Unit Dynamics Module Applications of Newton s Three Laws page 1 of 2 Solving Problems Using Newton s Laws Ropes and Tension Tension is a stretching or straining force for example the force applied to a rope An ideal rope doesn t stretch can only pull and is massless If a rope is massless the net force on it is zero The force on one end of the rope is equal in magnitude and opposite in direction to the force on the other end of the rope Pulleys change the direction but not the magnitude of forces on ropes Many common devices use forces on strings and ropes When you pull on one end of a string it can pull something on the other end Tension is a stretching or straining force The greater the tension the greater the force on the string In order to simplify physics problems ropes are often assumed to be ideal ropes An ideal rope doesn t stretch can only pull and is massless If a rope is massless then the net force on it is zero The force on one finger by the rope is equal in magnitude and opposite in direction to the force on the other end of the rope A heavy cart m1 is loaded with bricks A rope connects the cart to a bucket of bricks m2 that is hanging over a cliff The rope runs over a frictionless pulley Assume that the cart is on a frictionless surface and that the rope is an ideal rope You would like to know the acceleration of m1 Because m2 will move downward as a result of gravity the whole system will move A pulley changes the direction but not the magnitude of forces on ropes The magnitude of the acceleration of m1 and m2 will be the same Apply Newton s second law to the two masses in the system First focus on m1 You are interested in the x direction since the motion of m1 is horizontal The tension T is the only horizontal force on the cart Next focus on m2 You are only interested in its vertical motion In the upward direction m2 experiences a tension T and in the downward direction m2 experiences the force of gravity Notice that the acceleration of the bucket is in the negative y direction You now have a system of two equations and two unknowns T and a www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1843 doc rev 03 29 2001 Unit Dynamics Module Applications of Newton s Three Laws page 2 of 2 Solving Problems Using Newton s Laws Ropes and Tension Subtracting the two equations allows you to cancel the variable T You can easily solve for the acceleration of the masses Notice that the acceleration is less than g This must be true if the cart is moving to the right and the bucket is moving downward www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1843 doc rev 03 29 2001
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