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Making connections: illustrative example

The image contains two diagrams. On the far left, there is a vertical surface. In the lower part of the left diagram, there is a gray circle near the surface, with an arrow labeled v pointing from the circle to the surface. In the upper part, there is a gray circle near the surface, with an arrow labeled v prime pointing from the surface to the circle. The two arrows meet point to end at the vertical surface. Where they meet, two additional arrows point out from the surface, one labeled delta p and one labeled f. On the right side of the image, an arrow labeled v prime points up and to the right at the same angle as the arrow labeled v prime in the diagram on the left. Another arrow, labeled negative v, points down and to the right, at the same angle but opposite direction as the arrow labeled v in the diagram on the left. The point of the first arrow (v prime) meets the end of the second arrow (negative v). A third arrow runs from the end of v prime to the point of negative v. This arrow is labeled delta v, equal to v prime plus negative v.
A puck has an elastic, glancing collision with the edge of an air hockey table.

In [link] , a puck is shown colliding with the edge of an air hockey table at a glancing angle. During the collision, the edge of the table exerts a force F on the puck, and the velocity of the puck changes as a result of the collision. The change in momentum is found by the equation:

Δp = m Δv = m v' - m v = m ( v' + ( - v ) )

As shown, the direction of the change in velocity is the same as the direction of the change in momentum, which in turn is in the same direction as the force exerted by the edge of the table. Note that there is only a horizontal change in velocity. There is no difference in the vertical components of the initial and final velocity vectors; therefore, there is no vertical component to the change in velocity vector or the change in momentum vector. This is consistent with the fact that the force exerted by the edge of the table is purely in the horizontal direction.

Test prep for ap courses

A boy standing on a frictionless ice rink is initially at rest. He throws a snowball in the + x -direction, and it travels on a ballistic trajectory, hitting the ground some distance away. Which of the following is true about the boy while he is in the act of throwing the snowball?

  1. He feels an upward force to compensate for the downward trajectory of the snowball.
  2. He feels a backward force exerted by the snowball he is throwing.
  3. He feels no net force.
  4. He feels a forward force, the same force that propels the snowball.

(b)

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A 150-g baseball is initially moving 80 mi/h in the – x -direction. After colliding with a baseball bat for 20 ms, the baseball moves 80 mi/h in the + x -direction. What is the magnitude and direction of the average force exerted by the bat on the baseball?

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Section summary

  • Linear momentum ( momentum for brevity) is defined as the product of a system’s mass multiplied by its velocity.
  • In symbols, linear momentum p is defined to be
    p = m v , size 12{p=mv} {}
    where m size 12{m} {} is the mass of the system and v size 12{v} {} is its velocity.
  • The SI unit for momentum is kg · m/s size 12{"kg" cdot "m/s"} {} .
  • Newton’s second law of motion in terms of momentum states that the net external force equals the change in momentum of a system divided by the time over which it changes.
  • In symbols, Newton’s second law of motion is defined to be
    F net = Δ p Δ t , size 12{ F rSub { size 8{"net"} } = { {Δp} over {Δt} } = { {mΔv} over {Δt} } "." } {}
    F net is the net external force, Δ p size 12{Δp} {} is the change in momentum, and Δ t size 12{Δt} {} is the change time.

Conceptual questions

An object that has a small mass and an object that has a large mass have the same momentum. Which object has the largest kinetic energy?

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An object that has a small mass and an object that has a large mass have the same kinetic energy. Which mass has the largest momentum?

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Professional Application

Football coaches advise players to block, hit, and tackle with their feet on the ground rather than by leaping through the air. Using the concepts of momentum, work, and energy, explain how a football player can be more effective with his feet on the ground.

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How can a small force impart the same momentum to an object as a large force?

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Problems&Exercises

(a) Calculate the momentum of a 2000-kg elephant charging a hunter at a speed of 7 . 50 m/s size 12{7 "." "50"``"m/s"} {} . (b) Compare the elephant’s momentum with the momentum of a 0.0400-kg tranquilizer dart fired at a speed of 600 m/s size 12{"600"``"m/s"} {} . (c) What is the momentum of the 90.0-kg hunter running at 7 . 40 m/s size 12{7 "." "40"``"m/s"} {} after missing the elephant?

(a) 1.50 × 10 4 kg m/s size 12{1 "." "50" times "10" rSup { size 8{4} } `"kg" cdot "m/s"} {}

(b) 625 to 1

(c) 6 . 66 × 10 2 kg m/s size 12{6 "." "66" times "10" rSup { size 8{2} } `"kg" cdot "m/s"} {}

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(a) What is the mass of a large ship that has a momentum of 1 . 60 × 10 9 kg · m/s , when the ship is moving at a speed of 48.0 km/h? size 12{"48" "." 0``"km/h?"} {} (b) Compare the ship’s momentum to the momentum of a 1100-kg artillery shell fired at a speed of 1200 m/s size 12{"1200"``"m/s"} {} .

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(a) At what speed would a 2 . 00 × 10 4 -kg size 12{2 "." "00" times "10" rSup { size 8{4} } "-kg"} {} airplane have to fly to have a momentum of 1 . 60 × 10 9 kg · m/s size 12{1 "." "60" times "10" rSup { size 8{9} } "kg" cdot "m/s"} {} (the same as the ship’s momentum in the problem above)? (b) What is the plane’s momentum when it is taking off at a speed of 60.0 m/s size 12{"60" "." 0``"m/s"} {} ? (c) If the ship is an aircraft carrier that launches these airplanes with a catapult, discuss the implications of your answer to (b) as it relates to recoil effects of the catapult on the ship.

(a) 8 . 00 × 10 4 m/s size 12{8 "." "00" times "10" rSup { size 8{4} } " m/s"} {}

(b) 1 . 20 × 10 6 kg · m/s size 12{1 "." "20" times "10" rSup { size 8{6} } " kg" cdot "m/s"} {}

(c) Because the momentum of the airplane is 3 orders of magnitude smaller than of the ship, the ship will not recoil very much. The recoil would be 0 . 0100 m/s size 12{ - 0 "." "0100"`"m/s"} {} , which is probably not noticeable.

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(a) What is the momentum of a garbage truck that is 1 . 20 × 10 4 kg size 12{1 "." "20" times "10" rSup { size 8{4} } " kg"} {} and is moving at 10 . 0 m/s size 12{10 "." "0 m/s"} {} ? (b) At what speed would an 8.00-kg trash can have the same momentum as the truck?

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A runaway train car that has a mass of 15,000 kg travels at a speed of 5 .4 m/s size 12{5 "." 4`"m/s"} {} down a track. Compute the time required for a force of 1500 N to bring the car to rest.

54 s

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The mass of Earth is 5 . 972 × 10 24 kg size 12{5 "." "972" times 10 rSup { size 8{"24"} } " kg"} {} and its orbital radius is an average of 1 . 496 × 10 11 m size 12{1 "." "496" times 10 rSup { size 8{"11"} } " m"} {} . Calculate its linear momentum.

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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