ChemPhys 173/273

Unit 8: 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 some 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 = vo • t + 0.5 • a • t2 vf = vo + a • t vf2 = vo2 + 2 • a • d d = [( vo + vf ) / 2 ] • t

The above relationships are depicted in the following graphic:

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

• Construction of Free-Body Diagrams

A free-body diagram depicts the type and direction of all the individual forces acting upon an object. Such diagrams are fundamental to mechanical analyses. A free-body diagram (affectionately known as an FBD) relates individual force values to a net force value. Representing forces in a diagram facilitates the task of determining the net force from individual forces or determining an individual force value from the net force value.

• 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 Fgrav) and mass are related by the equation: Fgrav = m • g.

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.

Forces | Mass and Weight | Newton's Second Law | Determining Acceleration | Kinematic Equations

View Sample Problem Set.

 Problem Description Audio Link 1 Determine vertical acceleration of a rocket if given its mass and upward force. 2 Determine the tension force in a rope which acts on a bucket if given the mass of the bucket and its vertical acceleration. 3 Combine a kinematic analysis with a force analysis to determine the final speed of a puck being accelerated across ice. 4 Determine the tension force in a cable which acts on an elevator if given the mass of the elevator and its vertical acceleration. 5 Combine a kinematic analysis with a force analysis to determine the final speed of a bucket if given the mass of the bucket and the tension force which acts upon it. 6 Determine the tension force in a rope which acts on a bucket if given the mass of the bucket and its vertical acceleration. 7 Combine a kinematic analysis with a force analysis to determine the displacement of a shopping cart if given the applied force and the mass of the cart. 8 Referring to the previous problem; repeat the analysis for the case of the shopping cart being loaded with a child of known weight. 9 Combine a kinematic analysis with a force analysis to determine the applied force exerted upon a ball during its slowing down period of time in the catcher's mitt. 10 Referring to the previous problem; determine the force applied on the glove by the ball. 11 Determine the horizontal acceleration of a crate if given the mass, applied force and friction force. 12 Determine the applied force exerted upon an object if given the mass, acceleration and the friction force which it encounters. 13 Determine the friction force acting upon an object if given its mass, acceleration and the applied force exerted upon it. 14 Combine a kinematic analysis with a force analysis to determine the displacement of a train if given the resistive force and some kinematic quantities. 15 Combine a kinematic analysis with Newton's second law to determine the net force acting upon an object of known mass.

Audio Help for Problem: 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15

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