Thus far, you have seen the situation where the forces are balanced either for an object that is motionless or an object that is moving at a constant velocity. If, though, the force applied is larger than the friction force, the object will accelerate. These situations are no different from any of your other kinematics problems that deal with forces. A step-by-step approach is best.
Click through the tabs below to see the steps to solve when the problems start with forces and ask about the motion of the object and then the steps to solve when the problems start with the motion as ask you to quantify the forces or find the coefficient of friction.
Working "Forwards"
Working "Backwards"
To go from the forces involved to describing the motion of the object, follow these steps.
| Quantify Forces | Indentify and quantify all the forces involved. Use your knowledge of weight, normal force, force of friction, and applied forces. \(\small\mathsf{ \overrightarrow{W} = m \overrightarrow{g} }\) |
| Find the Net Force | Orient your coordinates so there is motion in one dimension. Find the net force in the direction of motion. \(\small\mathsf{ \overrightarrow{F_{net}} = \sum \overrightarrow{F} }\) |
| Apply Newton's Second Law | Use the net force in the Newton's Second Law equation to find the acceleration of the object. \(\small\mathsf{ \overrightarrow{F}_{net} = m \overrightarrow{a} }\) |
| Use Kinematic Equations to Solve | If something other than acceleration is asked for, use the appropriate kinematics equation to solve for the missing value. \(\mathsf{\overrightarrow{a} = \frac{\overrightarrow{v}_f - \overrightarrow{v}_i}{t} }\) |
Question
How is this different from what you've done before?
Nothing really, except that you may not be given the value of the force of friction, but the information in order to find it. Then, you would proceed as you have in previous problem solving.
To go from how the object is moving back to the force of friction and coefficient of friction, use this process.
| Use Kinematic Equations to Solve | If something other than acceleration is asked for, use the appropriate kinematics equation to solve for the missing value. \(\mathsf{\overrightarrow{a} = \frac{\overrightarrow{v}_f - \overrightarrow{v}_i}{t} }\) |
| Apply Newton's Second Law | Use the net force in the Newton's Second Law equation to find the acceleration of the object. \(\small\mathsf{ \overrightarrow{F}_{net} = m \overrightarrow{a} }\) |
| Find the Net Force | Orient your coordinates so there is motion in one one dimension. Find the net force in the direction of motion. \(\small\mathsf{ \overrightarrow{F_{net}} = \sum \overrightarrow{F} }\) |
| Quantify Forces & Find Coefficient of Friction | Indentify and quantify all the forces involved. Use your knowledge of weight, normal force, force of friction, and applied forces. \(\small\mathsf{ \overrightarrow{W} = m \overrightarrow{g} }\) |
Question
Will the coefficient of friction ever be negative?
No, the coefficient will always be positive. In the coefficient of friction equation, you are using magnitudes of the forces involved, because it is a ratio between the strengths of the forces involved.
