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Palestine Technical University – Khadoori
Department of Engineering Dynamics – Unit 1 Tutorial Sheet 3
Q (1)
Travelling with an initial speed of 70 km/h, a car accelerates at a rate of 600 km/ h 2 along a straight road. How long will it take to reach a speed 120km/h. Also, through what distance does the car travel during this time? [t=30 sec., s = 792 m]
Q (2)
A freight train travels at v= v 0 (1- e -bt), where (t) is the elapsed time. Determine the distance travelled in time t 1 , and the acceleration at this time, given that v 0 =60 ft/s, b=1/s and t = 3 s
[d = 123 ft, a = 2.99 ft/s^2 ]
Q (3)
The acceleration of a particle as it moves along a straight line is given by a = bt
- c. If s = s 0 and v = v 0 when t = 0, determine the particle’s velocity and position when t = t 1. Also, determine the total distance the particle travels during this time period.
Given: b = 2 m/s^3 , c = -1m/s 2 , s 0 = 1m , v 0 = 2m/s, t 1 = 6 s [v 1 = 32 m/s, s 1 = 67 m, d= 66 m]
Q (4)
Two particles A and B start from rest at the origin s = 0 and move along a straight line such that a (^) A = (at − b) and aB = (ct 2 − d), where t is in seconds. Determine the distance between them at t and the total distance each has travelled in time t.
Given: a = 6 ft/s^3 , b = 3 ft/s^2 , c = 12 ft/s 3 , d = 8 ft/s^2 , t = 4 s
[d (^) AB = 46.33 m, D = 70.714 m]
Q (5)
A stone A is dropped from rest down a well, and at time t 1 another stone B is dropped from rest. De termine the distance between the stones at a later tim e t 2. Given: d = 80ft , t 1 = 1 s , t 2 =2 s , g = 32.2 ft/ s^2 [d=48.3 m]
Q (6)
Ball A is released from rest at height h 1 at the same time that a second ball B is thrown upward from a distance h 2 above the ground. If the balls pass one another at a height h 3 determine the speed at which ball B was thrown upward.
Given: h 1 40ft , h 2 = 5ft , h 3 = 20ft , g = 32.2 ft/s 2 [vB0 = 31.403 ft/s]
Q (7)
A motorcycle starts from rest at s = 0 and travels along a straight road with the speed shown by the v-t graph. Determine the motorcycle's acceleration and position when t = t4 and t = t5.
Given: v 0 = 5 m/s, t 1 = 4 s , t 2 = 10 s, t 3 = 15 s, t 4 = 8 s , t 5 12 s [ a 4 = 0 m/s 2 , s 4 = 30 m, a 5 = -1 m/s 2 ]
Q (8)
Two cars start from rest side by side and travel along a straight road. Car A accelerates at the rate aA for a time t 1 , and then maintains a constant speed. Car B accelerates at the rate aB until reaching a constant speed vB and then maintains this speed. Construct the a-t, v-t, and s-t graphs for each car until t = t 2. What is the distance between the two cars when t = t 2?
Given: aA = 4m/s^2 , t 1 = 10s , aB = 5m/s 2 , vB = 25 m/s, = t 2 = 15s [d = 87.5 m]
Q (9)
Determine the height h on the wall to which the fire fighter can project water from the hose, if the angle θ is as specified and the speed of the water at the nozzle is vC.
Given: vC = 48 ft/s, h 1 =3ft, d = 30ft , θ = 40 deg , g = 32.2 ft/s 2 [h = 17. ft]
Q (10)
Measurements of a shot recorded on a videotape during a basketball game are shown. The ball passed through the hoop even though it barely cleared the hands of the player B who attempted to block it. Neglecting the size of the ball, determine the magnitude v (^) A of its initial velocity and the height h of the ball when it passes over player B.
Given: a = 7ft , b = 25ft , c = 5ft, d = 10ft, θ = 30deg , g = 32.2 ft/s 2 [ vA = 36.7ft/s, h = 11.489 ft]
At a given instant the train engine at E has speed (v) and acceleration (a) acting in the direction shown. Determine the rate of increase in the train's speed and the radius of curvature ρ of the path.
Given: v = 20 m/s , a = 14 m/s^2 , θ = 75deg
[at = 3.62 m/s 2 , a (^) n = 13,523 m/s^2 , ρ = 29.579 m]
Q (16)
The truck travels in a circular path having a radius (ρ) at a speed v 0. For a short distance from s = 0, its speed is increased by a (^) t = b*s. Determine its speed and the magnitude of its acceleration when it has moved a distance s = s 1. Given: ρ = 50m , s 1 = 10m , v 0 = 4m/s , b = 0.05/s 2 [v 1 = 4.583 m/s, a = 0.653 m/s^2 ]
Q (17)
The rod OA rotates counterclockwise with a constant angular velocity of θ'. Two pin-connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limaçon described by the equation r = (c − cos(θ)). Determine the speed of the slider blocks at the instant θ = θ 1. Given: θ' = 5 rad/s , b = 100 mm , c = 2 , θ 1 = 120 deg [v = 1.323 m/s] Q (18)
For a short time the bucket of the backhoe traces the path of the cardioid r = a(1 − cosθ). Determine the magnitudes of the velocity and acceleration of the bucket at θ = θ 1 if the boom is rotating with an angular velocity θ' and an angular acceleration θ'' at the instant shown.
Given: a = 25 ft , θ'= 2 rad/s , θ 1 = 120 deg , θ'' = 0.2 rad/s^2 [v = 86.6 ft/s , a = 266 ft/s 2 ]
Q (19)
A cameraman standing at A is following the movement of a race car, B, which is traveling around a curved track at constant speed v (^) B. Determine the angular rate at which the man must turn in order to keep the camera directed on the car at the instant θ = θ1.
Given: vB = 30 m/s , θ 1 = 30 deg , a = 20 m , b = 20 m , θ = θ 1 [θ' = 0.75 rad/ s]
Q (20)
The pin follows the path described by the equation r = a + bcosθ. At the instant θ = θ 1 , the angular velocity and angular acceleration are θ' and θ''. Determine the magnitudes of the pin’s velocity and acceleration at this instant. Neglect the size of the pin.
Given: a = 0.2m , b = 0.15m , θ 1 = 30 deg , θ' = 0.7 rad/s , θ'' = 0.5 rad/s 2
[v = 0.237 m/s, a = 0.278 m/s^2 ]
Q (21)
If the end of the cable at A is pulled down with speed v, determine the speed at which block B
Rises, if v = 2 m/s. [v (^) B = -1 m/s]
Q (22)
If the end of the cable at A is pulled down with speed v, determine the speed at which block B rises, if v = 2 m/s. [vB = - 0.5 m/s]
Q (23)
Determine the displacement of the block at B if A is pulled down a distance d = 4 m. [∆sB = - 2m]
