Coupled Motion and Simultaneous Equations Re-Made Version

Coupled Motion Coupled motion problems are problems in which the movement of one object directly impacts the motion of another object. We have already briefly covered this topic when talking about pulleys.

Review Pulleys General steps to solving a coupled motion problem. – 1.) Draw free body diagrams for the two (or more) objects. – 2.) Write net force equations for each object. – 3.) Write out equations concerning any additional information we might have. – 4.) Solve algebraically.

Pulleys Example 1 Mass 1 has a mass of 200kg and mass 2 has a mass of 150kg. The two masses are attached by a massless, inextensible cord which goes over a frictionless, massless pulley. What will be the acceleration of mass 1?

Pulleys Example 1

Is it possible for the acceleration to be zero? If so, how? What would happen if we changed our assumptions about friction etc?

Pulleys Example 1 Where have you seen a pulley used before? Have you ever used one yourself? What is the use of something like this?

Pulleys Example 1 Imagine that m 1 is an elevator car, what would m 2 be? What would be the point of it?

Pulley Example 2 In this example we are combining the coupled motion of the pulley system with the complexity of a problem involving a slope. In this example we will ignore the force of friction between mass 2 and the slope.

Pulley Example 2 General steps to solving a coupled motion problem. – 1.) Draw free body diagrams for the two (or more) objects. – 2.) Write net force equations for each object. – 3.) Write out equations concerning any additional information we might have. – 4.) Solve algebraically.

Pulley Example 2 Mass 1 has a mass of 100kg, mass 2 has a mass of 125kg and the angle of the slope is 25 degrees. There is no friction between mass 2 and the slope. The two masses are connected by a massless, inextensible cord over a frictionless, massless pulley. What will be the acceleration of mass 1?

Pulley Example 2

What would need to be different in order for the acceleration to be going in the opposite direction?

Simultaneous Equations in General In each of the two examples shown above we first wrote net force diagrams for each object involved. In each case, we could not solve for the variable in question because some terms were unknown. The solution was reached in each case through two steps. – 1.) Using additional known information to restate a given variable in terms of another variable. (reducing the total number of variables) – 2.) Solve and replace: when both equations have a variable in common, solve one equation for that variable and replace the other instance of that variable with the newfound solution.