Chapter 9 - 9.1 Model Model the car and the baseball as...

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9.1. Model: Model the car and the baseball as particles. Solve: (a) The momentum p mv ! "# " # 1500 kg 10 m/s ! 4 1.5 10 kg m/s. !$ (b) The momentum p mv ! " #" # 0.2 kg 40 m/s ! 8.0 kg m/s. !
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9.2. Model: Model the bicycle and its rider as a particle. Also model the car as a particle. Solve: From the definition of momentum, car bicycle pp ! car car car bicycle bicycle bicycle car bicycle m m v m v v v m " ! " ! #$ 1500 kg 5.0 m/s 75 m/s 100 kg %& !! ’( )* Assess: This is a very high speed ( 168 mph). + This problem shows the importance of mass in comparing two momenta.
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9.3. Visualize: Please refer to Figure EX9.3. Solve: The impulse x J is defined in Equation 9.6 as !" f i t xx t J F t dt ## $ area under the () x Ft curve between i t and f t ! "! " ! "! " 1 4 ms 1000 N 6 4 ms 1000 N 4 Ns 2 x J # % & #
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9.4. Model: The particle is subjected to an impulsive force. Visualize: Please refer to Figure EX9.4. Solve: Using Equation 9.6, the impulse is the area under the curve. From 0 s to 2 ms the impulse is !" ! " 3 1 2 500 N 2 10 s 0.5 N s Fdt # $ # % $ # & From 2 ms to 8 ms the impulse is ! "! " 1 2 2000 N 8 ms 2 ms 6.0 N s Fdt $ # $ ’ & From 8 ms to 10 ms the impulse is ! "! " 1 2 500 N 10 ms 8 ms 0.5 N s Fdt $ # # $ # & Thus, from 0 s to 10 ms the impulse is 0.5 6.0 0.5 N s 5.0 N s. # # $
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9.5. Visualize: Please refer to Figure EX9.5. Solve: The impulse is defined in Equation 9.6 as !" f i t xx t J F t dt ## $ area under the () x Ft curve between i t and f t ! "! " 3 1 max max 2 6.0 N s = 8 ms 1.5 10 N FF % % # &
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9.6. Model: Model the object as a particle and the interaction as a collision. Visualize: Please refer to Figure EX9.6. Solve: The object is initially moving to the right (positive momentum) and ends up moving to the left (negative momentum). Using the impulse-momentum theorem fi , x xx p pJ !" 2 kg m/s 6 kg m/s x J # ! " " 8 kg m/s 8 N s x J $ ! # ! # Since avg , x J Ft !% we have avg 8 N s % ! # 2 avg 8 N s 8 10 N 10 ms F # $ ! ! # & The force is ’ ( 2 8 10 N, left . F !& !
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9.7. Model: Model the object as a particle and the interaction with the force as a collision. Visualize: Please refer to Figure EX9.7. Solve: Using the equations fi x xx p pJ !" and f i () t t J F t dt ! ! # area under force curve $ % $ %$ % f 2.0 kg 2.0 kg 1.0 m/s x v (area under the force curve) $% $ %$ % f 1 1.0 m/s 1.0 s 2.0 N 2.0 m/s 2.0 kg x v & ! " ! Becaue f x v is positive, the object moves to the right at 2.0 m/s. Assess: For an object with positive velocity, a positive impulse increases the object’s speed. The opposite is true for an object with negative velocity.
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9.8. Model: Model the object as a particle and the interaction with the force as a collision. Visualize: Please refer to Figure EX9.8. Solve: Using the equations fi x xx p pJ !" and f i () t t J F t dt ! ! # area under force curve $ % $ %$ % f 2.0 kg 2.0 kg 1.0 m/s x v (area under the force curve) $% $ %$ % f 1 1.0 m/s 2.0 N 0.50 s 0.50 m/s 2.0 kg x v &’ ( ! " ) ! *+ ,- Assess: For an object with positive velocity, a negative impulse slows the object. The opposite is true for an object with negative velocity.
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9.9. Model: Use the particle model for the sled, the model of kinetic friction, and the impulse-momentum theorem.
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Chapter 9 - 9.1 Model Model the car and the baseball as...

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