To learn physics, science students need to solve lots of physics homework problems. Many physics students find learning to solve physics force problems difficult. Physics students should follow a general problem solving procedure and also apply the steps specific to physics force problems.
- Draw a free body diagram.
- Divide all forces and accelerations into components.
- Apply Newton's second law.
- Solve the resulting equations for unknown quantities
Draw a Free Body Diagram
After completely reading a problem and drawing a picture to visualize the problem, physics students should always start force problems with a free body diagram. The free body diagram should isolate the object of interest in the problem and show the forces acting on that object. The free body diagram should not show forces exerted by the object of interest on some other object.
For example the free body diagram of a skier sliding down a slope would show the forces on the skier but not the forces the skier exerts on the surroundings. This free body diagram shows the normal force of the slope on the skier, but not the force of the skier compressing the snow.
Physics students should remember that accelerations and velocities are not forces. Show velocities and accelerations relevant to the problem on a physical drawing of the problem or near the free body diagram but not as part of the free body diagram.
Divide Forces and Accelerations into Components
Forces and accelerations are vectors. Therefore students solving 2 or 3 dimensional problems must divide these vector quantities into components parallel to the x, y, and z coordinate axes.
Choose the axes to minimize the number of vectors that must be divided into components. For example on inclined plane problems, such as the skier, it is easier to define the x axis parallel to the slope and the y axis perpendicular. Draw the coordinate axes on the free body diagram. Then draw and define the relevant angles between the axes and the force vectors. Write the equations expressing the components of each vector parallel to the coordinate axes.
Apply Newton's Second Law
Newton's second law states that the vector sum of all the forces, Fnet, acting on an object equals the mass, m, of the object multiplied by the vector acceleration, a, of the object.
Fnet = ma
If the object of interest in the problem is not accelerating, then a is zero. The equation becomes Newton's first law and simplifies to:
Fnet = 0
Write down the Newton's second law equations for each direction in the problem. For example in a two dimensional problem, there will be two equations. One for the x components of Fnet and a and another for the y components.
Solve the Newton's Second Law Equations
Now substitute the known quantities into the equations. Solve the equations for the unknown quantities.
To have a solvable problem, there should be as many equations as unknown quantities. Newton's second law will give two equations for a two dimensional problem, so there can be two unknown quantities in the problem. Solve the two equations simultaneously for two unknowns. Three dimensional problems will have three equations, and one dimensional problems will only have one equation.
Finally for all physics problems, check the solution to see if it makes sense physically and ensure that the units are correct.
Following these steps can help physics students learn to solve even the most difficult force problems in their homework assignments.
Further Reading
Knight, R.D., Physics for Scientists and Engineers, Pearson, 2004.
Examples of Free Body Diagrams
Paul A. Heckert - I have a Ph.D. in astrophysics, over 30 years experience teaching physics and astronomy, and over 60 published research articles.
