Forces and Circular Motion

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# Forces and Circular Motion - PowerPoint PPT Presentation

Forces and Circular Motion. What is an object’s natural motion?. 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. Friction.

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### What is an object’s natural motion?

Newton’s 1st 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.
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?
Curling
• 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...”
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.
Newton’s 2nd 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.”
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/s2).
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?
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?
• The acceleration is 2 m/s2 to the right.
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?

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/s2.

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.
Newton’s 3rd 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.
Force Pairs

Notice in each case, the force pairs are the same type, magnitude, and oppositely directed.

Newton's 1st Law

Newton's 2nd Law

Newton's 3rd Law

Free-Body Diagrams and the 2nd 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 2nd 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.
Subsequent Motion
• Find the acceleration using Newton’s 2nd Law.
• Use the kinematics equations to find what is being asked.
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?

Writing Equations from
• Isolate the object of interest.
• Draw a free-body diagram.
Example

Objects A and B slide along a frictionless surface. Write their equations of motion.

AA

Fapp

A

B

B

Example

B

B

AA

Fapp

A

Objects A and B slide along frictionless surfaces. Write their equations of motion.

Example

B

B

AA

Fapp

A

Objects A and B slide along surfaces with friction. Write their equations of motion.

Example

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

Example

A bucket of water with total mass 2 kg is accelerated upward with an acceleration of 0.5 m/s2. Find the tension in the rope.

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.

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?

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?

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.

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

Period
• The time it takes for a moving object to complete one revolution or cycle: T
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.”
Example
• If a ball has a mass of 0.25 kg is swung at the end of a string of 1.0 m at a speed of 4 m/s, calculate the centripetal acceleration and the centripetal force.
Example
• The same ball (0.25 kg) at the end of a string that is 2.0 meters long now makes 5 revolutions in 10 seconds. How much tension is in the string?
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.