AP Physics I.B

Newton’s Laws of Motion

4.1 Contact and field forces

4.2 Newton’s First Law (the law of inertia) – an object at rest will

remain at rest, or an object in motion at a constant velocity will continue at a constant velocity,

unless acted upon by a net force.

An unlikely trio – Mr. Evans, James Lovell and Sir Isaac Newton

Net force – the sum of all the forces acting on an object

If the net force is zero . . .

• The object is not moving or . . .

• The object is moving at a constant velocity therefore . . .

• The object is in equilibrium

A net force changes velocity

Inertia and mass

4.3 Newton’s Second Law

Some examples

The acceleration of an object is directly proportional to the net force

and inversely proportional to its mass.

The more familiar mathematical form (a new unit)

Net force is a vector in the same direction as the acceleration

Note! If an object accelerates then the net force is NOT zero. If

the net force is zero, then the object is moving with a constant

velocity or it is at rest.

Use free body diagrams to show all of the forces acting on an

object.

Ex. A barge has a mass of 8.0 EE 3 kg. A force of 1.00 EE 4 N pulls on the barge toward the left while a force of 7.5 EE 3 N pulls in the opposite direction. What is the acceleration of the barge?

Forces are vectors and may have components like any other

vectors.

p. 121: 4-7, 9

4. 0.041 s

6. 2900 N

Ex. Two groovy people pulling on a boat between two docks.

Ex. Find the displacement of the boat if the forces are maintained for 10.0 s and the boat has an initial velocity of 0.50 m/s.

4.5 Newton’s Third Law (highly misunderstood)

Newton’s Third Law – when one object exerts a force on a second object, the second object exerts a force that is equal in magnitude, but in the opposite direction to

that of the first

“This third law is confusing!”

Remember – Newton’s Third Law deals with two forces and two objects,

not two forces on one object.

Ex. Two skaters with masses of 75 kg and 45 kg respectively, face each other and push away. If the acceleration of the 75 kg skater is 0.73 m/s2, what is the acceleration of the 45 kg skater?

p. 121: 10-12, 14-16

10. You do – easy one.

12. Note, only acceleration is horizontal. Ans. 1.2 m/s2, left.

14. Find ax and ay. Use kinematics eqns. to find east and south components of displacement. Use Py. Th. to find displacement (0.78 m 22º S of E)

16. Hint: total distance traveled by tug and asteroid is 450 m. (64 s).

The Four (or is it three?) Fundamental Forces

• The (real) strong nuclear force (short range – holds the protons and neutrons of an atom together)

• Electromagnetic forces (10-2 times the strong force) – long range, holds atoms and molecules together

• Weak nuclear force (10-6 times the strong force) – short range, responsible for radioactive decay

• The (really weak) gravitational force (10-43 times the strong force) long range

4.7 The gravitational force – more to say about this later, but

for now . . .

The gravitational force is always attractive and never repulsive.

Mass and weight

Finding weight the hard way

Ponder the lunar explorer . . .

Now, a much simpler method

4.8 The Normal Force

“As opposed to the abnormal force” The force a surface exerts on an

object, perpendicular to the surface

Some instructive illustrations

Ex. The tension in a rope applies a force of 100.0 N upward to a box that has a mass of 10.0 kg. What is the acceleration of the box?

Apparent weight (how much your mother or father weighs)

Ex. A rope attached to a box (what else?) with a mass of 10.0 kg applies a force of 40.0 N above the horizontal so that the blocks slides across a frictionless floor. a) What is the horizontal acceleration of the box? b) What is the normal force on the box?

Ex. Two boxes with masses of 12.0 kg and 10.0 kg respectively are attached with a cord. A second cord pulls the 10.0 kg box to the right. a) Find the acceleration of each box and b) the tension in the cord between the boxes.

4.9 Static and Kinetic friction

Friction: we love it, we hate it

The nature of friction

Static friction and the crate

Maximum static friction

• Independent of area (if surfaces are hard and nondeformable)

• Directly proportional to the normal force

• Depends on the surfaces in contact

• The equation is . . .

Kinetic friction is

• Independent of area

• At slow speeds, independent of speed

• Directly proportional to the normal force and the coefficient of kinetic friction

• The second equation is . . . (hmmm, looks familiar . . .)

Ex. A student attaches a rope to a box and pulls with a force of 90.0 N at an angle of 30.0º with the horizontal. The box has a mass of 20.0 kg and the coefficient of kinetic friction between the bottom of the box and the floor is 0.500. Find the acceleration of the box.

Ex. A sled reaches the bottom of a hill with a velocity of 4.0 m/s. It slides horizontally along the snow until it comes to a stop. What is the distance the sled slides if the coefficient of kinetic friction between the snow and the sled is 0.0500?

4.10 Tension

“These forces are killing me, give me an Excedrin.”

The nature of tension

4.11 Equilibrium – the net force is zero

• So the sum of the horizontal forces is zero

• And the sum of the vertical forces is zero

Ex. A bright physics student finds her car stuck in the mud. She ties a strong rope to the back of the bumper and the other end to a tree. She pushes at the midpoint with maximum effort, which she estimates to be 3.0 EE 2 N. The car just begins to budge (from the sludge) when the rope makes an angle of 5.0º. With what force is the rope pulling on the car?

Ex. Find the tension in each cable supporting the 6.0 EE 2 N cat burglar.

Ex. A cruel and uncaring parent pulls backward on a swing, where a frightened child screams and cries uncontrollably. The ropes of the swing makes an angle of 36.0º with the vertical and the applied force of the parent makes an angle of 20.0º with the horizontal. The unfortunate child has a pitiful weight of 36.0 N. What is the tension in the ropes and the applied force of the abusive parent?

p. 123: 46, 50-54, 57

46. a) yours b) 1.67 EE 9 N

50. 4260 N

52. a) 57 600 N b) 20 600 N

54. 310 N

4.12 Non-equilibrium applications – net force not equal

to zero

Ex. A supertanker is pulled by two tugboats. The cables connecting the tugs and tanker are at an angle of 30.0º to the direction of the tanker’s motion. A drive force of 75.0 EE 3 N powers the tanker forward and the water exerts a resistance force of 40.0 EE 3 N in the opposite direction. Find the tension in the two cables if the acceleration of the tanker is 2.00 EE –3 m/s2.

Ex. A crate rests on the bed of a truck which is moving along a hill at an angle of 10.0º with the horizontal. The coefficient of static friction between the crate and the bed of the truck is 0.350. What is the minimum acceleration of the truck before the crate begins to slip?

Ex. Accelerating Blocks (a pretty typical AP problem)

p. 125: 64, 67-68, 70, 74, 76

64. a) 1100 N b) 650 N

68. 1.5 m/s2

70. a) 1.60 EE 3 N b) 2630 N

74. a) 4.5 m/s2 b) 1170 N

76. 2740 N