**Unit 2: Newton's Laws of
Motion**

**Problem Set B**

**Overview:**

Problem Set B targets your ability to use Newton's laws and kinematic equations to analyze physical situations involving forces and motion. Problems within the set fall into one of following three categories:

**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 problems #10-#14, you will have to make connections between the accleration 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**_{i}•t + 0.5•a•t^{2}**v**_{f}= v_{i}+ a•t**v**_{f}^{2}= v_{i}^{2}+ 2•a•d

The above relationships are depicted in the following graphic:

Four additional understandings will contribute to your success on Problem Set B. These include:

**Construction of Free-Body Diagrams**A free-body diagram is a diagram which uses vector arrows to show the types and directions of all forces acting upon an object. Each force vector is labeled with a symbol according to its type; common symbols include F

_{grav}, F_{norm}, F_{frict}, F_{app}, F_{tens}and F_{air}. The free-body diagram is the starting point for all F_{net}= m•a analysis problems. It allows a student to make the mathematical connection between the values of all individual forces and the net force. To construct a free-body diagram, simply read the problem description and visualize the physical situation it describes. Using the list of all the types of forces, decide which of the forces act upon the object and in which direction. For each force acting upon the object, draw an arrow in the given direction and label it according to type.**Newton's First Law of Motion**If an object is either at rest or in motion with a constant velocity, then that object is not accelerating. The lack of acceleration indicates that all the forces acting upon the object are balanced. That is to say, the net force upon the object is 0 Newtons. The analysis of such objects with constant velocity motion will involve the understanding that the sum of all upward forces equal the sum of all downward forces. Similarly, the sum of all rightward forces equal the sum of all leftward forces.

**Mass-Weight Relationship**Mass is a quantity which is dependent upon the amount of matter present within an object; it is measured in kilograms and is independent of location. Weight, on the other hand, is the force of gravity which acts upon an object. Since gravitational forces vary with location, the weight of an object on the Earth's surface is different than its weight on the moon. Being a force, weight is expressed in the metric unit as Newtons. Every location in the universe is characterized by a gravitational constant represented by the symbol

**g**(sometimes referred to as the acceleration of gravity). Weight (or F_{grav}) and mass are related by the equation:**F**._{grav}= m • g**Friction Forces**An object which is moving (or event

*attempting*to move) across a surface encounters a force of friction. Friction force results from the two surfaces being pressed together closely, causing intermolecular attractive forces between molecules of different surfaces. As such, friction depends upon the nature of the two surfaces and upon the degree to which they are pressed together. The friction force can be calculated using the equation:**F**._{frict}= µ • F_{norm}The symbol µ (pronounced

*mu*ˆ) represents of the coefficient of friction and will be different for different surfaces.

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