Newton’s Laws of Motion 1. An object won’t change its motion unless a force acts on it: Inertia 2. Force is needed to change the state of motion: F = ma 3. When you push on something, it pushes back on you.

Qualitatively describe the system A block (m2) slides on a frictionless table pulled by a string attached to a mass (m1) hanging over the side. What is the acceleration of the system? a2 m2 What is the relationship between the magnitudes of the acceleration of the two blocks? A) a1 = a2 B) a1 < a2 C) a1 > a2 a1 m1 2

What is the net force on the system? A block (m2) slides on a frictionless table pulled by a string attached to a mass (m1) hanging over the side. What is the acceleration of the system? a2 a = F/m m2 M1 = 2 kg M2 = 3 kg a1 m1 3

What is the acceleration of the system now? M1 = 2 kg M2 = 3 kg

Train Example A locomotive pulls 10 freight cars Each car is 30,000 kg The locomotive is 50,000 kg The acceleration of the train is 0.05 m/s2 What is the force the locomotive provides? What is the force of each coupler between cars?

Qualitatively Describe the System 1st You are traveling on an elevator up the Sears tower. As you near the top floor and are slowing down, your acceleration A) is upward B) is downward C) is zero V a mg N

Qualitatively Describe the System 1st You are traveling on an elevator up the Sears tower, and you are standing on a bathroom scale that measures N. As you near the top floor and are slowing down, the Normal force is. A) More than your usual weight B) Less than your usual weight C) Your usual weight a mg N

Friction Force: Obeys Newton’s Laws Always opposes relative motion Contact force This force will depend on the material surfaces sliding and the normal force between the surfaces. Two kinds Kinetic: sliding taking place Static: no sliding  rolling

Static and Kinetic Frictional Forces Static friction opposes the impending relative motion between two objects. Kinetic friction opposes the relative sliding motion motions that actually does occur. is called the coefficient of kinetic friction.

Normal Force Normal force is the force perpendicular to the surface that prevents the objects from passing through each other. Direction: Perpendicular to surface and out Magnitude: As much or little required keep objects separate.

Static and Kinetic Frictional Forces When the two surfaces are not sliding across one another the friction is called static friction.

Static and Kinetic Frictional Forces The magnitude of the static frictional force can have any value from zero up to a maximum value. is called the coefficient of static friction.

Note that the magnitude of the frictional force does not depend on the contact area of the surfaces.

Friction Summary Static friction Kinetic friction f ≤ sn Magnitude can vary up to limit (sn) Kinetic friction f = kn

Example 2 kg box slides across a table. Coefficient of friction is 0.32 What is the frictional force?

Concept Check A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives. If the truck moves with constant accelerating to the left as shown, which of the following diagrams best describes the static frictional force acting on the box: S a A B C

What do you think? m2 m2 Case 1 (No Friction) Case 2 (With Friction) m1 m1 In which case is the acceleration of the blocks biggest? A) Case 1 B) Case 2 C) Same 17

What is the force on the front box? 10 kg 5 kg

Circular Motion and Gravity

Body moving in a circle

Body moving in a circle Velocity changes direction What direction is the change?

Circular motion

Body moving in a circle

Body moving in a circle Velocity changes toward the center of the circle (curve) Centripetal acceleration Velocity is always changing for circular motion There is always an acceleration

Centripetal Acceleration Acceleration = Dv/Dt = (vf – vi)/(tf - ti) No change in |v| Change in direction Velocity tangent to circle Acceleration toward center of circle a is constantly changing

Centripetal Acceleration a = v2/r Newton’s Second Law F = ma Centripetal force F = mv2/r

Centripetal Force Equations tell the size of the acceleration or the force What produces the force?

Centripetal Force: F = mv2/r The force can come from Friction Rope gravity

Centripetal Acceleration A car drives around a 20 m radius circle at a speed 10 m/s. What is the acceleration of the car? What is the force on the car?