NameDate
ScienceHelpNow.comPeriod
Impulse and Momentum : Section 05.01
“Impulse”Time - 48 Minutes : 31Seconds
NOTE : This Video can be viewed in two shorter sections as noted below
Section 05.01ATime - 26 Minutes : 23 Seconds
Section 05.01BTime - 22 Minutes : 06 Seconds
Vocabulary: Words and phrases introduced in this video have an asterisk. The rest of the vocabulary list will be introduced in other videos in this topic “Impulse and Momentum”
*collision - Acollisionis an event in which two or more bodies exert forces on each other for a relatively short time
The word “collision” does not imply the magnitude of the force. A bird brushing against a leaf as it lands on a tree limb is a collision, two tractor trailers colliding is a collision or two black holes merging are all “collisions”.
elastic collision - An elastic collision is a collision between two bodies in which both momentum and kinetic energy are conserved
inelastic collision - Aninelastic collision is a collisionin which momentum is conserved, but kinetic energy is not conserved due to the action ofinternal friction
*impulsive force - An impulsive force is a large force exerted over a short interval of time
*impulse - Impulse is defined as the product of a force times the duration of its contact with an object. A synonym for impulse is “change in momentum”. Impulse is a vector and the unit is the Newton-second (Ns). The symbol for impulse is J
momentum - Momentum is the product of the mass of an object times its velocity. Momentum is a vector and its unit is the kilogram meter per second (kg m/s). The symbol for momentum is a lower case Greek letter “rho” ( ρ ) which looks in the English alphabet like a lower case letter p. The plural of the word “momentum” is “momenta”
change in momentum - The final momentum minus the initial momentum of an object is called its “change in momentum”. The momentum can change when either the mass of an object or its velocity (or both) changes. “Difference” is a mathematical term for the result of subtraction, so the change in momentum is the difference between an object’s final and initial momenta
units of Impulse and Momentum - The unit for impulse is the Newton-second (Ns), while the unit for momentum and “Change in Momentum” is the kilogram meter per second (kg m/s). These units are equivalent and will be shown to be such in the video on “Momentum”
Page 1
What is a Collision?
A collision is ______
______
______
PAUSE THE VIDEO AND COME UP WITH TWO OF YOUR OWN EXAMPLES OF
“COLLISIONS”. EXAMPLE ONE SHOULD BE A SMALL COLLISION AND
EXAMPLE TWO A MUCH LARGER COLLISION.
1.
2.
An impulsive force is ______
______
PAUSE THE VIDEO AND COME UP WITH TWO OF YOUR OWN EXAMPLES OF
“IMPULSIVE FORCES”.
1.
2.
Graph of a Typical Impulsive Force (Foot Kicking a Soccer Ball)
Sketch a quick, simple graph here,
which shows how an “impulsive
force” can change with time, such
as a foot kicking a soccer ball.
Include all labels
This is an example of an applied force. The force begins when the foot
______the ball and ends when the foot is no longer touching
the ______. There is no force unless the two objects are ______
each other. When two objects are touching each other we say they are in
c ______.
Page 2
Describe what happens when a foot kicks a soccer ball
NOTE : The only way to calculate the area under the shape on the graph is to use calculus. We’re not going to do that. Actually you could also print the shape out onto paper, cut out the paper shape and weigh it……We’re not going to do that either. Later in the video I will show you a way to use the “average force” to estimate the area of the odd shape by drawing a rectangle instead, which will be a close approximation !!
Write the equation for “Impulse” ( J ) in the space below.
Explain what you know about impulse by looking at this equation.
Force and Impulse are ______related, meaning if time is held
constant, an increase in Force causes an increase in the ______.
Time and Impulse are also ______related, meaning if the
Force is held constant, an increase in Time causes an increase in the ______.
The Same Force Acting Over a Greater Time Interval Results in a Greater Impulse
Explain the difference when the paper ball just pops out the end of the blowgun and when it travels through the entire tube.
When the paper ball pops out the end, the Force acts for a small period of
time resulting in less ______.
When the paper ball travels through the entire length of the tube, the Force acts for a
longer period of time resulting in more ______.
More Impulse results in a ______velocity for the bullet that traveled
through the entire length of the tube (being pushed by the Force of my breath the whole time !!)
Page 3
The Physical Quantity “Impulse” - Its Symbol, Equation and Unit
QuantitySymbolEquationUnit
Impulse
PAUSE THE VIDEO WHILE YOU FIGURE OUT THE CORRECT UNIT FOR EACH QUANTITY SHOWN BELOW.
Figure out the Unit for each Physical Quantity Shown Below Based upon its Equation
F = m aW = F d
J = F tρ = m v
dΔ v
v = -----a = ------
t t
Page 4
Sample Impulse Problem #1
A bat applies an average force of 500.0 N to the right to a baseball for 10.0 ms. Calculate the impulse imparted to the ball.
GIVEN:FIND:
F = 500.0 N to the rightJ = _____ N s ?
t = 10.0 ms = 1.00 x 10-2 s
FORMULA:
J = F t
= 500.0 N ( 1.0 x 10-2 s )
= 5.00 N s to the Right
Sample Impulse Problem #2
A hammer applies an impulse of 30.0 Ns down on a nail in 2.0 ms. Calculate the average force on the nail during this time interval.
GIVEN:FIND:
J = 30.0 Ns downF = _____ N ?
t = 20.0 ms = 2.00 x 10-2 s
FORMULA:
J 30.0 Ns
F = ------= ------= 1500 N down
t2.00 x 10-2 s
Sample Impulse Problem #3
The gases from a gun going off push a bullet down the barrel of the gun with an average force of 20,000 N resulting in an impulse of 60.0 Ns. How long(time) was the bullet inside the barrel?
GIVEN:FIND:
J = 60.0 Ns t = _____ s ?
F = 20,000 N
FORMULA:
J 60.0 N s
t = ------= ------= 0.003 s
F20,000 N Page 5
Pause the Video and Complete these Problems on Your Own. You Have 6 Minutes !!
You must include GIVEN, FIND and FORMULA or NO CREDIT
FORMULA must include THREE STEPS 1 2 and 3 !!
1) A tennis racket applies an average force of 120.0 N to the right to a tennis ball for 20.0 ms. Calculate the impulse imparted to the ball.
GIVEN :FIND :
FORMULA :
2) A pool cue stick applies an impulse of 30.0 Ns to the right on a cue ball for 4.0 ms. Calculate the average force on the cue ball during this time interval.
GIVEN :FIND :
FORMULA :
3) The gases from a cannon going off push a cannonball down the barrel of the cannon with an average force of 5,000 N resulting in an impulse of 200.0 Ns. For how long (How much TIME?) did the force act on the cannonball as it traveled through the barrel of the cannon?
GIVEN :FIND :
FORMULA :
END OF VIDEO 05.01APage 6
START OF VIDEO 05.01B
A Collision Between Two Objects Typically Lasts Between 1.0ms and 10.0 ms
PREFIX METHOD
Convert the following decimal numbers to scientific notation
1.0 ms10.0 ms40.0 ms200.0 ms
Now, write 10-3 in place of the PREFIX “milli” for each example above and work out the correct exponent for each example as we did in the video to convert each example to seconds. (Essentially you are getting rid of the “milli” by incorporating it into the exponent for seconds)
FACTOR LABEL METHOD
Convert milliseconds to seconds using the Factor Label Method for each example below.
1.0 ms10.0 ms
40.0 ms200.0 ms
Page 7
Pause the Video and Complete these Problems on Your Own. You Have 10 Minutes !!
CONVERT MILLISECONDS TO SECONDS OR SECONDS TO MILLISECONDS ANY WAY YOU LIKE !! THE ONLY RULE IS……YOU HAVE TO GET THEM RIGHT !!
ALL OF YOUR FINAL ANSWERS MUST BE IN SCIENTIFIC NOTATION
#6 IS DONE FOR YOU AS AN EXAMPLE
1) 4,000 ms6) 0.0250 s 1000 ms
------=
1 s
Answer = 2.5 x 101 ms
2) 75 ms7) 20.0 s
3) 0.038 ms8) 500.0 s
4) 9 ms9) 0.0075 s
5) 0.15 ms10) 48,000,000 s
Page 8
How long a collision lasts depends upon the materials that the two objects are composed of, which determines whether the object has the ability to deform and spring back or not, which lengthens the duration of the force.
A collision between hard objects like two pool balls might last 1.0 millisecond.
Hard objects interact for a ______Time (Less Time, More Force)
A collision between two soft objects, one or both of which are able to “deform”, like a foot and a soccer ball (a kick) might last 10. milliseconds.
Deform means that the object “squooshes” in. In the case of an elastic object, like most balls, sponges, an airbag, etc….the object springs back to its original shape after it deforms.
Soft objects interact for a ______Time (More Time, Less Force)
How Does Impulse Work in Real Life?
A common example to explain how impulse applies to real life would be to describe how a seat belt or airbag works.
We will prove in a later video that the impulse delivered to the driver when a car gets into an accident is the same regardless of whether the driver wears a seatbelt (or an airbag deploys) or not. So, how does a seatbelt (or an airbag) lesson the damage to the driver?
Two factors affect the impulse, the force and the time interval over which the force acts.
When you don’t wear a seatbelt or use an airbag, and you get into an accident, the Force acts on your body over a very short Time. In other words, your body hits the dashboard very quickly and stops. Look at the numbers below. Without a seatbelt or airbag, for example, a Force of 2,000 N stops your body as you hit the dashboard and stop in 2.0 ms or 0.002 s resulting in an impulse of 4.00 N s.
J = F t
= 2,000 N ( 0.002 s )
J = 4.00 N s
When you use a seatbelt or an airbag, the seatbelt or airbag slows the amount of time it takes for your body to stop. The amount of time is longer. But, since the Impulse remains the same, the Force on your body decreases, as shown by the calculations below.
J 4.0 Ns
F = ------= ------= 500 N
t 0.008 s
A longer Time to come to a stop for the same Impulse means that the Force on your body is DECREASED, resulting in less damage to your body in the car accident.
Page 9
Another common example to explain how impulse applies to real life would be to describe how a championship boxer is able to knock out an opponent.
Delivering a punch of the same impulse in a shorter amount of time results in a larger force on the opponent’s face. A larger force will be more effective in knocking out the opponent.
Again, since Force and Time are INVERSELY RELATED according to the Impulse equation, punching faster (smaller time) while imparting the same Impulse, results in a punch with greater Force.
Explain how seatbelts and airbags work
______
______
Explain how a boxer delivers a more effective punch to an opponent
______
______
Page 10
Graph of an Impulsive Force
As we stated earlier, an impulsive force would be a relatively large force which acts for a relatively short time. Examples include a hammer hitting a nail, a foot kicking a ball, a speeding bullet hitting a glass window or a bow firing an arrow. Collisions and Explosions are generally considered to be examples of impulsive forces. Explosions would include a firecracker going off or a cannon firing a cannonball.
To make a graph that shows the force a foot exerts on a kicked ball, keep in mind that the force is zero until the foot contacts the ball, then the force increases as the foot pushes into the ball and “deforms” it. At maximum deformation, the force on the ball is at a maximum. Then the ball starts to recoil to its original shape and the force decreases to zero again as the ball leaves contact with the foot.
The graph of a typical impulsive force is shown below.
From the graph above, we see that the kick on the ball begins at the 20.0 ms point. The force on the ball is initially 0.0 N but increases as the ball deforms inwards to a maximum of 300 N at the 30.0 ms point, then decreases as the ball begins to resume its original shape. The entire kick takes 20.0 ms (the interval from 20.0 ms to 40.0 ms). At 40.0 ms the foot is no longer in contact with the ball, therefore the force has ended and we assume the ball is rolling across the field or has been kicked up into the air.
To find the meaning of the slope of any graph, look at Y divided by X
What is the meaning of the slope of this graph?
Force divided by Time has no physical meaning
To find the meaning of the area under any graph (line or curve doesn’t matter), look at
Y times X
What is the meaning of the area under this graph?
Force times Time is the definition of Impulse ( J )
Page 11
Using the Average Force to Calculate Impulse instead of the Changing Force
It would be pretty difficult to calculate the area under the curve shown in the graph on the previous page (and below). What is much easier and pretty close to accurate would be to graph the average force instead.
The average force is about 150 N. The duration of Time the force acts on the ball is the same 20.0 ms. That means that the area of the dotted box below is the Average Force times the Time and this is equal to the Impulse.
Calculate the area of the box as shown below.
Page 12
Practice Calculating Impulse on a Force vs Time Graph (Calculate the Area Under the Line or Curve)
Calculate the Impulse as represented by the shaded area of the graph below, which occurred between 25.0ms and 50.0 ms.
Calculate the Impulse as represented by the area under the line below for the time interval from 0.0 ms to 50.0 ms. Show your work in the space to the right of the graph
Calculate the Impulse for the graph above over the interval between 10.0ms and 40.0 ms.
Show your work here.
Page 13
Notes Summary:
Briefly, what have we learned about “Impulse” ?
An Impulse consists of a ______which acts over a certain amount of ______
Impulse is a ______( scalar or vector )
The symbol for Impulse is
The unit for Impulse is the ______
The magnitude of the Impulse is equal to ______
The direction of the Impulse is the same as the direction of the ______
Page 14