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INSTRUCTIONAL OBJECTIVES Students will • Use F = ma equation to compute force, mass, and acceleration NATIONAL MATHEMATICS STANDARDS Algebra • Generalize patterns using explicitly defined and recursively defined variables • Interpret representations of functions of two variables • Approximate and interpret rates of change from graphical and numerical data Problem Solving • Solve problems that arise in mathematics and in other contexts • Apply and adapt a variety of appropriate strategies to solve problems NATIONAL SCIENCE CONTENT STANDARD B Motions and forces • Objects change their motion only when a net force is applied. Laws of motion are used to calculate precisely the effects of forces on the motion of objects. The magnitude of the change in motion can be calculated using the relationship F = ma, which is independent of the nature of the force. Whenever one object exerts force on another, a force equal in magnitude and opposite in direction is exerted on the first object. INTRODUCTION “Force is equal to the change in momentum (mv) per change in time. For a constant mass, force equals mass times acceleration (∑F = ma).” For a nonconstant mass, force equals the change in momentum with change in time F = D (mv ) . For a Dt constant mass, force equals mass times the change in velocity with respect to time F = m(v1 −v0 ) = m Dv . (t −t ) Dt Newton’s Second Law of Motion 10 Acceleration is the change in velocity with respect to time. Therefore, another expression of Newton’s second law for a constant mass is force equals mass times the acceleration (F = ma). Note that force, acceleration, momen- tum, and velocity are all vector quantities; that is, they have both magnitude and direction. The net force acting on an object is the sum of all of the forces acting on that object. Any sum is denoted by the Greek letter sigma, ∑F. Fo=rmexaample, if F , F , and F are all acting on an object, then the net force acting xx123 F = F + F + F . Newton’s second law of motion F = ma can also be broken down into ∑ ∑Fx =max ∑Fy =may ∑Fz =maz on the object is the following three component equations: 1 2 3 (∑ ) where Fx is the force in the x-direction and so on. Force and acceleration are vector quantities and mass is a scalar quantity. Vector quantities have both magnitude and direction whereas scalars have only magnitude. A force can be written as follows: F = (3i + 2j) N, which means the force is applied three units in the positive Pushing the Envelope: A NASA Guide to Engines 49 PHYSICS AND MATHPDF Image | NASA Guide to Engines
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