**Unit 8: Newton's Laws
Applications**

**Problem Set C**

**Overview:**

Problem Set C targets your ability to use the a combination of Newton's second law of motion and kinematic equations in order to analyze the motion of objects. Most all of the problems involve objects which are moving in the presence of friction. Thus, the coefficient of friction value will have to be used to determine the amount of friction force. Problems within the set fall into three basic types:

**Determination of the Acceleration**Some problems will request that you determine the acceleration value for an object. Acceleration is related to the net force experienced by an object which is in turn related to the value of individual forces. Therefore, the strategy for determining the acceleration involves using a free-body diagram and individual force values to determine the net force. Once found, the net force and the mass can be used to determine the acceleration value.

**Determination of an Individual Force Value**Some problems will request that you determine the value of an individual force such as an applied force or friction force. Individual force values are related to the net force value which is in turn related to the acceleration. Therefore, the strategy for determining an individual force value involves using the acceleration value to determine the net force value. Once found, a free-body diagram can be used to determine the value of the individual force from the net force value.

**Combining Kinematics and Newton's Second Law**In many problems, you will have to make connections between the acceleration of an object and other kinematic quantities such as time, displacement or velocity. In such instances, you will have to recognize that all kinematic quantities are related to the acceleration of an object by the kinematic equations:

**d = v**_{o }• t + 0.5 • a • t^{2}**v**_{f }= v_{o }+ a • t**v**_{f}^{2}= v_{o}^{2}+ 2 • a • d**d = [( v**_{o}+ v_{f }) / 2 ] • tThe above relationships are depicted in the following graphic:

There are at least seven skills or conceptual understandings which you must have to be successful on Problem Set C. They include ...

- ... an understanding of the distinction between mass and weight and the ability to determine one if given the other. Mass is the quantity of matter present in an object and is expressed in units of kilograms (kg). Weight is the amount of gravitational force acting upon an object and is expressed in units of Newtons (N).
- ... an understanding that the acceleration of an object which is moving with a constant velocity is 0 m/s/s. Regardless of the actual velocity value, if it is constant, then there is an acceleration of 0 m/s/s.
- ... an ability to read a verbal description of a physical situation and to represent that situation in terms of the individual forces acting in the situation. This ability is most commonly referred to as the ability to construct a free-body diagram. An understanding of the various force types is essential to the task of drawing a free-body diagram.
- ... an ability to use Newton's second law equation and the concept of net force in order to read and interpret a word story problem and to determine the acceleration of an object from stated values of the individual forces.
- ... an ability to use Newton's second law equation and the concept of net force in order to read and interpret a word story problem and to determine the unknown value of an individual force if mass and acceleration information are known.
- ... an understanding of the relationship between friction
force and the coefficient of friction and the ability to use the
equation F
_{frict}=*mu*• F_{norm}to determine one value from the other. In this equation,*mu*represents the coefficient of friction; it is a unit-less coefficient which is specific to the two surfaces which are sliding across each other. - ... an ability to use a kinematic equation to calculate a kinematic quantity from knowledge of three other kinematic quantities.

**Additional Readings/Study
Aids:**

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the understanding of the concepts and mathematics associated with these problems.

Determining Individual Force Values | Friction Force | Kinematic Equations

View Sample Problem Set.

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