1. Chap 4:Dynamics: Newton’s Law of Motion
No Homework next week

2. Solving Problems Involving Projectile Motion
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.

3. Relative velocity Reference Frames y bug car vCA vBA x
Earth=A=stationary reference frame
vBA=velocity of the bug, B, relative to the earth , A
vCA= velocity of the lemon car, C, relative to the earth, A

4. Relative velocity
car y C A B
bug
vCA
vBA x
Earth=A=stationary reference frame
We can add reference frames to the bug, B and to the Lemon car, C
vBA=velocity of the bug, B, relative to the earth , A
VCA=-VAC
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.

5. Relative Velocity
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.
The relationship between the three velocities is:

6. 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?

7. Defining Force Two kinds of forces: Force = Units: A push or a pull
Newtons = kg.m/s2
Long range:
Contact:
Gravitational force
Electromagnetic force
Everything else
Whenever two objects touch

8. Measuring 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

9. Ah, but force is a vector.
Images:

10. Kinds of forces and direction
Gravitational Force: (W) or Fg attraction between earth and an object.
Forces on the
Most Common Contact Forces:
Friction: (f)
parallel to contact surface N
Normal: (N)
Perpendicular to contact surface T f
Tension: (T)
along rope or cord or… W

11. 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.
Figure 4-3. Caption: F represents the force applied by the person and Ffr represents the force of friction.

12. 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!

13. Mass
Mass 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.

14. Equilibrium
When the net force acting on an object is zero, then it is in equilibrium.
and
and
An object in motion remains in motion
And An object at rest remains at rest
if the net external force acting on the object is zero.
a=0, v=constant

15. Question
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

16. Question
An airplane is flying due East at a constant velocity of 590 mph. The net force on the airplane is
1) zero
2) due east
3) upwards
4) downwards

17. Question
The Earth travels around the Sun with a constant speed. The net force on the Earth is
zero
nonzero

18. Question
A skydiver is falling toward the Earth at terminal velocity, that is, at constant speed. The net force on the skydiver is
zero
nonzero

19. Newton’s Second Law of Motion
Newton’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.
Figure 4-5. Caption: The bobsled accelerates because the team exerts a force.

20. 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.

21. 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?
Figure 4-6.
4-2. Use Newton’s second law: acceleration is about 5 m/s2, so F is about 5000 N for the car and 1 N for the apple.
4-3. First, find the acceleration (assumed constant) from the initial and final speeds and the stopping distance; a = -7.1 m/s2. Then use Newton’s second law: F = -1.1 x 104 N.