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< The Physics Problem Solver
Impulse can be regarded as the change in momentum of an object to which a force is applied. The impulse may be expressed in a simpler form when both the force and the mass are constant:
where
- F is the constant total net force applied,
- Δt is the time interval over which the force is applied,
- m is the constant mass of the object,
- Δv is the change in velocity produced by the force in the considered time interval, and
- m Δv = Δ(mv) is the change in linear momentum.
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Impulse problems[edit]
Beginner[edit]
1) A 0.145 kg baseball pitched at 39 m/s is hit on a horizontal line drive straight back at the pitcher at 52 m/s. If the contact time was 3*10-3s calculate the average force between the ball and the bat. Filmstro pro.
- As we see above, final momentum - initial momentum.
- Therefore: F*3*10-3 = (7.54 kgm/s) - (5.655 kgm/s)
- F*3*10-3 = (0.145*52) - (-0.145*39) = 1.885kgm/s
- Dividing both sides by 3*10-3 gives us: F = 628.33 N
- Therefore, the average force experienced by the ball is approximately 630 Newtons.
Intermediate[edit]
1) It is well-known that bullets and other missiles fired at superman simply bounce off his chest. Suppose that a gangster sprays the chest of the Man of Steel with 3g bullets at the rate of 100 bullets/min, and the speed of each bullet is 500 m/s. Suppose too that the bullets rebound straight back with no change in their speed. What is the magnitude of the average force on his chest?
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The first thing we should do is convert this problem into standard units:
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- Each bullet is 3g = 3*10-3kg/bullet
- 103 bullets/minute = 100/60 bullets/second.
- speed of each bullet before impact is 500 m/s.
- 'the bullets rebound straight back with no change in their speed' -> The speed of the bullet after impact is -500m/s
As we know from the equation above, So the average force, F equals
In order to find the change in momentum we first need to find the total initial momentum: Isoftphone pro 4 2 4 x 6.
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- The initial state is (103/60 bullets/second) * (3*10-3kg/bullet) * (500 m/s) = 100/60*500*3*10-3kgm/s^2 = 2.575 kgm/s^2 = 2.575N
- The final state is (103/60 bullets/second) * (3*10-3kg/bullet) * (-500 m/s) = 100/60*(-500)*3*10-3kgm/s^2 = -2.575 kgm/s^2 = -2.575N
- Final - Initial = 2.575 - (-2.575)= 5.15 N
2) Recent studies have raised concern about 'heading' in youth soccer (i.e., hitting the ball with the head). A soccer player 'heads' a size 4 ball, deflecting it by 43.0 degrees, but keeping its speed of 19.40 m/s constant. A size 4 ball has a mass of approximately 0.302 kg. What is the magnitude of the impulse which the player imparts to the ball?
As we know, Impulse = Change of momentum. The initial momentum is m*v = 0.302kg * 19.40 m/s = 5.8588 kg*m/s in the +x direction.After the impact, the momentum is now 5.8588 kg*m/s at an angle of 43.0 degrees. Therefore, in the momentum is 5.8588*cos(43) in the +x direction, and 5.8588*sin(43) in the +y direction.
- Final - Initial = 5.8588*cos(43) - 5.8588 = in the x direction, and 5.8588*sin(43) - 0 in the y direction. The magnitude of the two combined is 1.5739 in the -x direction, and 3.99569 in the y direction. The magnitude of the two is: sqrt((-1.5739)^2 + (-3.99569)^2) = 4.2945 Ns
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