Transcript Wagon Race

Day 1 - Do Now
• Take 1 minute to answer the question:
– Why would we want to measure force? (i.e. under
what circumstances is measuring force useful?)
– Please write an example.
Sir Isaac Newton
Newton’s 2nd Law
• Newton’s 2nd Law gives us the ability to
calculate how much force is required to move
an object
The formula
• F=mXa
(force = mass times acceleration)
F = ma
Playing with the formula
F
F
• F= ma OR m= -------- OR a= --------a
m
• Units: unit for force is N (Newton)
m = kg
a = m/sec2
Newton = Kg xm
sec2
Formula Trick
Cover the
symbol you are
trying to find!
F
M
A
2nd Law Quick Practice
• A 100 Kg linebacker hits the running back
while accelerating at 3 m/s2. What is the force
the linebacker hits the running back? Answer
in Newtons
Quick Practice
F=mxa
mass = 100 Kg
accel. = 3 m/s2
F = 100 Kg x 3 m/s2
F = 300 Kg x m / s2
Day 2 - Do Now
• Please take two minutes to answer this
question:
• What is the funniest or most fun race you
have ever participated in or have seen?
Wagon Race
Scenario
• One Saturday morning you and your
eleven friends decide to have a
wagon race. Each wagon team has a
total of four people, arranged in the
following manner and shown below
in the diagrams:
• Wagon 1 – 2 people pushing the
wagon and 2 people sitting in the
wagon
• Wagon 2 - 3 people pushing the
wagon and 1 person sitting in the
wagon
• Wagon 3 - 1 person pushing the
wagon and 3 people sitting in the
wagon
WAGON #1
Force of Each Person Pushing the
Wagon
Person number
Force (N)
1
53
2
55
WAGON #1
Mass of Each Person in the Wagon
Person number
3
4
Mass (Kg)
31
37
WAGON #2
Force of Each Person Pushing the Wagon
Person number
5
6
7
Force (N)
55
31
11
WAGON #2
Mass of Each Person in the Wagon
Person number
8
Mass (Kg)
40
WAGON #3
Force of Each Person Pushing the
Wagon
Person number
9
Force (N)
80
WAGON #3
Mass of Each Person in the Wagon
Person number
Mass (Kg)
10
37
11
56
12
29
The following formulae may
be used in this task:
F = ma
d=½
2
at
v=at
Units
Distance
Mass
Velocity
Acceleration
Time
Force (Newton)
Symbol
d
m
v
a
s
N
Unit
m (meter)
kg (kilogram)
m/s
m/s2
s (second)
kg . m/s2
Step 1
1. Using the information contained in
the prompt, calculate the
acceleration of each wagon. Show
all work and be sure to include all
units in your calculations and
answers.
The Accelerations
F=ma
ΣF=(Σm)a
Ex. F1+F2=(m1+m2)a
Σ = Summation or Sum Of or Total Of
Force on Wagon #1
Force of Each Person Pushing the Wagon
Person number
Force (N)
1
53
2
55
ΣF= F1+F2 = 53N+55N = 108N
Mass of Wagon #1
Mass of Each Person in the Wagon
Person number
3
4
Mass (kg)
31
37
Σm= m3+m4 = 31kg+37kg = 68kg
Acceleration of Wagon #1
ΣF=(Σm)a = (F1+F2)=(m1+m2)a
Convert N to kg . m/s2
(53N545N)=(53kg . m/s2 + 55kg . m/s2)
(53kg . m/s2 + 55kg . m/s2)=(31kg+37kg)a
(108kg . m/s2)= (68kg)a
(108kg . m/s2) = (68kg)a = 1.59 m/s2
(68kg)
(68kg)
Force on Wagon #2
Force of Each Person Pushing the Wagon
Person number
5
6
7
Force (N)
55
31
11
ΣF= F5+F6+F7 = 55N+31N+11N = 97N
Mass of Wagon #2
Mass of Each Person in the Wagon
Person number
8
Σm= m8 = 40kg
Mass (Kg)
40
Acceleration of Wagon #2
ΣF=(Σm)a = (F5+F6+F7)=(m8)a
Convert N to kg . m/s2
(55N+31N+11N)=(55kg . m/s2 + 31kg . m/s2 +11kg . m/s2)
(55kg . m/s2 + 31kg . m/s2 +11kg . m/s2)=(40kg)a
(97kg . m/s2)= (40kg)a
(97kg . m/s2) = (40kg)a = 2.425 m/s2
(40kg)
(40kg)
Force of Wagon #3
Force of Each Person Pushing the Wagon
Person number
9
Σm= m9 = 80kg
Force (N)
80
Mass on Wagon #3
Mass of Each Person in the Wagon
Person number
10
11
12
Mass (Kg)
27
46
19
ΣF= F10+F11+F12 = 27N+46N+19N = 92N
Acceleration of Wagon #3
ΣF=(Σm)a = (F9)=(m10+m11+m12)a
Convert N to kg . m/s2
(100N)=(100kg . m/s2)
(100kg . m/s2)=(27kg+46kg+19kg)a
(100kg . m/s2)= (92kg)a
(100kg . m/s2) = (92kg)a = 1.0870 m/s2
(92kg)
(92kg)
Day 3 - Do Now
• What kind of information can you calculate
using the formula F=ma?
• How can you use these problems in real life?
Table Assumptions
2a. Assuming that each wagon maintains a
constant acceleration for five seconds,
construct a table which compares the speed
and time of each wagon. Your table should
represent every second from resting to five
seconds.
Table
Time (seconds)
0
1
2
3
4
5
Speed (meters/seconds)
Using the Table
2b. Using the table you created, construct a
single graph plotting the speed vs. time data
for each of the three wagons.
GRAPHING
Calculating distance
• What is the distance travelled by each wagon?
Wagon 1
• d = ½ at2
• d = ½ (1.59 m/s2) 5 s 2
• d = ½ (1.59 m/s2) (25 s2)
• d= ½ (39.75)
• d= 19.88
The race!
• If a 200 meter race was held, which wagon
would win?
• First of all how long is 200 meters? Bolt!
• Use words to describe your thinking and relate
it to Newton’s second law:
– Acceleration, mass and force!!!