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**NEWTON'S LAWS OF MOTION There are three of them.**

They explain the motion of an object as resulting from the forces acting on the object.

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**What is a force? An interaction between TWO objects.**

For example, pushes and pulls are forces. We must be careful to think about a force as acting on one object from (or due to ) another object.

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**Adding Forces Examples: + = + =**

Forces are vectors (They have both magnitude and direction) and so add as follows: In one dimension, note direction using a + or – sign then add like scalar quantities (regular numbers with no direction associated with them) Examples: = = +3 N +3 N +6 N 0 N +3 N -3 N

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Newton’s First Law Consider a body on which no net force acts. If the body is at rest, it will remain at rest. If the body is moving with constant velocity, it will continue to do so.

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**“Consider a body on which no net force acts…”**

An important word here is NET. It means “total” or “sum of all” (forces). It is not that no force at all can act on the body. It is just that all the forces must add to zero (cancel each other out).

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**Under this condition (no net force acting on the body):**

If the body is at rest, it will remain at rest. If the body is moving with constant velocity, it will continue to do so. What if the body is moving with a velocity which is not constant? Why isn’t this discussed?

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**Newton’s Second Law in One Dimension**

Commonly shortened to “F=ma”. Correctly, it is : Only forces which act on that object affect the acceleration of the object. Forces exert by the object on another object do not.

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**Using Newton’s 2nd Law to Solve Problems**

Identify all forces acting on the object -Pushes or Pulls Frictional forces -Tension in a string -Gravitational Force (or weight = mg where g is 9.8 m/s2) - “Normal forces” (one object touching another). Draw a “Freebody Diagram” -draw the object, show all forces acting on that object as vectors pointing in the correct direction. Show the direction of the acceleration. Chose a coordinate system. Translate the freebody diagram into an algebraic expression based on Newton’s second law.

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Consider an elevator moving downward and speeding up with an acceleration of 2 m/s2. The mass of the elevator is 100 kg. Ignore air resistance. What is the tension in the cable? Identify Forces: Tension in cable, weight of the elevator Draw freebody diagram Chose coordinate system: Let up be the +y direction and down –y. Then : Translate the FBD into an algebraic expression. T-W = m(-a) so T-(100 kg)(9.8 m/s2) = (100 kg)(-2 m/s2) v T W=Fg earthelevator. a Note: No negative sign

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Newton’s Third Law Whenever one object (object A) exerts a force on another object (object B), the second object exerts a force back on the first object. These forces are ALWAYS equal in magnitude (but they point in opposite directions). Such forces are called “Newton’s third law force pairs”. Not all forces that are equal and opposite are third law force pairs. The forces are on different bodies, so do not add to zero.

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