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HNRS 227 Lecture #2 Chapter 2 Motion presented by Prof. Geller

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Recall from Chapter 1 zUnits of length, mass and time zMetric Prefixes zDensity and its units zThe Scientific Method

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Main Concepts for 2 zSpeed vs. Velocity zAcceleration zForce zFalling Objects zNewton’s Laws of Motion zMomentum zCircular Motion zUniversal Law of Gravity

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Speed and Velocity zSpeed ydistance traveled in a unit of time ya scalar quantity zVelocity yspeed and direction ya vector quantity

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Questions for Thought zWhat is the difference between speed and velocity? zSpeed is a scalar, and velocity is a vector. Speed is the magnitude of the velocity vector.

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Questions for Thought zWhat is acceleration? zAcceleration is the ratio of the change in velocity per change in time. Acceleration can also be viewed as the derivative (remember calculus?) of the velocity.

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Questions for Thought zAn insect inside a bus flies from the back toward the front at 5.0 miles/hour. The bus is moving in a straight line at 50 miles/hour. What is the speed of the insect? zThe speed of the insect relative to the ground is the 50.0 mi/hr of the bus plus the 5.0 mi/hr of the insect relative to the bus for a total of 55 mi/hr. Relative to the bus alone the speed of the insect is 5.0 mi/hr.

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Force zDefinition of force ysomething that causes a change in the motion of an object xa push or pull xan electric, magnetic, gravitational effect xa vector quantity zNet force - Resultant Force

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Inertia zDefining Inertia ytendency of an object to remain in its current state of motion xthe more massive the more inertia xthink of stopping a car vs. truck

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Acceleration Due to Gravity zDirection of acceleration due to gravity ydirected to center of Earth zThink: scalar or vector? ya vector quantity zWhy? yhas magnitude and direction

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Generalized Motion zMotion can be viewed as a combination of movements yvertical component xtypically gravitational acceleration yhorizontal component xsome force from muscle, gunpowder, etc.

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Question for Thought zWhat happens to the velocity and acceleration of an object in free fall? zAssuming a short free fall distance near the earth’s surface, the velocity increases downward as the acceleration remains constant.

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Question for Thought zIn the equation d=1/2*a*t 2, if a is 9.8 meters per second per second and t is in seconds, what is the unit of d? zMeters.

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Question for Thought zWhat is inertia? zInertia is the property of matter that an object will remain in unchanging motion or at rest in the absence of an unbalanced force.

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Question for Thought zWhere does the unit s 2 (or concept of “square second”) come from? zAcceleration is change in velocity per change in time, with units of (m/s)/s. When the fraction is simplified, you get meters per second squared. The “seconds squared” indicates that something that changes in time is changing in time, that is, the ratio of change in distance per unit of time is changing in time.

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Question for Thought zNeglecting air resistance, what are the forces acting on a bullet that has left the barrel of a rifle? zAfter it leaves the rifle barrel, the force of gravity acting straight down is the only force acting on the bullet.

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Question for Thought zHow does the force of gravity on a ball change as a ball is thrown straight up in the air? zThe force of gravity on the ball remains constant because the force of gravity is independent of the motion of the object near the surface of the earth.

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Sample Question zAn object falls from a bridge and hits the water 2.5 seconds later. yA) With what velocity did it strike the water? yB) What is the average velocity during the fall? yC) How high is the bridge?

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Sample Answer

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Newton’s Laws of Motion zNewton’s First Law of Motion ybody at rest tends to stay at rest and body in uniform motion will stay in straight line uniform motion unless acted upon by an outside force zNewton’s Second Law of Motion ythe acceleration of a body is proportional to the force being applied F = m*a

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Newton’s Laws of Motion zNewton’s Third Law of Motion yfor every force there is an equal and opposite force (action and reaction)

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Question for Thought zHow can there ever be an unbalanced force on an object if every action has an equal and opposite reaction? The action and reaction forces are between two objects that are interacting. An unbalanced force occurs on a single object as the result of one or more interactions with other objects.

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Question B 4 (page 46) zWhat force would an asphalt road have to be to give a 6,000 kilogram truck in order to accelerate it at 2.2 meters per second per second?

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Question B 4 (page 46)

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Momentum zBy definition momentum is the product of y mass and velocity zConservation of momentum ytotal momentum of a closed system remains constant

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Question for Thought Is it possible for a small car to have the same momentum as a large truck? Explain. Yes, the small car would have to be moving with a much higher velocity, but it can have the same momentum since momentum is mass times velocity.

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Question B 9 (p. 46) zA 30.0 kilogram shell is fired from a 2,000 kilogram cannon with a velocity of 500 meters per second. What will be the velocity of the cannon?

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B 9 (p. 46)

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Circular Motion zCentripetal Force yusually gravity, but can be any force (such as the pull of a string) that forces an object into circular motion zCentrifugal Force ya fictitious force, an apparent outward force felt by an object in circular motion zAcceleration in circular motion is a = v 2 / r ytherefore in circular motion F = mv 2 / r

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Sample Question zWhat is the maximum speed at which a 1000 kilogram car can move around a curve with a radius of 30.0 meters if the tires provide a maximum frictional force of 2700 Newtons? (1 Newton is a unit of force needed to accelerate a 1 kilogram mass 1 meter per second per second.)

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Sample Question

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Universal Law of Gravity zNewton’s Universal Law of Gravitational Attraction yevery object is attracted to every other object ythe force is proportional to masses and inversely proportional to the distance squared –F = (G*m*M) / r 2

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A Problem of Very Little Attraction zWhat is the gravitational force between two 100 kilogram people separated by 1 meter?

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Really just a little Use the formula for the force of gravity: F = G*m*M / r 2 where G = 6.67 x Nm 2 /kg 2 and m = 100 kg and M = 100 kg and r = 1 ======================= Then F = 6.67 x Nm 2 /kg 2 *100 kg*100 kg / (1 meter) 2 F = 6.67 x N

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