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11.10 Impulse

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Impulse

Impulse is the product of the net force and the time interval for which the force acts. Impulse is defined as:

Impulse = F · Δ t

However, from Newton's Second Law, we know that

F = Δ p Δ t ∴ F · Δ t = Δ p = Impulse

Therefore,

Impulse = Δ p

Impulse is equal to the change in momentum of an object. From this equation we see, that for a given change in momentum, F n e t Δ t is fixed. Thus, if F n e t is reduced, Δ t must be increased (i.e. a smaller resultant force must be applied for longer to bring about the same change in momentum). Alternatively if Δ t is reduced (i.e. the resultant force is applied for a shorter period) then the resultant force must be increased to bring about the same change in momentum.

A 150 N resultant force acts on a 300 kg trailer. Calculate how long it takes this force to change the trailer's velocity from 2 m · s - 1 to 6 m · s - 1 in the same direction. Assume that the forces acts to the right.

  1. The question explicitly gives

    • the trailer's mass as 300 kg,
    • the trailer's initial velocity as 2 m · s - 1 to the right,
    • the trailer's final velocity as 6 m · s - 1 to the right, and
    • the resultant force acting on the object

    all in the correct units!

    We are asked to calculate the time taken Δ t to accelerate the trailer from the 2 to 6 m · s - 1 . From the Law of Momentum,

    F n e t Δ t = Δ p = m v f - m v i = m ( v f - v i ) .

    Thus we have everything we need to find Δ t !

  2. Choose right as the positive direction.

  3. F n e t Δ t = m ( v f - v i ) ( + 150 N ) Δ t = ( 300 kg ) ( ( + 6 m · s - 1 ) - ( + 2 m · s - 1 ) ) ( + 150 N ) Δ t = ( 300 kg ) ( + 4 m · s - 1 ) Δ t = ( 300 kg ) ( + 4 m · s - 1 ) + 150 N Δ t = 8 s

    It takes 8 s for the force to change the object's velocity from 2 m · s - 1 to the right to 6 m · s - 1 to the right.

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A cricket ball weighing 156 g is moving at 54 km · hr - 1 towards a batsman. It is hit by the batsman back towards the bowler at 36 km · hr - 1 . Calculate

  1. the ball's impulse, and
  2. the average force exerted by the bat if the ball is in contact with the bat for 0,13 s.

  1. The question explicitly gives

    • the ball's mass,
    • the ball's initial velocity,
    • the ball's final velocity, and
    • the time of contact between bat and ball

    We are asked to calculate the impulse

    Impulse = Δ p = F n e t Δ t

    Since we do not have the force exerted by the bat on the ball (F n e t ), we have to calculate the impulse from the change in momentum of the ball. Now, since

    Δ p = p f - p i = m v f - m v i ,

    we need the ball's mass, initial velocity and final velocity, which we are given.

  2. Firstly let us change units for the mass

    1000 g = 1 kg So , 1 g = 1 1000 kg ∴ 156 × 1 g = 156 × 1 1000 kg = 0 , 156 kg

    Next we change units for the velocity

    1 km · h - 1 = 1000 m 3 600 s ∴ 54 × 1 km · h - 1 = 54 × 1 000 m 3 600 s = 15 m · s - 1

    Similarly, 36 km · hr - 1 = 10 m · s - 1 .

  3. Let us choose the direction from the batsman to the bowler as the positive direction. Then the initial velocity of the ball is v i = -15 m · s - 1 , while the final velocity of the ball is v f = 10 m · s - 1 .

  4. Now we calculate the change in momentum,

    p = p f - p i = m v f - m v i = m ( v f - v i ) = ( 0 , 156 kg ) ( ( + 10 m · s - 1 ) - ( - 15 m · s - 1 ) ) = + 3 , 9 kg · m · s - 1 = 3 , 9 kg · m · s - 1 in the direction from batsman to bowler

  5. Finally since impulse is just the change in momentum of the ball,

    Impulse = Δ p = 3 , 9 kg · m · s - 1 in the direction from the batsman to the bowler
  6. Impulse = F n e t Δ t = Δ p

    We are given Δ t and we have calculated the impulse of the ball.

    F n e t Δ t = Impulse F n e t ( 0 , 13 s ) = + 3 , 9 N · s F n e t = + 3 , 9 N · s 0 , 13 s = + 30 N = 30 N in the direction from batsman to bowler
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Exercise

  1. Which one of the following is NOT a unit of impulse?
    1. N · s
    2. k g · m · s - 1
    3. J · m · s - 1
    4. J · m - 1 · s
  2. A toy car of mass 1 kg moves eastwards with a speed of 2 m · s - 1 . It collides head-on with a toy train. The train has a mass of 2 kg and is moving at a speed of 1,5 m · s - 1 westwards. The car rebounds (bounces back) at 3,4 m · s - 1 and the train rebounds at 1,2 m · s - 1 .
    1. Calculate the change in momentum for each toy.
    2. Determine the impulse for each toy.
    3. Determine the duration of the collision if the magnitude of the force exerted by each toy is 8 N.
  3. A bullet of mass 20 g strikes a target at 300 m · s - 1 and exits at 200 m · s - 1 . The tip of the bullet takes 0,0001s to pass through the target. Determine:
    1. the change of momentum of the bullet.
    2. the impulse of the bullet.
    3. the magnitude of the force experienced by the bullet.
  4. A bullet of mass 20 g strikes a target at 300 m · s - 1 . Determine under which circumstances the bullet experiences the greatest change in momentum, and hence impulse:
    1. When the bullet exits the target at 200 m · s - 1 .
    2. When the bullet stops in the target.
    3. When the bullet rebounds at 200 m · s - 1 .
  5. A ball with a mass of 200 g strikes a wall at right angles at a velocity of 12 m · s - 1 and rebounds at a velocity of 9 m · s - 1 .
    1. Calculate the change in the momentum of the ball.
    2. What is the impulse of the wall on the ball?
    3. Calculate the magnitude of the force exerted by the wall on the ball if the collision takes 0,02s.
  6. If the ball in the previous problem is replaced with a piece of clay of 200 g which is thrown against the wall with the same velocity, but then sticks to the wall, calculate:
    1. The impulse of the clay on the wall.
    2. The force exerted by the clay on the wall if it is in contact with the wall for 0,5 s before it comes to rest.

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
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Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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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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