Newton’s Laws, Part 2
Mark Lesmeister
Dawson High School Physics
NEWTON’S 2ND LAW
Force, Mass and Acceleration
Lab Notes


On the LabQuest unit, select “File”, “Open”
and choose the file labeled “n2l”.
In the trials where the force is varied,



Carefully raise the ramp until the force is what
you want it to be.
Use the same cart each trial.
In the trials where the mass is varied,

The total mass includes the mass of the cart,
fan and added mass.
Warm-up Quiz Question 1:
Force, Mass and Acceleration

The graph on the
right most likely
shows


A) Acceleration vs.
mass.
B) Acceleration vs.
force
14
12
10
8
6
4
2
0
0

5
10
Warm-up Quiz Question 2:
Force, Mass and Acceleration

The graph on the
right most likely
shows:


A) Acceleration vs.
mass.
B) Acceleration vs.
force
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
2
4
Warm-up Quiz Question 3:
Force, Mass and Acceleration

Which of the following statements
agrees with the results of the lab?




A) Acceleration is directly proportional to
force and mass.
B) Acceleration is inversely proportional to
force and mass.
C) Acceleration is directly proportional to
force and inversely proportional to mass.
D) Acceleration is inversely proportional to
force and directly proportional to mass.
Acceleration and Net Force

Acceleration is
directly proportional
to net force.
a  FNet
Acceleration vs.
Force
a (m/s2)

14
12
10
8
6
4
2
0
0
5
F (N)
10
Acceleration and Mass

Acceleration is
inversely
proportional to
mass.
1
a
m
Acceleration vs. Mass
a (m/s2)

4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
2
m (kg)
4
Combining Our Results


The acceleration of an object is directly
proportional to the net external force
and inversely proportional to the
object’s mass.
FNet
a
m
FNet
ak
m
FNet
a
m
Newton’s Second Law

The acceleration
experienced by an
object is directly
proportional to and in
the same direction as
the net force that acts
on it, and inversely
proportional to the
mass of the object.
FNET  ma
Newton’s Second Law
FNET  ma
Newton’s Second Law in
Component Form


Force and acceleration are vectors,
which can be broken into components.
Newton’s Second Law can be applied in
each component direction separately.
FNET  ma
F
x
 ma x
F
y
 ma y
Practice problem 1


Space shuttle astronauts experience
accelerations of about 35 m/s2 during
takeoff. What magnitude of force does
a 75 kg astronaut experience during an
acceleration of this magnitude?
Answer- 2600 N
Practice problem 2


A 7.5 kg bowling ball initially at rest is
dropped from the top of an 11 m
building. It hits the ground 1.5 s later.
Find the net force on the bowling ball,
including direction and magnitude.
Down is negative.
Answer: -73 N
Example: Free Fall

Show that the acceleration of free-fall is
the same as the factor for converting
mass to weight.
Fnet  ma
 FG  ma y
FG=mg
 mg  ma y
 g  ay
Practice Problems 3-4, p. 138


A car has a mass of 1.5 x 103 kg. If the
force acting on the car is 6.75 x 103 N
to the east, what is the car’s
acceleration?
A 2.0 kg otter starts from rest at the
top of a muddy incline 85 cm long and
slides to the bottom in 0.50 s. What
net external force acts on the otter?
Practice Problems 3-4, p. 138


3. 4.5 m/s2 to the east.
4. 14 N
Challenge Problem:
p. 155, #63

Three blocks are in
contact with each other
on a frictionless
horizontal surface. A
horizontal force of 180N
is applied to the right.



Find the acceleration of the
blocks.
Find the net force on Block
1.
Find the force of Block 1 on
block 2.
4 kg
2 kg
3 kg
BASIC PROBLEM SOLVING
WITH NEWTON’S LAWS
Constant Force Model vs.
Equilibrium Model
Equilibrium



∑F = 0.
Object will be at rest or
move with constant
velocity.
Position vs. time graph-
Constant Force



∑ F = constant.
Object will accelerate in
the direction of the net
force.
Position vs. time graph-
Solving Equilibrium Problems

Givens and Unknowns:






Sketch and label a diagram of the object and its
surroundings.
Enclose your object in a boundary to help identify outside
forces.
Draw a free body diagram. If there is motion, choose one
axis in the direction of motion.
Identify all forces that act on the object, and draw them on
the diagram.
Model: Equilibrium
Method


Apply Newton’s 1st Law in component form.
Fnet = 0 so ΣFx = 0 and ΣFy=0
Example 1: Equilibrium

Find the tension in each rope, as a
function of the angle.
30o
5.0 kg
Solution to Example 1



Givens and
F1 =?
Unknowns- as
shown in diagrams
to the right.
Model- Equilibrium
Method𝐹𝑥 = 0 and
𝐹𝑦 = 0
F1y =F1 sinq
Fg=mg
F2y =F2 sinq
F1x =F1 cos q F2x =F2 cos q
Solution to Example 1,
Continued

Implement

From the horizontal
equation
F1 =?
F2 cos q  F1 cos q  0

F1  F2
From the vertical
equation
Fg=mg
F1 sin q  F2 sin q  mg  0
F2x =F2 cos q
2 F2 sin q  mg
mg
F2 
2 sin q
F2y =F2 sinq
F1y =F1 sinq
F1x =F1 cos q
Solving Constant Force
(Acceleration) Problems

Givens and Unknowns:






Sketch and label a diagram of the object and its
surroundings.
Enclose your object in a boundary to help identify outside
forces.
Draw a free body diagram. If there is motion, choose one
axis in the direction of motion.
Identify all forces that act on the object, and draw them on
the diagram.
Model: Constant Force
Method


Apply Newton’s 1st and 2nd Laws in component form.
Fnet = ma so ΣFx = max and ΣFy= may
Constant Force Example

A truck is pulling a trailer with a force of
2200 N. Resistive forces opposed to
the motion of the trailer total 1200 N.
The trailer has a mass of 500 kg. How
long will the trailer take to reach 20
m/s?
Constant Force Example



Givens and Unknown- as in
diagram to the right, and
 m = 500 kg
 v0 = 0 and v = 20 m/s
 t = ?
FN
Ffriction-Trailer
= 1200 N
FTruck-Trailer
= 2200 N
Model- Equilibrium in y,
constant force (so constant
acceleration) in x.
Method-
F
x
 ma
v  v0  at
Vertical direction not needed, since no acceleration.
Fg=mg
Example 2 Solution

Implement
2200 N - 1200 N  ma
1000 N
2
 a  2.0 m/s
500 kg
v  0  at
v
20 m/s
t 
 10 s
2
a
2.0 m/s
FN
Ffriction-Trailer
= 1200 N
FTruck-Trailer
= 2200 N
Fg=mg
Additional Practice, Newton’s
Laws



From OpenSTAX College Physics:
Normal, Tension and Other Forces,
Exercises 2, 4 and 6.
Problem Solving Strategies, Exercises
2,4, 10,
Part 3:
Special Situations with Newton’s
Laws
Systems of Objects

This device is called
Atwood’s Machine.
Problem: Find the
acceleration in terms
of the masses and g.
m1
m2
Systems of Objects: Practice
Problem

Find T1 and T2 in terms of m1, m2 and
the acceleration a.
m1
T1
m2
T2

The “apparent weight” is what the scale
reads, i.e. the normal force.
©2012 OpenSTAX College
Accelerating Reference
Frames
Accelerating reference frames:
Practice Problem

©2012 OpenSTAX College
The man has a mass of 80 kg.
G = 10 m/s2. What does the
scale read when
 The elevator is moving up
with a constant velocity of
30 m/s?
 The elevator is moving
down with a constant
velocity of 30 m/s?
 The elevator is moving up
and gaining speed at 2
m/s2?
 The elevator is moving up
and slowing down from 10
m/s to 0 m/s in 2 s?
Additional Practice

Systems of Objects:


OpenSTAX College, Problem Solving
Strategies, Exercises 5,6 and7
Accelerated Reference Frames

OpenSTAX College, Further Applications of
Newton’s Laws, Exercises 10 and 12