Concept explainers
Block B starts from rest, block A moves with a constant acceleration, and slider block C moves to the right with a constant acceleration of 75 mm/s2. Knowing that at t = 2 s the velocities of B and C are 480 mm/s downward and 280 mm/s to the right, respectively, determine (a) the accelerations of A and B, (b) the initial velocities of A and C, (c) the change in position of slider block C after 3 s.
Fig. P11.57 and P11.58
(a)
The acceleration of block A
Answer to Problem 11.57P
The acceleration of block A
Explanation of Solution
Given information:
The acceleration
At time (t) 2 sec the velocity
At time (t) 2 sec the velocity
Calculation:
Show the length and position of the cables as in Figure (1).
Choose the coordinate downward positive and right side positive.
Write the express for total lengths of cables.
Differentiate the above equation with respective to time (t).
Denotes
Differentiate the equation (2) with respective to time (t).
Denotes
Calculate the velocity
Here,
Substitute 0 for
Calculate the acceleration of block A:
Substitute
Therefore, the acceleration of block A
(b)
The initial velocities of block A
Answer to Problem 11.57P
The initial velocities of block A
Explanation of Solution
Given information:
The acceleration
At time (t) 2 sec the velocity
At time (t) 2 sec the velocity
Calculation:
Calculate the initial velocity
Substitute
Calculate the initial velocity
Modify equation (1) as,
At time (t) is 0 the initial velocity
Substitute at 0 for
Therefore, the initial velocities of block A
(c)
The change in position
Answer to Problem 11.57P
The change in position
Explanation of Solution
Given information:
The acceleration
At time (t) 2 sec the velocity
At time (t) 2 sec the velocity
Calculation:
Calculate the change in positon
Here,
Substitute
Therefore, the change in position
Want to see more full solutions like this?
Chapter 11 Solutions
VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)
- A £ C B Collar A starts from rest at t=0 and moves downward with a constant acceleration of 10 in/s². Collar B moves upward with a constant acceleration, and its initial velocity is 5 in/s. Knowing that collar B moves through 15.4 in between t = 0 and t = 2 s, determine the acceleration block C (in in/s²).arrow_forwardAn engine driver suddenly puts on his brake and shuts off steam when he is running at full speed; in the first second afteruwards the train travels 28 m and in the next second 26 m. Find (i) the original speed of the train, (ii) the time before it comes to rest, (iii) the distance it will travel in that interval, asuming the brake to cause a constant retardation. Find also the time the train will take, if it be 30 m long, to pass a spectator standing at a point 150 m ahead of the train at the instant when the brake was applied.arrow_forward3. The system shown begins its motion from rest and each component moves with a constant acceleration. If the relative acceleration of block C with respect to collar B is 60 mm / s2 upwards and the relative acceleration of block D with respect to block A is 110 mm / s2 downwards, determine: a) The velocity of block C after 3 s. b) The change in position of block D after 5 s. They solve in the English system.arrow_forward
- A robot arm moves so that Ptravels in a circle about Point B, which is not moving. P starts from rest, and its speed increases at a constant rate of 11 mm/s2. Determine (a) the magnitude of the acceleration when t=4 s, (b) the time for the magnitude of the acceleration to be 80 mm/s2. 0.8 m В mm/s2. The magnitude of the acceleration is The time required is S.arrow_forwardBlock C starts from rest and moves downward with a constant acceleration. Knowing that after 10 s the velocity of block A is 465 mm/s, determine 1. The accelerations of A, B, and C 2. The velocity of block B after 8 s. D Select one A BA = 38 mm/s (downward): ag = 25.3 mm/s (upward): ac = 12.7 mm/s (downward); and Va = 202.7 mm/s (upward) B = 45.6 mm/s (downward); as = 304 mm/s (upward), ac = 15,2 mm/s (downward) and Vi = 1216 mm/s (upward) C B= 465 mm/s (downward): as = 31 mm/s (upward): ac = 15.5 mm/s (downward); and Va = 248 mm/s (upward) D 31 = 36 mm/s (downward); ag = 25,3 mm/s (upward) ac = 127 mm/s (downward); and Vg = 1013 mm/s (upward)arrow_forwardA motorist starts from rest at point A on a circular entrance ramp when t=0, increases the speed of her automobile at a constant rate and enters the highway at point B. Knowing that her speed continues to increase at the same rate until it reaches 62.5 mph at point C, determine themagnitude of the normal acceleration (ft/s2) at t=10s.arrow_forward
- The elevator E shown starts from rest and moves upward with a constant acceleration. If the counterweight W moves through 30 ft in 5 s, determine (a) the acceleration of the elevator and the cable C, (b) the velocity of the elevator after 5 s.arrow_forwardTwo automobiles A and B are approaching each other in adjacent highway lanes. At t= 0, A and B are 3200 ft apart, their speeds are VA = 65 mi/h and VB = 40 mi/h, and they are at points P and Q , respectively. Knowing that A passes point Q 40 s after B was there and that B passes point P 42 s after A was there, determine (a ) the uniform accelerations of A and B,(b) when the vehicles pass each other, (c) the speed of B at that time.arrow_forwardBlock C starts from rest and moves downward with a constant acceleration. Knowing that after 8 s the velocity of block A is 456 mm/s, determine the accelerations of A, B, and C A Select one: A. a₁ = 57 mm/s (downward); a = 38 mm/s (upward); a = 19 mm/s (downward) B. a = 38 mm/s (downward); a = 25.3 mm/s (upward); a = 12.7 mm/s (downward) C. 8A = 45.6 mm/s (downward): a = 30,4 mm/s (upward); a = 15.2 mm/s (downward) CD a = 45.6 mm/s (downward): a = 30.4 mm/s (upward); a = 15.2 mm/s (downward) Carrow_forward
- As relay runner A enters the 65-ft-long exchange zone with a speed of 30 ft/s, he begins to slow down. He hands the baton to runner B 2.5 s later as they leave the exchange zone with the same velocity. Determine (a) the uniform acceleration of each of the runners, (b) when runner B should begin to run.arrow_forward4- A monorail train starts from rest on a curve of radius 400 m and accelerates at the constant rate a,. If the maximum total acceleration of the train must not exceed 1.5 m/ s2, determine (a) the shortest distance in which the train can reach a speed of 72 km/h, (b) the corresponding constant rate of acceleration at.arrow_forward2. A truck's speed increased uniformly from 20 km/hr to 70 km/hr in 30 sec. determine (a) the average speed (b) the acceleration and (C) the distance traveld.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