ENG1040 Engineering Dynamics
Practice Class 2 Translational Kinematics See Moodle for worked solutions to this practice class at the end of this week This Practice Class is aimed at testing your knowledge of translation and rotation of a particle. These topics were covered in lectures 3 – 6 of the series. This practice class will be assessed at the conclusion of your allocated practice class session. For assessment purposes, you must complete parts 1 – 4. The assessed problems are taken from Meriam and Kraige (7th edition), Chapter 2 & 3, while the private study problems are taken from Hibbeler (12th edition), Chapter 12 & 13.
Part 1: Particle motion / kinematics 2/1
The velocity of a particle is given by v = 20t2 -100t +50, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 6 seconds of motion and evaluate the velocity when a is zero.
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2/17
The car is traveling at a constant speed v0 = 100 km/h on the level portion of the road. When the 6-percent (tanθ = 6/100) incline is encountered, the driver does not change the throttle setting and consequently the car decelerates at the constant rate g sin θ. Determine the speed of the car (a) 10 seconds after passing point A and (b) when s = 100 m.
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2/23
Car A is traveling at a constant speed vA = 130 km /h at a location where the speed limit is 100 km/h. The police officer in car P observes this speed via radar. At the moment when A passes P, the police car be- gins to accelerate at the constant rate of 6 m/s2 until a speed of 160 km/h is achieved, and that speed is then maintained. Determine the distance required for the police officer to overtake car A. Neglect any nonrectilinear motion of P.
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2/53
On its takeoff roll, the airplane starts from rest and accelerates according to a = a 0 -kv2, where a0 is the constant acceleration resulting from the engine thrust and -kv2 is the acceleration due to aerody- namic drag. If a0 = 2 m/s2, k = 0.00004 m-1, and v is in meters per second, determine the design length of runway required for the airplane to reach the takeoff speed of 250 km/h if the drag term is (a) excluded and (b) included.
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Part 2: Projectile motion 2/67
A roofer tosses a small tool to the ground. What minimum magnitude v0 of horizontal velocity is required to just miss the roof corner B? Also determine the distance d.
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2/75
The pilot of an airplane carrying a package of mail to a remote outpost wishes to release the package at the right moment to hit the recovery location A. What angle θ with the horizontal should the pilot’s line of sight to the target make at the instant of re- lease? The airplane is flying horizontally at an altitude of 100 m with a velocity of 200 km/h.
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Part 3: Pulley motion 2/207 If block B has a leftward velocity of 1.2 m/s, determine the velocity of cylinder A.
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2/211 Determine the vertical rise h of the load W during 5 seconds if the hoisting drum wraps cable around it at the constant rate of 320 mm/s.
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Following are supplementary questions that may be more challenging. Demonstrators will be happy to assist students with these problems, but they need not be completed within the class for assessment purposes. These additional problems are taken from Hibbeler: Engineering Mechanics: Dynamics, 12th Edition, Pearson. 12.20
A particle is moving along a straight line such that its speed is defined as v = (-4s2) m/s, where s is in meters. If s = 2 m when t = 0, determine the velocity and acceleration as functions of time.
12.22
A particle moving along a straight line is subjected to a deceleration a = (-2v3) m/s2, where v is in m/s. If it has a velocity v = 8 m/s and a position s = 10 m when t = 0, determine its velocity and position when t = 4 s.
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12.53
The snowmobile moves along a straight course according to the v–t graph. Construct the s-t and a–t graphs for the same 50-s time interval. When t = 0, s = 0.
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12.63
The rocket has an acceleration described by the graph. If it starts from rest, construct the v-t and s-t graphs for the motion for the time interval 0 ≤ t ≤ 14 s.
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12.109 Determine the horizontal velocity vA of a tennis ball at A so that it just clears the net at B. Also, find the distance s where the ball strikes the ground.
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12.110 It is observed that the skier leaves the ramp A at an angle θA = 25° with the horizontal. If he strikes the ground at B, determine his initial speed vA and the time of flight tAB.
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12.198 If end A of the rope moves downward with a speed of 5 m/s, determine the speed of cylinder B.
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12.199 Determine the speed of the elevator if each motor draws in the cable with a constant speed of 5 m/s.
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