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Homework Help: Mechanics Help Needed

  1. Mar 27, 2006 #1
    MECHANICS - Help Needed!!!

    Hi guys, ive got this tutorial sheet to do, and im pretty stuck on it, i don't really need the answers i can do them myself i just need somewhere to start on the questions and and idea of what to do. Help much appreciated!

    1. A car starts from rest and moves along a straight road with acceleration 9ms-2. After 5 seconds another car starts from rest at the same point and moves along the same road with acceleration 16ms-2.
    • How long after the first car starts will the second car catch it up?
    • What are the velocities of the two cars when they first meet?
    • The second car now stops accelerating and travels at constant velocity. How many more seconds after the first meeting will they meet again?

    2. Particle A of mass 2 kg and particle B of mass 5 kg are connected by a light inextensible string, which passes over a smooth fixed pulley at the top of a smooth plane inclined at 30° to the horizontal. A is on the plane and B is hanging vertically. At t = 0 both particles are moving with speed 4ms-1 with A moving downwards and B moving upwards and A is 1 m from the top of the plane.
    • Calculate when A reaches the top of the plane.

    3. A constant horizontal force of 30 N is applied to a particle of mass 5 kg which moves up a smooth plane inclined at 20° to the horizontal. The particle is initially at rest. Find the velocity and the work done by the force after t seconds.

    4. Particle A has mass 5kg and particle B has mass 1kg. They lie on a smooth horizontal surface and the line joining them is normal to a vertical wall with B closer to the wall. The coefficient of restitution between the two particles is Ep = 0.8 and the coefficient of restitution between B and the wall is Ew = 0.5. Initially A is at rest and B is moving towards A at a speed of 2m/s. B collides first with A and then with the wall.
    • Will it collide with A again?
    • What is the final velocity of A?
     
    Last edited: Mar 27, 2006
  2. jcsd
  3. Mar 27, 2006 #2

    daniel_i_l

    User Avatar
    Gold Member

    People won't like to help you if you don't show some work!
     
  4. Mar 27, 2006 #3
    The kinematics problems are easy, you need to use the three kinematical equations, that's all.

    For the mechanics problems, you should refer to http://www.csupomona.edu/~ajm/materials/n2.html [Broken]. IT has a superb guide to solving them.

    But, yes, show us some work if you want our help on the specific problems.
    :)
     
    Last edited by a moderator: May 2, 2017
  5. Mar 28, 2006 #4
    Q1

    So far ive got:

    for car A: a= 9, u=0, v=?, t=(?+5), s=?
    for car B: a= 16, u=0, v=?, t=?, s=?

    Find distance car A travels after 5 seconds, ie
    s = ut + 1/2 * a * t^2
    s = 0*5 + 1/2*9*5^2 = 112.5 m
    I know that sb = sa + 112.5 m

    Find velocity of car A after 5 seconds,
    v^2 = u^2 + 2as
    v^2 = 0^2 + 2*9*112.5
    v^2 = 2000 => v=SQRT[2000] => 44.72 ms-1

    Now i need to find the time it takes for car B to reach car A if it starts 5 seconds after car A. So i need to find t and most probably v & s.

    Im thinking the following:
    using: s = ut + 1/2 * a * t^2 in sb = sa + 112.5 m
    so,0.5*16*(t)^2 = 0.5*9*(t+5)^2 + 112.5

    If I get t I should be able to find everything else for now.

    Thanks, rob
     
    Last edited: Mar 28, 2006
  6. Mar 28, 2006 #5
    1. when the second car got the same speed with the first one, it can catch up the first one. by using v=u+at, you get all the things.

    2. by conservation of energy: KEi+PEi=KEf+PEf, you can get the distance traveled by A along the inclined plane just before it came to instantaneous rest. then, the problem can be done as if two particles are at rest initally.

    3. by F=ma, a can be found, then by v=u+at and s=u+1/2at^2, done!!

    4. for such problem, recalling the conservation of momentum and thinking about what do the system include.
     
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