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Section summary

  • Impulse, or change in momentum, equals the average net external force multiplied by the time this force acts:
    Δ p = F net Δ t .
  • Forces are usually not constant over a period of time.

Conceptual questions

Professional Application

Explain in terms of impulse how padding reduces forces in a collision. State this in terms of a real example, such as the advantages of a carpeted vs. tile floor for a day care center.

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While jumping on a trampoline, sometimes you land on your back and other times on your feet. In which case can you reach a greater height and why?

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Professional Application

Tennis racquets have “sweet spots.” If the ball hits a sweet spot then the player's arm is not jarred as much as it would be otherwise. Explain why this is the case.

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Problems&Exercises

A bullet is accelerated down the barrel of a gun by hot gases produced in the combustion of gun powder. What is the average force exerted on a 0.0300-kg bullet to accelerate it to a speed of 600 m/s in a time of 2.00 ms (milliseconds)?

9 . 00 × 10 3 N size 12{9 "." "00" times "10" rSup { size 8{3} } `N} {}

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Professional Application

A car moving at 10 m/s crashes into a tree and stops in 0.26 s. Calculate the force the seat belt exerts on a passenger in the car to bring him to a halt. The mass of the passenger is 70 kg.

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A person slaps her leg with her hand, bringing her hand to rest in 2.50 milliseconds from an initial speed of 4.00 m/s. (a) What is the average force exerted on the leg, taking the effective mass of the hand and forearm to be 1.50 kg? (b) Would the force be any different if the woman clapped her hands together at the same speed and brought them to rest in the same time? Explain why or why not.

a) 2 . 40 × 10 3 N size 12{2 "." "40" times "10" rSup { size 8{3} } " N"} {} toward the leg

b) The force on each hand would have the same magnitude as that found in part (a) (but in opposite directions by Newton’s third law) because the change in momentum and the time interval are the same.

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Professional Application

A professional boxer hits his opponent with a 1000-N horizontal blow that lasts for 0.150 s. (a) Calculate the impulse imparted by this blow. (b) What is the opponent’s final velocity, if his mass is 105 kg and he is motionless in midair when struck near his center of mass? (c) Calculate the recoil velocity of the opponent’s 10.0-kg head if hit in this manner, assuming the head does not initially transfer significant momentum to the boxer’s body. (d) Discuss the implications of your answers for parts (b) and (c).

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Professional Application

Suppose a child drives a bumper car head on into the side rail, which exerts a force of 4000 N on the car for 0.200 s. (a) What impulse is imparted by this force? (b) Find the final velocity of the bumper car if its initial velocity was 2.80 m/s and the car plus driver have a mass of 200 kg. You may neglect friction between the car and floor.

a) 800 kg m/s size 12{"800"`"kg" cdot "m/s"} {} away from the wall

b) 1 . 20 m/s size 12{1 "." "20"`"m/s"} {} away from the wall

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Professional Application

One hazard of space travel is debris left by previous missions. There are several thousand objects orbiting Earth that are large enough to be detected by radar, but there are far greater numbers of very small objects, such as flakes of paint. Calculate the force exerted by a 0.100-mg chip of paint that strikes a spacecraft window at a relative speed of 4 . 00 × 10 3 m/s size 12{4 "." "00" times "10" rSup { size 8{3} } "m/s"} {} , given the collision lasts 6 . 00 × 10 8 s .

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Professional Application

A 75.0-kg person is riding in a car moving at 20.0 m/s when the car runs into a bridge abutment. (a) Calculate the average force on the person if he is stopped by a padded dashboard that compresses an average of 1.00 cm. (b) Calculate the average force on the person if he is stopped by an air bag that compresses an average of 15.0 cm.

(a) 1 . 50 × 10 6 N size 12{ - 1 "." "50" times "10" rSup { size 8{6} } N} {} away from the dashboard

(b) 1 . 00 × 10 5 N size 12{ - 1 "." "00" times "10" rSup { size 8{5} } N} {} away from the dashboard

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Professional Application

Military rifles have a mechanism for reducing the recoil forces of the gun on the person firing it. An internal part recoils over a relatively large distance and is stopped by damping mechanisms in the gun. The larger distance reduces the average force needed to stop the internal part. (a) Calculate the recoil velocity of a 1.00-kg plunger that directly interacts with a 0.0200-kg bullet fired at 600 m/s from the gun. (b) If this part is stopped over a distance of 20.0 cm, what average force is exerted upon it by the gun? (c) Compare this to the force exerted on the gun if the bullet is accelerated to its velocity in 10.0 ms (milliseconds).

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A cruise ship with a mass of 1 . 00 × 10 7 kg size 12{1 "." "00" times "10" rSup { size 8{7} } " kg"} {} strikes a pier at a speed of 0.750 m/s. It comes to rest 6.00 m later, damaging the ship, the pier, and the tugboat captain’s finances. Calculate the average force exerted on the pier using the concept of impulse. (Hint: First calculate the time it took to bring the ship to rest.)

4 . 69 × 10 5 N size 12{4 "." "69" times "10" rSup { size 8{5} } " N"} {} in the boat’s original direction of motion

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Calculate the final speed of a 110-kg rugby player who is initially running at 8.00 m/s but collides head-on with a padded goalpost and experiences a backward force of 1 . 76 × 10 4 N size 12{1 "." "76" times "10" rSup { size 8{4} } " N"} {} for 5 . 50 × 10 –2 s size 12{5 "." "50" times "10" rSup { size 8{"-2"} } " s"} {} .

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Water from a fire hose is directed horizontally against a wall at a rate of 50.0 kg/s and a speed of 42.0 m/s. Calculate the magnitude of the force exerted on the wall, assuming the water’s horizontal momentum is reduced to zero.

2 . 10 × 10 3 N size 12{2 "." "10" times "10" rSup { size 8{3} } `N} {} away from the wall

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A 0.450-kg hammer is moving horizontally at 7.00 m/s when it strikes a nail and comes to rest after driving the nail 1.00 cm into a board. (a) Calculate the duration of the impact. (b) What was the average force exerted on the nail?

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Starting with the definitions of momentum and kinetic energy, derive an equation for the kinetic energy of a particle expressed as a function of its momentum.

p = m v p 2 = m 2 v 2 p 2 m = mv 2 p 2 2 m = 1 2 mv 2 = KE KE = p 2 2 m alignl { stack { size 12{p=mv drarrow p rSup { size 8{2} } =m rSup { size 8{2} } v rSup { size 8{2} } drarrow { {p rSup { size 8{2} } } over {m} } =mv rSup { size 8{2} } } {} #drarrow { {p rSup { size 8{2} } } over {2m} } = { {1} over {2} } mv rSup { size 8{2} } = ital "KE" {} # {underline { ital "KE"= { {p rSup { size 8{2} } } over {2m} } }} {}} } {}

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A ball with an initial velocity of 10 m/s moves at an angle 60º above the + x size 12{+x} {} -direction. The ball hits a vertical wall and bounces off so that it is moving 60º above the x size 12{ - x} {} -direction with the same speed. What is the impulse delivered by the wall?

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When serving a tennis ball, a player hits the ball when its velocity is zero (at the highest point of a vertical toss). The racquet exerts a force of 540 N on the ball for 5.00 ms, giving it a final velocity of 45.0 m/s. Using these data, find the mass of the ball.

60.0 g

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A punter drops a ball from rest vertically 1 meter down onto his foot. The ball leaves the foot with a speed of 18 m/s at an angle 55º size 12{"55"°} {} above the horizontal. What is the impulse delivered by the foot (magnitude and direction)?

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Questions & Answers

how vapour pressure of a liquid lost through convection
Yomzi Reply
Roofs are sometimes pushed off vertically during a tropical cyclone, and buildings sometimes explode outward when hit by a tornado. Use Bernoulli’s principle to explain these phenomena.
Aliraza Reply
Plz answer the question ☝️☝️
Aliraza
what's the basic si unit of acceleration
ELLOIN Reply
Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.
Fabian Reply
Insulators (nonmetals) have a higher BE than metals, and it is more difficult for photons to eject electrons from insulators. Discuss how this relates to the free charges in metals that make them good conductors.
Muhammad Reply
Is the photoelectric effect a direct consequence of the wave character of EM radiation or of the particle character of EM radiation? Explain briefly.
Muhammad
Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0m by 8.5m whose uniform depth is 1 .8m.
Henny Reply
how solve this problem?
Foday
P(pressure)=density ×depth×acceleration due to gravity Force =P×Area(28.0x8.5)
Fomukom
for the answer to complete, the units need specified why
muqaddas Reply
That's just how the AP grades. Otherwise, you could be talking about m/s when the answer requires m/s^2. They need to know what you are referring to.
Kyle
Suppose a speck of dust in an electrostatic precipitator has 1.0000×1012 protons in it and has a net charge of –5.00 nC (a very large charge for a small speck). How many electrons does it have?
Alexia Reply
how would I work this problem
Alexia
how can you have not an integer number of protons? If, on the other hand it supposed to be 1e12, then 1.6e-19C/proton • 1e12 protons=1.6e-7 C is the charge of the protons in the speck, so the difference between this and 5e-9C is made up by electrons
Igor
what is angular velocity
Obaapa Reply
angular velocity can be defined as the rate of change in radian over seconds.
Fidelis
Why does earth exert only a tiny downward pull?
Mya Reply
hello
Islam
Why is light bright?
Abraham Reply
what is radioactive element
Attah Reply
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
Aisha Reply
thanks so much. i undersooth well
Valdes Reply
what is physics
Nwafor Reply
is the study of matter in relation to energy
Kintu
physics can be defined as the natural science that deals with the study of motion through space,time along with its related concepts which are energy and force
Fidelis
Practice Key Terms 2

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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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