Ask Experts Questions for FREE Help !
Ask
    illinihawks's Avatar
    illinihawks Posts: 10, Reputation: 1
    New Member
    		  
    #1

    Mar 22, 2011, 08:47 PM
    Momentum + Pendelum Question
    Hi, I need help with a question on a practice exam. I got the first two questions, but I have no clue on where to start as to figuring out how far the cart has moved. Anyone have any suggestions? Thanks!

    A cart of mass M = 9 kg rolls without friction on a horizontal surface. It is attached through a freely pivoting initially-horizontal massless rod of length L to a ball of mass m = 3 kg. The system is initially at rest when the ball is released. The pendulum swings down and to the left, and at the bottom of its swing the ball is observed to have a velocity of 3.5 m/sec to the left.



    What is the speed of the cart when the ball is at the bottom? 1.17 m/s
    What is the length L of the pendulum? 83 m
    How far to the right has the cart moved, when the ball is at the bottom??
    jcaron2's Avatar
    jcaron2 Posts: 986, Reputation: 204
    Senior Member
    		  
    #2

    Mar 22, 2011, 09:22 PM
    Here are a couple different ways to think about it:

    1) You figured out that the cart will be moving to the right at 1/3 the speed of the pendulum moving to the left (because of the 3kg/9kg mass ratio). But there was nothing magic about the fact that the pendulum happened to be at the bottom of its arc. What if the pendulum had only dropped 45 degrees? The horizontal component of its speed would be smaller than at 90 degrees, but the cart would still be traveling to the right at 1/3 of that speed (regardless of what it was). Hence, even though the leftward speed of the pendulum changes throughout it's flight, the rightward speed of the cart is always 1/3 as much. Hence, no matter how the speed of the pendulum varied, the cart traveled to the right only 1/3 as far as the pendulum traveled left.

    2) Keep in mind that the horizontal center of mass of the system will not have changed. Since the 3 kg mass has moved 83 cm to the left, how far has the 9 kg cart moved to the right to compensate? 1/3 that far, right?
    illinihawks's Avatar
    illinihawks Posts: 10, Reputation: 1
    New Member
    		  
    #3

    Mar 23, 2011, 12:32 PM
    Comment on jcaron2's post
    The answer according to the practice test is L/4 or 1/4 of the length of the pendulum. I see how L/3 is possible but how does L/4 work?
    jcaron2's Avatar
    jcaron2 Posts: 986, Reputation: 204
    Senior Member
    		  
    #4

    Mar 23, 2011, 01:53 PM
    Oops. Sorry about that. :o

    I forgot that since that pendulum is tied to the cart, the pendulum's horizontal travel isn't L, it's L-x, where x is the distance that the cart moved.

    Let's try that again:





    Now substituting the first equation into the second:
Not your question? Ask your question View similar questions
 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

Why does the Pendelum gets so heavy at times? It's like someone is pulling from below [ 3 Answers ]

Momentum and Colissions. Question: stationary life raft of mass 160kg is carrying t [ 1 Answers ]

A stationary life raft of mass 160kg is carrying two survivors with masses of 55kg and 72kg, respectively. They dive off the raft at the same instant, the 55kg person East at 4.4m/s and the 72kg person North at 4.2m/s. At what speed and in what direction does the raft start to move?

Crystal Pendelum? [ 13 Answers ]

I am not sure if this makes any sense, but I heard if you hold a pendulum on a chain or string and it moves in circles w/out you moving your wrist or fingers it means that there are spirits,ghost,or evil in your home? I have done this several times I honestly don't move it intentianly, I ask it to...

Question on Momentum [ 2 Answers ]

A ball of mass m1, moving with speed v, collides with a stationary ball of mass m2. The first ball rebounds with speed 1/5 v, whereas the other moves off with speed 4/5 v in the direction of the original velocity of the first ball. 1. Use the conservation of momentum to show that (m1/m2) = 2/3

Pendelum swings in circles and makes direct line to the word. What is the difference [ 1 Answers ]

I use a pendelum and a board that has yes on one side and no on the other. When I ask questions that require a yes/no answer it will usually go in circles, but sometimes it will make a line from the middle directly to the word. What is the difference between the circles over the word and the...

View more questions Search