Results 1 to 4 of 4

Math Help - Three problems related to Newton's Laws of Motion

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    40

    Three problems related to Newton's Laws of Motion

    1. A simple accelerometer consists of a ball of non-zero mass attached to the end of a light, inextensible string as shown in the diagram below. If the angle between the string and the vertical direction is and the constant gravitational field is g, what is the acceleration of the device?




    ------------------------------------------------------------------------

    2. A small block of mass m is placed on top of a frictionless table top. A light, inextensible string is threaded through a hole in the centre of the table and attached to the small block. The other end of the string is attach a large block of mass M which hangs below the table as shown. The small block is then made to move in a circle with radius r from the hole such that the large block remains suspended in equilibrium below. What is the expression for v, the speed of the small block given that there is a constant gravitational field, g.



    ---------------------------------------------------------------------

    3. A ball of mass m is attached to the end of a piece of string. The ball is then given a kick such that it moves in a vertical circle of radius, r. If there is a constant, gravitational field g what is the downwards tension in the string when the ball is at the top of the circle given that at the top of the circle the ball is moving with a speed v?




    Any help is greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello jpatrie
    Quote Originally Posted by jpatrie View Post
    1. A simple accelerometer consists of a ball of non-zero mass attached to the end of a light, inextensible string as shown in the diagram below. If the angle between the string and the vertical direction is and the constant gravitational field is g, what is the acceleration of the device?
    There is no diagram attached, and we would need to know the velocity of the particle and the length of the string in order to get the acceleration towards the centre.

    The acceleration perpendicular to the string (along a tangent to the circle) is given by resolving in this direction, and is simply g\sin\theta.


    2. A small block of mass m is placed on top of a frictionless table top. A light, inextensible string is threaded through a hole in the centre of the table and attached to the small block. The other end of the string is attach a large block of mass M which hangs below the table as shown. The small block is then made to move in a circle with radius r from the hole such that the large block remains suspended in equilibrium below. What is the expression for v, the speed of the small block given that there is a constant gravitational field, g.
    The tension in the string is Mg, since the lower mass is in equilibrium. So if we resolve along the string for the upper mass:

    Mg = \frac{mv^2}{r}

    \Rightarrow v = \sqrt{\frac{Mgr}{m}}

    3. A ball of mass m is attached to the end of a piece of string. The ball is then given a kick such that it moves in a vertical circle of radius, r. If there is a constant, gravitational field g what is the downwards tension in the string when the ball is at the top of the circle given that at the top of the circle the ball is moving with a speed v?
    Resolve vertically downwards:

    T + mg = \frac{mv^2}{r}

    \Rightarrow T = \frac{mv^2}{r}-mg

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
    40
    Here's the picture for question 1.



    There is no other information given, such as velocity and the length of the string. sine theta unfortunately was not the answer.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,628
    Thanks
    430
    Quote Originally Posted by jpatrie View Post
    Here's the picture for question 1.



    There is no other information given, such as velocity and the length of the string. sine theta unfortunately was not the answer.
    grandad did not say the acceleration was \sin{\theta}. this is what he stated ...

    ... and is simply .
    ...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mechanics question - newton's laws, please help :(?
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: April 27th 2010, 02:50 AM
  2. [SOLVED] Newton's Laws of Motion
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: November 6th 2009, 11:04 AM
  3. forces and application of Newton's laws
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: November 23rd 2008, 03:35 PM
  4. newton's fundamental laws
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: April 20th 2008, 07:50 AM
  5. Hammer problem: Newton's Laws
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: July 25th 2007, 06:25 AM

Search Tags


/mathhelpforum @mathhelpforum