Download PH 306 PROCEDURES for Solving Net Force Problems

PH 306 PROCEDURES for Solving Net Force Problems
Your textbook provides an excellent guide for solving net force problems. Elements of the method are
given on pp. 124, 128 and 132 examples of using the method are provided. A wise student will study the
method and examples carefully. Details regarding important parts of the method are given below.
As in any problem, list the givens and the goal.
Draw a picture of the situation and indicate the directions of the acceleration and velocity.
Isolate the object of interest and sketch the forces
Use a point to represent the object and vectors to represent the forces acting on the object of interest. Label
the forces using standard symbols: W for weight, N for normal, T for tension, f for friction. There's
generally not a need for other labels. Use subscripts when there is more than one of a particular type of
force in a problem.
If there is more than one object of interest in a problem, then you would need to draw a force diagram for
each object. However, we won't get to that until a later chapter.
Choose a convenient coordinate system
An inconvenient choice can ruin your day by making the algebra much more complicated than it need be or
by leading you to an incorrect solution. Generally follow this rule: Select one of the positive axes to be in
the direction of the acceleration. This way, the acceleration will be positive and will have one component
that is 0. In some problems--inclined planes, for example--this will mean that your axes won't be horizontal
and vertical. Instead, they'll be parallel and perpendicular to the plane.
Resolve the forces into components
Many net force problems are 2-dimensional. So you'll need to determine the components of the forces.
Remember to do this symbolically. As always, numbers aren't substituted until the last step.
Apply Newton's Second Law to each coordinate direction
Newton's Second Law may be stated in compact form as
. The net force and the acceleration
are both vectors. Be sure to use the 'net' subscript to distinguish the net force from the generic force
symbol. In component form:
In writing the Fnet equations, treat the individual force symbols as representing magnitudes (positive
numbers) and explicitly indicate direction by placing a + or - sign in front of the force symbol. For
example, for an object resting on a horizontal table with the positive direction defined to be up, the net
force equation in the vertical direction is Fnet,y = N - W. In this equation, both N and W represent positive
numbers. The - sign indicates that the direction of the weight is down.
Solving the problem
Setting up the problem as described above is the physics. The rest is mostly algebra. Having written your
net force equations, solve them for the unknown(s). Apply any specific conditions, constraints, or
assumptions that are needed to solve the problem. Examples include equality of tension forces exerted by
the same string on different objects, frictionless surfaces, massless and inextensible (unstretchable) strings,
and massless and frictionless pulleys. State such conditions and make it clear how you apply them. Once
you've solved algebraically for the unknown, substitute given values with units and reduce.
Checking your answer
As always, check that the signs, units, and values in your final answer make sense.