Download Newton`s Second Law NOTES

Sections 4.4 What Forces Do and 4.5 Newton’s Second Law NOTES
AP Physics I
If something has a net constant force applied to it, experiment shows that it
moves at a constant acceleration. For a force F, say, the velocity -vs- time
curve might look something like:
velocity
slope4 = 4a
apply force 4F
slope3 = 3a
slope2 = 2a
slope1 = a
apply force 3F
apply force 2F
apply force F
time
Mass constant
acceleration
4a
3a
2a
a
F
2F
3F
4F
Force
Mass constant
From this we see that acceleration is directly _____________ to force:
Next we perform a series of experiments where we keep the force constant but
vary the mass.
velocity
apply mass m
slope = a
a
slope =
2
apply mass 2m
a
slope =
4
apply mass 4m
time
Force Constant
acceleration
a
3a/4
a /2
a /4
m
2m
3m
4m
mass
Force Constant
Acceleration is _________________ proportional to the mass:
Small digression for directly and inversely proportional relationships:
Things that are directly proportional have the general form:
(as one variable increases, the other variable increases).
The relationships for two coordinates on a curve that is directly proportional
(x1, y1) and (x2, y2) are:
Things that are inversely proportional have the general form:
(as one variable increases, the other variable decreases).
The relationships for two coordinates on a curve that is directly proportional
(x1, y1) and (x2, y2) are:
Example Problems:
A man pulling an empty wagon causes it to accelerate at 2.5 m/s2. What will
the acceleration be if he pulls with the same force when the wagon contains a
child whose mass is six times that of the wagon?
A truck has a maximum acceleration of 10.0 m/s2. What will the maximum
acceleration be if the truck is towing a car whose mass is half that of the truck?
Section 4.5 Newton’s Second Law
From last section we found that acceleration, a, is directly proportional to the
______________ and inversely proportional to the ___________. We can put
these two relationships together into one equation relating acceleration, force,
and mass:
This relationship is called ________________________________.
  
An object of mass m is subjected to forces F1 , F2 , F3 ... will undergo an

acceleration a given by:

 

where the net force Fnet  F1  F2  F3 ... is the vector sum of all forces
acing on the object. The acceleration vector points in the same direction
as the _______________ vector.
Newton’s Second Law equation is more often written in the rearranged
form:
Using the rearranged form of Newton’s Second Law we can easily derive
the units of force for the SI system:
1 kg m/s2 is called a _______________, ______.
The English system’s unit of force is called the _____________, ____.
The conversion between Newtons and pounds is: 1 pound = 4.45 N.
Example Problems:
Scallops eject water from their shells to provide a thrust force. The graph below
shows a smoothed graph of actual data for the initial motion of a 25 g scallop
speeding up to escape a predator.
v (m/s)
0.4
0.3
0.2
0.1
0.1
0.2
0.3 0.4 t (s)
a.) What is the magnitude of the net force needed to achieve this motion?
b.) How does this force compare to the 0.25 N weight of the scallop?
Very small forces can have tremendous effects on the motion of very small
objects. This is particularly apparent at the scale of the atom. An electron,
mass 9.1 x 10-31 kg, experiences a force of 1.6 x 10-17 N in a typical electric field
at the earth’s surface. From rest, how much time would it take for the electron
to reach a speed of 3.0 x 106 m/s, 1% of the speed of light.
Assignment Newton’s First and Second Laws
AP Physics I
(numbers correspond with problem numbers of text on pages 155 to 156)
13.) The figure below shows an acceleration-vs-force graph for three objects
pulled by rubber bands. the mass of object 2 is 0.20 kg. What are the
masses of objects 1 and 3? Explain your reasoning.
a (m/s2)
6
1
2
5
4
3
3
2
1
0
0
1
4
5
2
3
6
Force (number of rubber bands)
14.) A constant force applied to object A causes it to accelerate at 9 m/s 2. The
same force applied to object B causes an acceleration of 24 m/s2. Applied
to object C, it causes an acceleration of 14 m/s2.
a.) Which object has the largest mass?
b.) Which object has the smallest mass?
c.) What is the ration of mass A to mass B (mA/mB)?
15.) A utility vehicle has a maximum acceleration of 6.0 m/s2 when it carries
only the driver and has a total mass of 5000 kg. What is its maximum
acceleration after picking up six passengers and their luggage, adding an
additional 800 kg of mass?
16.) A constant force is applied to an object, causing the object to accelerate at
10 m/s2. What will the acceleration be if
a.) the force is halved?
b.) the object’s mass is halved?
c.) the force and the object’s mass are both halved?
d.) the force is halved and the object’s mass is doubled?
17.) A constant force is applied to an object, causing the object to accelerate at
10.0 m/s2. What will the acceleration be if
a.) the force is doubled?
b.) the object’s mass is doubled?
c.) the force and the object’s mass are both doubled?
d.) the force is halved and the object’s mass is halved?
21.) The figure below shows an object’s acceleration-versus-force graph. What
is the object’s mass?
a (m/s2)
6
5
4
3
2
1
0
0.0
0.5
1.0
1.5
F (N)
22.) In t-ball, young players use a bat to hit a stationary ball off a stand. The
140 g ball has about the same mass as a baseball, but it is larger and softer.
In one hit, the ball leaves the bat at 12 m/s after being in contact with the
bat for 2.0 ms. Assume constant acceleration during the hit.
a.) What is the acceleration of the ball?
b.) What is the net force on the ball during the hit?
23.) Two children fight over a 500 g toy car. The 30 kg boy pulls to the right
with a 12 N force and the 25 kg boy pulls to the left with a 15 N force.
Ignore all other forces on the toy car (such as its weight).
a.) At this instant, can you say what the velocity of the car is? If so, what
are the magnitude and direction of the velocity?
b.) at this instant, can you say what the acceleration of the car is? If so,
what are the magnitude and direction of the acceleration?
24.) A 5000 kg truck is traveling along a straight road at 10 m/s. Two seconds
later its speed is 9 m/s. What is the magnitude of the net force acting on
the truck during this time?
25.) The motion of a very massive object can be minimally affected by what
would seem to be a substantial force. Consider an oil supertanker with
mass 3.0 x 108 kg. Suppose you strapped two jet engines (with thrust as
given below) onto the sides of the tanker. Ignoring the drag of the water
(which, in reality, is not a very good approximation), how long will it take
the tanker, starting from rest, to reach a typical cruising speed of 6.0 m/s?