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Forces and Circular Motion

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What is an object’s natural motion?

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Newton’s 1 st Law and Inertia An object at rest remains at rest or an object in motion with constant velocity stays in motion at constant velocity unless acted upon by an unbalanced net force.

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Friction Everyday motion slows down and stops due to friction. Imagine if friction were decreased until it was no longer there. What would happen to the motion of an object?

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Curling “…other players on the team "sweep" in front of the curling stone…reduces the friction between stone and ice, which causes the stone to travel further...”

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Inertia and Motion An object’s tendency to remain at rest or move at constant velocity. An object’s tendency to resist any attempt to change its velocity.

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Newton’s 2 nd Law The net external force acting on an object causes the object to accelerate. The direction of the acceleration is in the direction of the net force. “Σ” (Greek letter sigma) means “sum.”

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Definitions Force: push or pull on an object having magnitude and direction; may be either a contact or long-range force (N). Mass: the amount of matter of an object (kg). Acceleration: the rate which velocity is changing (m/s 2 ).

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Example: Single Force An object with a mass of 5 kg is acted upon by a force of 10 newtons (N) to the right. What is the object’s acceleration?

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Example: Single Force

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Example: Multiple Forces An object laying on a frictionless floor with a mass of 2 kg is acted upon by an applied force of 8 newtons (N) to the right. What is the object’s acceleration?

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The net force is 8 N directed to the right. The acceleration is also directed to the right and has a magnitude of 8 N/2 kg = 4 m/s 2.

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Force Conditions No force: a = 0. → No motion or motion at constant velocity. Net force = 0: a = 0. → No motion or motion at constant velocity. Net force ≠ 0 (unbalanced forces): a ≠ 0. → Velocity changes.

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Newton’s 3 rd Law For every force there is an equal-in-magnitude and oppositely directed force. The force pair is of the same type (gravitational, electrical, normal, etc.) The force pair acts on different objects.

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Force Pairs Action ForceReaction Force Cue ball exerting a contact force on a billiard ball. Billiard ball exerting an opposite contact force on cue ball. An apple’s weight.The gravitational force on Earth due to the force exerted by the apple. Frictional force on a foot by the floor to move the walker across the floor. The foot exerts a frictional force on the floor. A fan exerts a force to move air molecules forward. The air molecules exert a force back on to the fan. Notice in each case, the force pairs are the same type, magnitude, and oppositely directed.

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Newton's 2nd Law Newton's 3rd Law Newton's 1st Law

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Free-Body Diagrams and the 2 nd Law To draw a free body diagram, isolate the object(s) of interest. Account for all of the external forces that act on it. The net force is the vector sum of all forces acting on the object. Use Newton’s 2 nd Law to find the magnitude and direction of acceleration. The acceleration will determine the motion of the object due to all of the forces acting on it.

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Subsequent Motion Find the acceleration using Newton’s 2 nd Law. Use the kinematics equations to find what is being asked.

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Example A particle is traveling west at a constant speed of 25.0 m/s. Suddenly, a force of 15.0 N acts on it, bringing it to a stop in a distance of 62.5 m. A) What is the direction of the force? B) What is its mass?

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Example AA B A B F app Objects A and B slide along a frictionless surface. Write their equations of motion.

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Example AA B A B F app Objects A and B slide along frictionless surfaces. Write their equations of motion.

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Example AA B A B F app Objects A and B slide along surfaces with friction. Write their equations of motion.

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3 rd Law Revisited: Apple on Table ForceTypeObjectDirection Actiongravitationalappledown ReactiongravitationalEarthup ForceTypeObjectDirection Actionnormalappleup Reactionnormaltabledown FNFN W

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Example A ball is falling through the air and experiences air drag. Draw the free-body diagram for the ball. Identify its reaction forces.

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Example A bucket of water with total mass 2 kg is accelerated upward with an acceleration of 0.5 m/s 2. Find the tension in the rope.

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Example A 200-N box is pulled to the right with a force of 50 N at constant velocity. Calculate its mass. What is the magnitude of the frictional force? Calculate the coefficient of friction.

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Example A box starting at 5 m/s to the right slides to a stop after traveling 10 meters. What is the magnitude and direction of the frictional force?

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Example While driving, Susie stops suddenly to avoid a chicken crossing the road. She notices that the stack of physics books she has in her back seat slid forward off the seat. Why did this happen?

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Geometry of Circles

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Circular Motion A type of accelerated motion where the force directed to the center of the trajectory is related to the object’s tangential velocity and its distance from the axis of rotation.

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The velocity vector is tangent to the circle; the centripetal force and centripetal acceleration are directed toward center of the circle.

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Period

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Centripetal Force The centripetal force is a description of the net force that points toward the center of the circle to keep the object moving at constant speed. (gravitational force, tension, etc.) This force could be a vector sum of multiple forces or a component of a single force. “Centripetal” means “center seeking.”

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What kind of force is the centripetal force?

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Example

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Circular Motion in Space

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Centrifugal Effect The sensation of being thrown away from the center of rotation due to being in an accelerated frame of reference. In the absence of the force, the motion of an object is along a straight line at constant speed (velocity). The centrifugal force is a pseudoforce; it is an effect of inertia.

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