Concept explainers
The end point B of a boom is originally 5 m from fixed point A when the driver starts to retract the boom with a constant radial acceleration of r = −1.0 m/s2 and lower it with a constant angular acceleration θ = −0.5 rad/ s2. At t = 2 s, determine (a) the velocity of point B,(b) the acceleration of point B, (c) the radius of curvature of the path.
Fig. P11.192
(a)
The velocity
Answer to Problem 11.192RP
The velocity
Explanation of Solution
Given information:
The distance
The boom with a constant radial velocity
The boom with a constant radial acceleration
The boom with a constant angular acceleration
The time (t) is 2 sec.
Calculation:
Write the expression for rectangular position coordinate (r) of point B using equation of motion:
Here,
The radial initial velocity of point B is 0.
Calculate the radial coordinate (r) of point B:
Substitute 5m for
Calculate the radial velocity
Substitute 0 for
Calculate the angular coordinate
Here,
Angular coordinate of initial velocity of point B is 0. Thus,
Substitute
Calculate the
Substitute zero for
Calculate velocity
Here,
Rewrite Equation (2) in terms of r,
Substitute
Calculate the magnitude of
Substitute
Calculate unit vector
Substitute
Calculate angle
Substitute
Calculate the angle
Substitute
Therefore, the velocity
(b)
The acceleration
Answer to Problem 11.192RP
The acceleration
Explanation of Solution
Given information:
The distance
The boom with a constant radial acceleration
The boom with a constant radial acceleration
The boom with a constant angular acceleration
The time (t) is 2 sec.
Calculation:
Show the values of
Write acceleration
Here,
Rewrite the above equation in term of r,
Substitute
Here,
Calculate the magnitude of
Substitute
Calculate the angle
Substitute
Calculate the angle
Substitute
Therefore, the acceleration
(c)
The radius of curvature
Answer to Problem 11.192RP
The radius of curvature
Explanation of Solution
Given information:
The distance
The boom with a constant radial acceleration
The boom with a constant radial acceleration
The boom with a constant angular acceleration
The time (t) is 2 sec.
Calculation:
Calculate the tangential component of acceleration
Substitute
Write normal component
Substitute
Substitute
Calculate the normal acceleration
Substitute
Calculate the radius of curvature
Rewrite Equation for radius of curvature.
Substitute
Therefore, the radius of curvature
Want to see more full solutions like this?
Chapter 11 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- Based on observations, the speed of a jogger can be approximated by the relation v= 7.5(1 - 0.04x) 0.3, where v and x are expressed in mi/h and miles, respectively. Knowing that x = 0 at t= 0, determine (a) the distance the jogger has run when t= 1 h, (b) the jogger’s acceleration in ft/s2 at t=0, (c) the time required for the jogger to run 6 mi.arrow_forwardA Scotch yoke is a mechanism that transforms the circular motion of a crank into the reciprocating motion of a shaft (or vice versa). It has been used in a number of different internal combustion engines and in control valves. In the Scotch yoke shown, the acceleration of point A is defined by the relation a = -1.8 sin kt, where a and t are expressed in m/s2 and seconds, respectively, and k = 3 rad/s. Knowing that x= 0 and v = 0.6 m/s when t= 0, determine the velocity and position of point A when t = 0.5 s.arrow_forwardA Scotch yoke is a mechanism that transforms the circular motion of a crank into the reciprocating motion of a shaft (or vice versa). It has been used in a number of different internal combustion engines and in control valves. In the Scotch yoke shown, the acceleration of Point A is defined by the relation a=-1.5sin(kt) , where a and t are expressed in m/s2 and seconds, respectively, and k=3 rad/s. Knowing that x=0 and v=0.6 m/s when t =0, determine the position of Point A when t=0.5 s.arrow_forward
- 6. The speed of a particle moving in a circle with radius 2.0 m increases its speed constantly at a rate of 4.4 m / s2. At an instant when the magnitude of the total acceleration is 6.0 m / s2, what is the velocity of the particle? Answers: a) 3.9 m/s b) 2.9 m/s c) 3.5 m/s d) 3.0 m/s e) 1.4 m/sarrow_forwardThe acceleration record shown was obtained for a small airplane traveling along a straight course. Knowing that x= 0 and v= 60 m/s when t= 0, determine (a) the velocity and position of the plane at t= 20 s, (b) its average velocity during the interval 6 s < t< 14 s.arrow_forwardAn accelerometer record for the motion of a given part of a mechanism is approximated by an arc of a parabola for 0.2 s and a straight line for the next 0.2 s as shown in the figure. Knowing that v = 0 when t= 0 and x= 0.8 ft when t= 0.4 s, (a) construct the v-t curve for 0 ≤ t≤ 0.4 s, (b) determine the position of the part at t= 0.3 s and t= 0.2 s.arrow_forward
- Two 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_forwardA motorist is traveling on a curved section of highway with a radius of 2500 ft at a speed of 60 mi/h. The motorist suddenly applies the brakes, causing the automobile to slow down at a constant rate. If the speed has been reduced to 45 mi/h after 8 s, determine the acceleration of the automobile immediately after the brakes have been applied.arrow_forwardA motorcyclist is moving on a vertical circular path with a radius of 200 m and is accelerating at a rate of 0.4t m/s2 along the path, where t is in seconds. If he starts from rest, determine the tangential acceleration when he moves 60 degrees from the initial point.a. 6.12 m/s2 b. 7.73 m/s2c. 5.86 m/s2 d. 8.24 m/s2arrow_forward
- A commuter train traveling at 40 mi/h is 3 mi from a station. The train then decelerates so that its speed is 20 mi/h when it is 0.5 mi from the station. Knowing that the train arrives at the station 7.5 min after beginning to decelerate and assuming constant decelerations, determine (a) the time required for the train to travel the first 2.5 mi, (b) the speed of the train as it arrives at the station, (c) the final constant deceleration of the train.arrow_forwardA robot arm moves so that P travels in a circle about point B , which is not moving. Knowing that P starts from rest, and its speed increases at a constant rate of 10 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.arrow_forwardA person walks radially inward on a platform that is rotating counterclockwise about its center. Knowing that the platform has a constant angular velocity ω and the person walks with a constant speed u relative to the platform, what is the direction of the acceleration of the person at the instant shown?a. Negative xb. Negative yc. Negative x and Positive yd. Positive x and Positive ye. Negative x and Negative yarrow_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