C. Newton’s Laws & Forces AP Physics I. Mechanics C. Newton’s Laws & Forces AP Physics

Intro to Forces Why do objects move? Force: a push or pull on an object Forces cause objects to accelerate (speed up, slow down, change direction) Forces are VECTORS!

Force Diagrams A book rests on a table. Draw the forces on the book:

Force Diagrams vs. Free Body Diagrams

Diagram Practice Draw a force diagram and a free body diagram for a monkey hanging by one arm from a tree branch:

Newton’s Laws of Motion A long, long time ago, this philosopher/ scientist guy Aristotle noticed that moving things around him would eventually come to rest. He believed that the natural state was at rest, and that forces were needed to keep things moving.

Newton’s Laws of Motion Eventually, this other scientist guy, Galileo, decided that things in motion (like the moon) remained in motion, and if there was no friction, then everything else would remain in motion, too! Newton’s First Law of Motion (aka the Law of Inertia): Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.

Newton’s Laws of Motion So, an object keeps doing what it’s doing until a force is applied. Inertia: the tendency of an object to maintain its state of rest or uniform motion; laziness Mass: (kg) the quantity of matter in an object, or the measure of inertia of an object Weight: the gravitational force on an object

Newton’s 1st Law Practice A robot is accidentally fired out of a spaceship . Diagram the forces acting on the robot after he has been launched from the ship. Describe the motion of the robot after he has been launched.

Net Force Net force is the SUM of the forces on an object If the net force is zero, the forces are balanced and the object does not accelerate.

3. Newton’s Second Law of Motion What if an object’s velocity does change? Acceleration is affected by Force on the object and the object’s mass OR: Force is measured in Newtons, mass in kilograms, and acceleration in m/s2

Working 2nd Law Problems Identify the system being accelerated Define a coordinate system Identify forces by drawing a force or free body diagram Explicitly write ΣF=ma Replace ΣF with the actual forces in your diagram (separate eqns for x and y motion) Solve for unknowns, substitute, & calculate

Newton’s Second Law Practice Moe, Larry, and Curly push on a 752-kg boat that floats next to a dock. They each exert an 80.5-N force parallel to the dock. What is the acceleration of the boat if they all push in the same direction? What is the acceleration of the boat if Larry and Curly push in the opposite direction of Moe’s push?

More Practice 3. In a grocery store, you push a 14.5 kg cart with a force of 12.0 N. If the cart starts at rest, how far does it move in 3.00 seconds?

Types of Forces: Gravity Acceleration from gravity = g Force of gravity:

Normal Force Normal Force – acts perpendicular to surface in contact with the object The normal force is only as large as the force of the object on the surface

Normal Force Derive an expression for the normal force of a box on a flat table

Normal Force Derive an expression for the normal force of a box sitting on a ramp

Normal Force Derive the normal force for the box in the picture below. Ignore friction.

Friction Frictional forces oppose motion

Friction Sliding friction/Kinetic friction: Static friction: a) b) K = coefficient of kinetic friction (depends on the surface – p. 90) FN = normal force Static friction: Greater than kinetic friction

Friction Practice A 10-kg box rests on a ramp that is lying flat. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.30. What is the maximum horizontal force that can be applied to the box before it begins to slide? What force is necessary to keep the box sliding at constant velocity?

More Forces Tension: a pulling force from ropes/strings; assume they have a mass of 0 kg

Tension Practice A 1,500 kg crate hangs from a crane cable. What is the tension in the cable when the crate is motionless? (assume the cable has zero mass) Suppose the crane accelerates the crate upward at 1.2 m/s/s. What is the tension in the cable now?

Spring Forces (Hooke’s Law) The force exerted by a spring is proportional to how far the spring is stretched F = -kx F: force exerted by the spring (N) k: force constant of the spring (N/m or N/cm) x: displacement from equilibrium (unstretched) position (m or cm)

Hooke’s Law Practice A 1.50 kg object hangs motionless from a spring with a force constant of k = 250 N/m. How far is the spring stretched from its equilibrium length?

4. Newton’s Third Law of Motion Where do forces come from? For every action force, there is an equal and opposite reaction force. Forces act on different objects

Practice You rest an empty glass on a table Identify the forces on the glass with an FBD Are the forces equal and opposite? Are the forces an action-reaction pair? Why/why not?

Practice Problem A force of magnitude 7.50 N pushes three boxes as shown. Find the acceleration of the system.

Practice Part 2 A force of magnitude 7.50 N pushes three boxes as shown. Find the force that box 2 exerts on box 3.

Connected Objects A 5.0 kg object is connected to a 10.0 kg object by a string. If a pulling force of 20 N is applied to the 5.0 kg object: Assume a frictionless surface What is the acceleration of the system? What is the tension in the connecting string?

Pulleys Pulleys are MAGIC!!! Pulleys bend the line of action of the force of gravity without affecting tension Pulleys are MAGIC!!! Pulleys have no mass, no friction, and no effect on tension

Pulley Practice Derive an expression for the acceleration due to gravity of the system, AND for the tension in the string

Inclines To resolve forces on an object on an incline, choose the simplest frame of reference – tilt axes with incline! Gravity always directed toward center of Earth Normal force always perpendicular to surface

Sample Problem How long will it take a 1.0 kg block initially at rest to slide down a frictionless 20.0 m long ramp that is at a 15 degree angle with the horizontal? (hint: use forces to find acceleration!)

Friction and Inclines A 10-kg box rests on a ramp that is lying flat. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.30. What is the friction force between the box and the ramp if: The ramp is at a 25 degree angle? The ramp is at a 45 degree angle?