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INSTRUCTIONAL OBJECTIVES Students will • Use rate equation to compute distance and time • Evaluate acceleration as a change in velocity over time 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 “Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it.” Another way of stating Newton’s first law of motion is that when the sum of the forces ∑F (net force) act- ing on a body is zero, its acceleration a is zero. Any (a) (b) (c) time t, which is acceleration. This law has two parts: (1) An object at rest stays at rest unless acted upon by an unbalanced force. (2) An object in motion stays in motion unless acted upon by an unbalanced force. This law is normally taken as the definition of inertia. Inertia is the property of matter that makes an object stay in motion if it is moving or remain motionless if it is not moving. For example, a coin placed on a note card on a jar can be used to demonstrate the first law. In part (a) of the fig- ure above, Fn + (–Fw) = 0, where Fw is the force due to the coin’s weight and Fn is the normal force. This means that the net force acting on the coin is zero. If one flicks the card from left to right in part (b), the coin will fall into the jar. If the card is flicked fast enough, there is little friction between the coin and the card. Thus, since no force was applied directly to the coin, the coin does not accelerate horizontally. With the card no longer in place, there is an unbalanced force Fw acting on the coin in part (c). Newton’s First Law of Motion Fw Fn sum is denoted by the Greek letter sigma, ∑F. Symbolically, this is written as “if, ∑F = 0 then a = 0.” This therefore implies, Dvt = 0 where Dvt is the ratio of the change of velocity v to the change in Pushing the Envelope: A NASA Guide to Engines 47 PHYSICS AND MATHPDF Image | NASA Guide to Engines
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