ChemPhys 173/273

Unit 8: Newton's Laws of Motion

Problem Set A

Overview:

Problem Set A targets your understanding of Newton's second law of motion and of the distinction between mass and weight. There are a few routine problems and several more complicated multistep problems. The mathematical rigor of the problem set is not high; most student difficulties will lie in the area of conceptual misunderstandings. There are at least four skills needed to be successful on Problem Set A:

• A strong conceptual understanding of the relationship and distinction between mass and weight. 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.

• An ability to manipulate the Fnet = m•a equation in order to solve for an unknown quantity. Additionally, a student will need to understand the meaning of net force as the vector sum of all individual forces acting upon an object. If all individual forces are known, the net force can be calculated by simply adding the individual forces while paying attention to their vector nature. An up force and a down force can be added by assigning the down force a negative value. A right force and a left force can be added by assigning the left force a negative value.

• An ability to use the Fnet = m•a equation as a guide to thinking about how alterations in the mass of or net force acting upon an object will subsequently effect the acceleration of the object. Rather than using the equation as an algebraic recipe for problem-solving, one will have to use it to think about how a twofold, threefold or X-fold increase or decrease in one of the variables would effect the acceleration value.

• An ability to use a kinematic equation to solve for an unknown kinematic quantity. Kinematics pertains to a description of the motion of an object and focuses on questions of how far?, how fast?, how much time? and with what acceleration? To assist in answering such questions four kinematic equations were presented in the 1-Dimensional Kinematics unit:
•   d = vo • t + 0.5 • a • t2 vf = vo + a • t vf2 = vo2 + 2 • a • d d = [( vo + vf ) / 2 ] • t

Newton's laws and kinematics share one of these questions in common: with what acceleration? The acceleration of the Fnet = m•a equation is the same acceleration of the kinematic equations. Common tasks thus involve i) using kinematics information to determine an acceleration and then using the acceleration in a Newton's laws analysis, or ii) using force and mass information to determine an acceleration value and then using the acceleration in a kinematic analysis.

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in accomplishing the above tasks.

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

View Sample Problem Set.

 Problem Description Audio Link 1 Routine calculation of net force from mass and acceleration. 2 Routine calculation of acceleration from mass and net force. 3 Routine calculation of mass from net force and acceleration. 4 Use of equations as a guide to thinking about how alterations in net force effect the acceleration. 5 Use of equations as a guide to thinking about how alterations in mass effect the acceleration. 6 Use of equations as a guide to thinking about how alterations in net force and mass effect the acceleration. 7 Use of equations as a guide to thinking about how alterations in net force and mass effect the acceleration. 8 Routine calculation of the mass of an object from knowledge of its weight. 9 Routine calculation of the weight of an object from knowledge of its mass. 10 Routine calculation of the mass of an object from knowledge of its weight. 11 Routine calculation of the weight of an object on a different planet from knowledge of its mass. 12 Routine calculation of the acceleration from the net force and the weight of the object. 13 Determination of the net force from knowledge of the individual forces acting upon the object. 14 Referring to the previous problem; determination of the horizontal acceleration from the net force (previous problem) and the weight of the object. 15 Determination of the net force from knowledge of the individual forces acting upon the object. 16 Referring to the previous problem; determination of the horizontal acceleration from the net force (previous problem) and the weight of the object. 17 Calculation of the vertical acceleration of an object from knowledge of the individual forces acting upon the object (including the weight of the object). 18 Determination of the vertical acceleration of a skydiver from knowledge of the air resistance force and the mass of the skydiver; requires the construction of a free-body diagram. 19 Determination of the horizontal acceleration of a skidding car from knowledge of the friction forces and the mass of the car; requires the construction of a free-body diagram. 20 Referring to the previous problem; determination of the skidding distance using the acceleration from the previous problem.

Audio Help for Problem: 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16 || 17 || 18 || 19 || 20

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