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Change in momentum

Let us consider a tennis ball (mass = 0,1 kg) that is dropped at an initial velocity of 5 m · s - 1 and bounces back at a final velocity of 3 m · s - 1 . As the ball approaches the floor it has a momentum that we call the momentum before the collision. When it moves away from the floor it has a different momentum called the momentum after the collision. The bounce on the floor can be thought of as a collision taking place where the floor exerts a force on the tennis ball to change its momentum.

The momentum before the bounce can be calculated as follows:

Because momentum and velocity are vectors, we have to choose a direction as positive. For this example we choose the initial direction of motion as positive, in other words, downwards is positive.

p i = m · v i = ( 0 , 1 kg ) ( + 5 m · s - 1 ) = 0 , 5 kg · m · s - 1 downwards

When the tennis ball bounces back it changes direction. The final velocity will thus have a negative value. The momentum after the bounce can be calculated as follows:

p f = m · v f = ( 0 , 1 kg ) ( - 3 m · s - 1 ) = - 0 , 3 kg · m · s - 1 = 0 , 3 kg · m · s - 1 upwards

Now let us look at what happens to the momentum of the tennis ball. The momentum changes during this bounce. We can calculate the change in momentum as follows:

Again we have to choose a direction as positive and we will stick to our initial choice as downwards is positive. This means that the final momentum will have a negative number.

Δ p = p f - p i = m · v f - m · v i = ( - 0 , 3 kg ) - ( 0 , 5 m · s - 1 ) = - 0 , 8 kg · m · s - 1 = 0 , 8 kg · m · s - 1 upwards

You will notice that this number is bigger than the previous momenta calculated. This is should be the case as the ball needed to be stopped and then given momentum to bounce back.

A rubber ball of mass 0,8 kg is dropped and strikes the floor with an initial velocity of 6 m · s - 1 . It bounces back with a final velocity of 4 m · s - 1 . Calculate the change in the momentum of the rubber ball caused by the floor.

  1. The question explicitly gives

    • the ball's mass (m = 0,8 kg),
    • the ball's initial velocity (v i = 6 m · s - 1 ), and
    • the ball's final velocity (v f = 4 m · s - 1 )

    all in the correct units.

    We are asked to calculate the change in momentum of the ball,

    Δ p = m v f - m v i

    We have everything we need to find Δ p . Since the initial momentum is directed downwards and the final momentum is in the upward direction, we can use the algebraic method of subtraction discussed in the vectors chapter.

  2. Let us choose down as the positive direction.

  3. Δ p = m v f - m v i = ( 0 , 8 kg ) ( - 4 m · s - 1 ) - ( 0 , 8 kg ) ( + 6 m · s - 1 ) = ( - 3 , 2 kg · m · s - 1 ) - ( 4 , 8 kg · m · s - 1 ) = - 8 = 8 kg · m · s - 1 upwards
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Exercise

  1. Which expression accurately describes the change of momentum of an object?
    1. F m
    2. F t
    3. F · m
    4. F · t
  2. A child drops a ball of mass 100 g. The ball strikes the ground with a velocity of 5 m · s - 1 and rebounds with a velocity of 4 m · s - 1 . Calculate the change of momentum of the ball.
  3. A 700 kg truck is travelling north at a velocity of 40 km · hr - 1 when it is approached by a 500 kg car travelling south at a velocity of 100 km · hr - 1 . Calculate the total momentum of the system.

Newton's second law revisited

You have learned about Newton's Second Law of motion earlier in this chapter. Newton's Second Law describes the relationship between the motion of an object and the net force on the object. We said that the motion of an object, and therefore its momentum, can only change when a resultant force is acting on it. We can therefore say that because a net force causes an object to move, it also causes its momentum to change. We can now define Newton's Second Law of motion in terms of momentum.

Newton's Second Law of Motion (N2)

The net or resultant force acting on an object is equal to the rate of change of momentum.

Mathematically, Newton's Second Law can be stated as:

F n e t = Δ p Δ t

Questions & Answers

What is a vector
Mercii Reply
vector is anything that has both a direction and a magnitude .they are usually drawn as pointed arrows ,the length of which represents a vector's magnitude
Tetteh
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Edward
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why is HCl considered a strong acid
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it dissociate almost completely
Tetteh
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what is an electric field?
Noluthando Reply
is the charge of an electron always 1,6 ×10^-19? and the mass is always 9,1×10^-13?
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how to calculate a distance between charges
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juss apply the formula of the Electrostatic force
Noluthando
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Use previous years question papers to understand how questions are answered and asked
Joseph
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Slindile
Then the best thing to do is that immediately you are done reading through a certain topic, and you think you understood everything in that topic that's when you can use previous question papers and answer questions related to the topic. I think that's not difficult
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Slindile
Good
Joseph
Here's a tip in reading textbooks, don't read it like a novel. First, flip through the pages—scan the chapter that you wanted to read. Second, go to the end of the chapter. Usually, there's a quiz at the end, so if will give you the important information that you need to know.
Sarah
Third, go to the beginning of the chapter and read through the words that were printed in bold: Titles, subtitles, headings, important words —because it helps to break down information.
Sarah
Fourth, read the first sentence of the chapter—if it is written by a good author; therefore, it will also have a good introduction. Check also the last sentence of the chapter to sum it up. Finally, read the whole chapter. You won't read it twice anymore.
Sarah
It looks hard, cause there are so much to do but read it thoroughly, it's easy and it will help you to save time and comprehend better. If you don't really have interest on reading—there are various of videos in youtube😊
Sarah
Oh, so em dashes turn into question marks :' (( nvm. Goodluck to all of us!
Sarah
How many ways can we calculate the empirical formula
Joseph Reply
How is current divided between resistors in parallel
Joseph
1/R=1/R+1/R
Slindile
tanx
Joseph
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Slindile
what's the other way
Joseph
What is the meaning of Coulomb's law
Nozipho Reply
Electronic magnetic field
Pride Reply
what is an emf ?
Nobuhle Reply
electromotive force
Tetteh
what are moments of a force
Mercy Reply
the moment of a force" is a measure of a tendency to cause a body to rotate about a specific point or axis....a moment is due to force not having equal and opposite force directly along its line of action.
Bhuboy
how to calculate the magnitude of the force of repulsion
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Source:  OpenStax, Siyavula textbooks: grade 11 physical science. OpenStax CNX. Jul 29, 2011 Download for free at http://cnx.org/content/col11241/1.2
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