Chap 4:Dynamics: Chap 4:Dynamics: Newton’s Law of Newton’s Law of

MotionMotion

No Homework next week

Solving Problems Involving Projectile Solving Problems Involving Projectile

MotionMotion

Example 3-7: A kicked football.

A football is kicked at an angle θ0 = 37.0° with a velocity of 20.0 m/s, as shown. Calculate (a) the maximum height, (b) the time of travel before the football hits the ground, (c) how far away it hits the ground, (d) the velocity vector at the maximum height, and (e) the acceleration vector at maximum height. Assume the ball leaves the foot at ground level, and ignore air resistance and rotation of the ball.

Relative velocityRelative velocityReference Frames

x

y

Earth=A=stationary reference frame

vBA vCA

bug car

vBA=velocity of the bug, B, relative to the earth , AvCA= velocity of the lemon car, C, relative to the earth, A

Relative velocityRelative velocity

x

y

Earth=A=stationary reference frameWe can add reference frames to the bug, B and to the Lemon car, C

vBAvCA

bugcar

vBA=velocity of the bug, B, relative to the earth , AVCA=-VAC

B CA

vBC=vBA-vCA

Or vBC=vBA+vAC

Notice how the outer subscripts on the right side of the equation correspond with those on the left, and how the inner subscripts are the same but do not exist on the left. Think of them as canceling.

Here, vWS is the velocity of the water in the shore frame, vBS is the velocity of the boat in the shore frame, and vBW is the velocity of the boat in the water frame.

Relative Velocity

The relationship between the three velocities is:

Relative Velocity

Example 3-14: Heading upstream.

A boat’s speed in still water is vBW = 1.85 m/s. If the boat is to travel directly across a river whose current has speed vWS = 1.20 m/s, at what upstream angle must the boat head?

Defining ForceDefining Force• Force = • Units:

Two kinds of forces:

A push or a pull

Newtons = kg.m/s2

Long range:

Contact:

Gravitational forceElectromagnetic force

Everything else

Whenever two objects touch

Measuring ForceMeasuring Force• We can use a calibrated spring scale

to measure force

• Force is a vector!

• Net Force = the vector sum of all forces acting on an object

Ah, but force is a Ah, but force is a vector.vector.

Images: http://library.thinkquest.org/25844/dynamics/images/ski.gif; http://www.mwit.ac.th/~physicslab/applet_04/physics_classroom/Class/vectors/u3l3b

Kinds of forces and Kinds of forces and directiondirection

Gravitational Force: (W) or Fg attraction between earth and an object.

Most Common Contact Forces:

Friction: (f)

Normal: (N)f

N

Tension: (T)

T

W

parallel to contact surface

Perpendicular to contact surface

along rope or cord or…

Forces on the

Newton’s First Law of Motion

This is Newton’s first law, which is often called 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.

0F

Newton’s First Law of Motion

Inertial reference frames:

Newton’s first law does not hold in every reference frame, such as a reference frame that is accelerating or rotating.

An inertial reference frame is one in which Newton’s first law is valid. This excludes rotating and accelerating frames.

How can we tell if we are in an inertial reference frame? By checking to see if Newton’s first law holds!

MassMass is the measure of inertia of an object; mass is a measure of an object’s resistance to change its velocity. In the SI system, mass is measured in kilograms.

Mass is not weight.

Mass is a property of an object. Weight is the force exerted on that object by gravity.

If you go to the Moon, whose gravitational acceleration is about 1/6 g, you will weigh much less. Your mass, however, will be the same.

EquilibriumEquilibrium• When the net force acting on an

object is zero, then it is in equilibrium.

and and

An object in motion remains in motionAnd An object at rest remains at restif the net external force acting on

the object is zero.a=0, v=constant

QuestionQuestion• A UFO is hovering, stationary, 2000m above

the earth. The net force on the UFO is• 1) zero• 2) due east• 3) upwards• 4) downwards

QuestionQuestionAn airplane is flying due East at a constant velocity of 590 mph. The net force on the airplane is1) zero2) due east3) upwards4) downwards

QuestionQuestionThe Earth travels around the Sun with a constant speed. The net force on the Earth isa)zerob)nonzero

QuestionQuestionA skydiver is falling toward the Earth at terminal velocity, that is, at constant speed. The net force on the skydiver is a) zerob) nonzero

Newton’s Second Law of MotionNewton’s second law is the relation between acceleration and force. Acceleration is proportional to force and inversely proportional to mass.

It takes a force to change either the direction or the speed of an object. More force means more acceleration; the same force exerted on a more massive object will yield less acceleration.

Newton’s Second Law of Motion

Force is a vector, so is true along each coordinate axis.

The unit of force in the SI system is the newton (N).

Note that the pound is a unit of force, not of mass, and can therefore be equated to Newtons but not to kilograms.

Newton’s Second Law of Motion

Example 4-2: Force to accelerate a fast car.

Estimate the net force needed to accelerate (a) a 1000-kg car at ½ g; (b) a 200-g apple at the same rate.

Example 4-3: Force to stop a car.

What average net force is required to bring a 1500-kg car to rest from a speed of 100 km/h within a distance of 55 m?