b - v1b) / (v1a - v2a)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