lecture problems on dynamics

8/10/2019 Lecture Problems on Dynamics

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The position of a particle along a straight line is given by s p = at 3 + bt 2 + ct. Determine itsmaximum acceleration and maximum velocity during the time interval t 0 t t f .


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Two particles A and B start from rest at the origin s = 0 and move along a straight line suchthat a A = (at b) and a B = (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.


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A stone A is dropped from rest down a well, and at time t 1 another stone B isdropped from rest. Determine the distance between the stones at a later time t 2.


4/37

Ball A is released from rest at height h 1 at the same time that a second ball B is thrownupward from a distance h 2 above the ground. If the balls pass one another at a height h3 determine the speed at which ball B was thrown upward.


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The acceleration of a particle along a straight line is defined by a p = b t + c. At t = 0, s p = sp 0and v p = v p0. When t = t 1 determine (a) the particle's position, (b) the total distance traveled,and (c) the velocity.


6/37

When two cars A and B are next to one another, they are travelling in the same direction withspeeds v A0 and v B0 respectively. If B maintains its constant speed, while A begins todecelerate at the rate a A , determine the distance d between the cars at the instant A stops.


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A particle travels along the curve from A to B in time t1. If it takes time t2 for it to go from A to C, determine its average velocity when it goes from B to C.


8/37

A particle travels along the curve from A to B in time t1. It takes time t2 for it to go fromB to C and then time t3 to go from C to D. Determine its average speed when it goes

from A to D.


9/37

A car traveling along the straight portions of the road has the velocities indicated in thefigure when it arrives at points A, B, and C. If it takes time t AB to go from A to B, andthen time t bc to go from B to C, determine the average acceleration between points Aand B and between points A and C.


10/37

When a rocket reaches altitude h1 it begins to travel along the parabolic path (y h 1 )2 = b x.If the component of velocity in the vertical direction is constant at vy = v0, determine themagnitudes of the rockets velocity and acceleration when it reaches altitude h2.


11/37

The fireman standing on the ladder directs the flow of water from his hose to the fire atB. Determine the velocity of the water at A if it is observed that the hose is held at angle.


12/37

Show that if a projectile is fired at an angle from the horizontal with an initial velocityv 0 , the maximum range the projectile can travel is given by Rmax = v 0 2/ g, where g is theacceleration of gravity. What is the angle for this condition?


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14/37

Determine the height h on the wall to which the firefighter can project water from thehose, if the angle is as specified and the speed of the water at the nozzle is v C .


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16/37

A ball bounces on the inclined plane such that it rebounds perpendicular to the inclinewith a velocity v A. Determine the distance R to where it strikes the plane at B.


17/37

The man stands a distance d from the wall and throws a ball at it with a speed v 0. Determinethe angle at which he should release the ball so that it strikes the wall at the highest point possible. What is this height? The room has a ceiling height h2.


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A car is travelling along a circular curve that has radius . If its speed is v and the speed isincreasing uniformly at rate at, determine the magnitude of its acceleration at this

instant.


19/37

A particle is moving along a curved path at a constant speed v. The radii ofcurvature of the path at points P and P' are and ', respectively. If it takes the particle time t to go from P to P', determine the acceleration of the particle atP and P'.


20/37

The automobile is originally at rest at s = 0. If its speed is increased by dv/dt =bt 2 , determine the magnitudes of its velocity and acceleration when t = t 1.


21/37

A car moves along a circular track of radius such that its speed for ashort period of time 0 t t 2 , is v = b t + c t 2. Determine the magnitudeof its acceleration when t = t 1. How far has it traveled at time t 1?


22/37

At a given instant the jet plane has speed v and acceleration a acting in the directionsshown. Determine the rate of increase in the planes speed and the radius of curvature of the path.


23/37

The Ferris wheel turns such that the speed of the passengers is increased by a t = bt. If thewheel starts from rest when = 0 , determine the magnitudes of the velocity andacceleration of the passengers when the wheel turns = 1.


24/37

The car travels around the portion of a circular track having a radius r such that when it isat point A it has a velocity v1 which is increasing at the rate of d v/dt = ks. Determine themagnitudes of its velocity and acceleration when it has traveled three-fourths the wayaround the track.


25/37

The two particles A and B start at the origin O and travel in opposite directions along thecircular path at constant speeds V A and V B respectively. Determine at t = t 1 =2 sec, (a) thedisplacement along the path of each particle, (b) the position vector to each particle, and(c) the shortest distance between the particles.


26/37

If the end of the cable at A is pulled down with speed v, determine the speed at whichblock B rises.


27/37

If the end of the cable at A is pulled down with speed v, determine the speed at whichblock B rises.


28/37

Determine the constant speed at which the cable at A must be drawn in by the motor inorder to hoist the load at B a distance d in a time t.


29/37

Determine the time needed for the load at B to attain speed v, starting from rest, if thecable is drawn into the motor with acceleration a.


30/37

The girl at C stands near the edge of the pier and pulls in the rope horizontally atconstant speed Vc (6 ft/s ). Determine how fast the boat approaches the pier at theinstant the rope length AB is d (50 ft). Note : h = 8 ft.


31/37

The man pulls the boy up to the tree limb C by walking backward. If he starts from restwhen x a = 0 and moves backward with constant acceleration a A (0.2 m/s 2 ), determine thespeed of the boy at the instant y b = y B1 (4 m) . Neglect the size of the limb. When x A = 0, y B =h = 8 m, so that A and B are coincident, i.e., the rope is 2 h long.


32/37

The boy A is moving in a straight line away from the building at a constant speed v A. Theboy C throws the ball B horizontally when A is at d. At what speed must C throw the ball sothat A can catch it? Also determine the relative speed of the ball with respect to boy A atthe instant the catch is made.


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34/37

Two planes, A and B, are flying at the same altitude. If their velocities are v A and v B suchthat the angle between their straight- line courses is , determine the velocity of plane Bwith respect to plane A.


35/37

A man jumps from a balloon which is risingvertically at a constant rate of 2mps at anelevation of 1415m above the ground. Theman waits 10 seconds before pulling theparachute cord. The parachute decelerateshim at a uniform rate of 6 mps^2 until aspeed of 6 mps is attained. The man thendescends to the ground at this constantspeed. How long will it take him to reach theground from the time he jumps from theballoon?


36/37

The rectilinear motion of a particle isgoverned by the equation : a = 6t-4, where ais in mps^2 and t is in seconds. When t=0,the acceleration of the particle is 4mps^2 tothe left. During the interval from t= 2s to to=4s, the displacement of the particle is 20mto the right.Determine : a) Initial velocity of the particle,b) the velocity of the particle at the end ofthe displacement period and c) the positionof the particle when t=3s


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lecture problems on dynamics

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