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Calculation of the force (Basic)

  1. Feb 27, 2013 #1
    1. The problem statement, all variables and given/known data

    Calculate the force acting on a 5.0 kg mass which accelerates for 3. 0 s. During this time its velocity changes from 2.5 m s^-1 east to 17.5 m s^-1 west.

    2. Relevant equations

    F=ma

    3. The attempt at a solution

    Not sure what the acceleration is, i am only accustomed to getting a specific value e.g. 2.5 ms -1, how do i work out the acceleration, do i do:

    17.5 - 2.5 = 15.0 ms west then

    5.0 kg/15.0 ms west.

    P.S. I started preliminary physics 1 week ago, and this is one homework question i cannot do, Thanks in advance
     
  2. jcsd
  3. Feb 27, 2013 #2
    Hello RobinsoKo

    What's the definition of acceleration? (it will be average acceleration in this case).
     
  4. Feb 27, 2013 #3
    The time rate of change of velocity.

    Final velocity - Initial Velocity over 3 seconds?
     
  5. Feb 27, 2013 #4
    Yeah, but you need to pay attention to the "east" and "west" bits of the problem. Velocity is a vector--it has both a magnitude AND direction. You can't ignore the direction! To help you out, say the mass is moving on the x-axis. Then think of east as the +x direction and west as the -x direction (or vice versa). So what do you think the average acceleration is then?
     
  6. Feb 27, 2013 #5
    I worked out the acceleration to be 15ms^-1 over 3 = 5 ms-1?

    So therefore the force is 25n west?
     
  7. Feb 27, 2013 #6
    Not quite. You didn't take into account the direction. Remember, it's the CHANGE in velocity over 3 seconds. If you were going 2.5 m/s to the east and ended up going 17.5 m/s to the west you actually switched directions, right?

    What you did was found the acceleration if you were going 2.5 m/s to the west and accelerated to 17.5 m/s to the west. So there was no directional change. You're missing the change from 2.5 m/s to the east to 2.5 m/s to the west!

    You have to take the direction into account! Can you figure out how?
     
  8. Feb 27, 2013 #7
    I have no idea, and this is first week into physics i am hopeless :(
     
  9. Feb 27, 2013 #8
    Let's just look at a separate problem to sort of guide you there:

    Say your initial velocity is 2 m/s to the west and your final velocity is 2 m/s to the east. You accelerate from your initial velocity to your final velocity in 1 second. What's your acceleration?

    Let me give you an idea of what's happening.

    1. First you're going 2 m/s to the west. Let this arrow represent that: <--
    2. After a bit (0.5 seconds to be exact) you're going 0 m/s. Why? Because you're changing directions from the west to the east! So in the transition from going to the west to going to the east, you'll have to go 0 m/s at *some* point, right? It's like turning around in your car.
    3. Now you're going 2 m/s to the east, after 1 second. Let this arrow represent that: -->

    Can you tell me what your acceleration was?
     
  10. Feb 27, 2013 #9
    2ms^2 east
     
  11. Feb 27, 2013 #10
    No. What are you using for your change in velocity?
     
  12. Feb 27, 2013 #11
    Initial - 2m/s east
    Final - 2m/s west

    Wait.. Is it zero?
     
  13. Feb 27, 2013 #12
    No, why would it be zero? Again, you're failing to understand the relevance of direction. It's not only about magnitude. If you're driving your car down the highway at 60km/hr and you turn around, you'll have to first slow down and then speed back up to 60km/hr in the other direction. You're accelerating the whole time!

    Let's set up the situation on an axis:


    WEST --------------------------------------------------EAST

    So first you're going 2m/s to the west:

    <---- 2m/s

    WEST --------------------------------------------------EAST


    And at the end you're going 2m/s to the east:

    ----> 2m/s
    WEST --------------------------------------------------EAST



    I don't know about you, but this looks a lot like the x-axis to me. So let's rename WEST and EAST to -x and +x:

    -x <--------------------------------------------------> +x

    So at first you're going 2m/s to the west. But now west is the negative x direction. So instead of having to say "2m/s to the west" each time let's just say your initial velocity is -2m/s. At the end you're going 2m/s to the east. But now the east is the positive x direction. So let's say your final velocity is +2m/s.

    Now, given that acceleration is equal to

    change in velocity/change in time = (final velocity - initial velocity)/change in time, tell me what your acceleration should be. Show your work.

    A final, visual way to think about it is in terms of the arrows (vectors):

    What arrow do I have to add to:

    <----

    to get

    ----> ? Hint: <---- + ----> = 0.

    You probably haven't covered vectors yet, but you should sort of have an intuitive idea.
     
    Last edited: Feb 27, 2013
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