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A large change in momentum occurs only when there is a large impulse A large impulse can result either from a large force acting over a short period of time or from a smaller force acting over a long period of time What happens to the driver when a crash suddenly stops a car An impulse is needed to bring the driver s momentum to zero According to the impulse-momentum equation, F t pf pi The final momentum, pf , is zero The initial momentum, pi, is the same with or without an air bag Thus, the impulse, F t, also is the same An air bag, such as the one shown in Figure 9-2, reduces the force by increasing the time interval during which it acts It also exerts the force over a larger area of the person s body, thereby reducing the likelihood of injuries

Average Force A 2200-kg vehicle traveling at 94 km/h (26 m/s) can be stopped in 21s by gently applying the brakes It can be stopped in 38 s if the driver slams on the brakes, or in 022 s if it hits a concrete wall What average force is exerted on the vehicle in each of these stops

Sketch the system Include a coordinate axis and select the positive direction to be the direction of the velocity of the car Draw a vector diagram for momentum and impulse Known:

Unknown:

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Determine the initial momentum, pi pi mvi (2200 kg)( 26 m/s) Substitute m 57 104 kg m/s Determine the final momentum, pf pf mvf (2200 kg)( 00 m/s) Substitute m 00 kg m/s

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Apply the impulse-momentum theorem to obtain the force needed to stop the vehicle F t pf pi F t ( 00 kg m/s) (57 104 kg m/s) Substitute pf 00 kg m/s, pi 57 104 kg m/s 57 104 kg m/s F

26 105 N

Are the units correct Force is measured in newtons Does the direction make sense Force is exerted in the direction opposite to the velocity of the car and thus, is negative Is the magnitude realistic People weigh hundreds of newtons, so it is reasonable that the force needed to stop a car would be in the thousands of newtons The impulse is the same for all three stops Thus, as the stopping time is shortened by more than a factor of 10, the force is increased by more than a factor of 10

1 A compact car, with mass 725 kg, is moving at 115 km/h toward the east Sketch the moving car a Find the magnitude and direction of its momentum Draw an arrow on your sketch showing the momentum b A second car, with a mass of 2175 kg, has the same momentum What is its velocity 2 The driver of the compact car in the previous problem suddenly applies the brakes hard for 20 s As a result, an average force of 50 103 N is exerted on the car to slow it down

a What is the change in momentum; that is, the magnitude and direction of the impulse, on the car b

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Force (N) 5 0 5 1 2

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Force (N) 5 0 5

1 2 Time (s)

b Complete the before and after sketches, and determine the momentum and the velocity of the car now 3 A 70-kg bowling ball is rolling down the alley with a velocity of 20 m/s For each impulse, shown in Figures 9-3a and 9-3b, find the resulting speed and direction of motion of the bowling ball 4 The driver accelerates a 2400-kg snowmobile, which results in a force being exerted that speeds up the snowmobile from 600 m/s to 280 m/s over a time interval of 600 s a Sketch the event, showing the initial and final situations b What is the snowmobile s change in momentum What is the impulse on the snowmobile

Time (s) Figure 9-3

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