Concept explainers
(a)
The initial tension in the cable.
Answer to Problem 12.72P
The initial tension:
Explanation of Solution
Given information:
The velocity of block A is
Mass of the pulley and the effect of the friction is negligible.
From results of part (b), the initial acceleration of block A:
Calculations:
From the free body and kinetic diagram of block A:
Conclusion:
The initial tension in the cable is
(b)
The initial acceleration of block A.
Answer to Problem 12.72P
The initial acceleration of block A:
Explanation of Solution
Given information:
The figure:
The velocity of block A is
Mass of the pulley and the effect of the friction is negligible.
Calculation:
Draw the free body and kinetic diagram of block A:
Draw the free body and kinetic diagram of block B:
Representing the components of acceleration of block A as shown in the below diagram:
Conclusion:
The initial acceleration of block A:
(c)
The initial acceleration of block B.
Answer to Problem 12.72P
The initial acceleration of block B:
Explanation of Solution
Given information:
The velocity of block A is
Mass of the pulley and the effect of the friction is negligible.
From results of part (b), the initial acceleration of block A:
Calculations:
From eq. (6) defined in part (b):
Conclusion:
The initial acceleration of block B is
Want to see more full solutions like this?
Chapter 12 Solutions
Vector Mechanics for Engineers: Dynamics
- The 195-g slider has a speed v = 1.9 m/s as it passes point A of the smooth guide, which lies in a horizontal plane. Determine the magnitude R of the force which the guide exerts on the slider (a) just before it passes point A of the guide and (b) as it passes point B. Answers: (a) RA= (b) RB i i 225 mm B N Narrow_forwardA worker develops a tension T in the cable as he attempts to move the 48-kg cart up the 21° incline. Determine the resulting acceleration a of the cart if (a) T = 135 N and (b) T = 222 N. Neglect all friction, except that at the worker's feet. The acceleration a is positive if up the slope, negative if down the slope. 48 kg 15° Answers: 21 O (a) T = 135 N, (b) T = 222 N, a = a =arrow_forwardDuring a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed v in a horizontal circle as shown. If p= 0.93 m and 0= 60°, determine (a) the tension in wire BC, (b) the speed of the hammer’s head.arrow_forward
- A spring is connected between the 1-kg slider A and the frame. The spring has a stiffness of 5N/m and it is undeformed when x = 0.1m. Knowing that the frame is rotating in the horizontal plane about O at the constant angularspeed ˙ θ = 2 rad/s, determine the distance x. Neglect friction.arrow_forwardYour answer is partially correct. Airplane A is flying horizontally with a speed of 218 km/h which is increasing at the rate of 4.8 km/h each second and is towing the glider B, which is gaining altitude. If the tow cable has a length r = 80 m, and the cable is unreeling at the constant rate r = 1.8 m/s while 0 = 19° is kept constant, determine the magnitudes of the velocity v and acceleration a of the glider. VA A Answers: V = a = i 58.8 1.33 km/h m/s²arrow_forward4. Below is shown an 8.05 |b particle sliding along the frictionless wire. At the position shown, determine (a) The normal force, N, from the wire onto the particle (b) The tangential acceleration of the particle. y = - v =3 fps (x,y) = (4,-1) ftarrow_forward
- A worker develops a tension Tin the cable as he attempts to move the 50-kg cart up the 20° incline. Determine the resulting acceleration a of the cart if (a) T = 132 N and (b) T = 196 N. Neglect all friction, except that at the worker's feet. The acceleration a is positive if up the slope, negative if down the slope. T 50 kg 150 20° Answers: (a) T= 132 N, a = i m/s? (b) T = 196 N, a = i m/s?arrow_forwardThe two blocks shown start from rest. The horizontal plane and the pulley are frictionless, and the pulley is assumed to be of negligible mass. Determine the acceleration of each block and the tension in each cable. A Cable 1 100 kg Cable 2 300 kg вarrow_forwardThe 565,000-lb jetliner A has four engines, each of which produces a nearly constant thrust of 47,000 lb during the takeoff roll. A small commuter aircraft B taxis toward the end of the runway at a constant speed vg = 20 mi/hr. Determine the velocity and acceleration which A appears to have relative to an observer in B 13 seconds after A begins its takeoff roll. Neglect air and rolling resistance. A L. B. 270 Answers: VA/B = ( i i+ j) mi/hr aA/B = i+ j) ft/sec2arrow_forward
- A 2-kg small block B fits inside a smooth slot cut in arm OA. The arm rotates counterclockwise in a vertical plane at a constant rate of 5 rad/s and r= 0.5 – 0.3 cos 0 in meters. At the instant that 0= 30°, determine (a) the force exerted by the spring on block B, (b) the normal force exerted by the arm OA on block B. Use radial and transverse components. spring Aarrow_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. A 60-kg engineering student decides to bungy jump from the famous Kawarau Bridge in Queenstown. The bridge is 43 m above the river and the operators choose a 30-m long cable for her (i.e. she will free-fall the first 30 metres). After the cable is taught, her downward acceleration is given by 9.81 – 6.4s m/s? where s is measured from point B as shown on the right. Assume her initial velocity at A is zero. Ignore air resistance and any horizontal motion. Treat the student as a particle. A (a) Calculate her velocity at point B. (b) Calculate the smallest clearance, d, between her centre of mass and the river. 30 m 43 m Drawing not to scalearrow_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