HW5 - PHYS125 Homework Assignment #5 Grading Rubric Stage 1...

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PHYS125 Homework Assignment #5 Grading Rubric Stage 1 5 points total Problem 9.25 (3 points), 9.40 (2 points)
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Stage 0 Solutions: 9.5, 9.7, 9.11, 9.13. 9.17, 9.19, 9.21 More Good Problems: Knight 9.27, 9.29, 9.37, 9.39, 9.51 9.5. Model: The particle is subjected to an impulsive force. Visualize: Please refer to Figure Ex9.5. Solve: Using Equation 9.5, the impulse is the area under the curve. From 0 s to 2 ms the impulse is Fdt = 1 2 500 N ( ) 2 × 10 3 s ( ) =− 0.5 N s From 2 ms to 8 ms the impulse is Fdt = 1 2 + 2000 N ( ) 8 ms 2 ms ( )=+ 6.0 N s From 8 ms to 10 ms the impulse is Fdt = 1 2 500 N ( ) 10 ms 8 ms ( )=− 0.5 N s Thus, from 0 s to 10 ms the impulse is 0.5 + 6.0 0.5 ( N s ) = 5.0 N s. 9.11. Model: Model the glider cart as a particle, and its interaction with the spring as a collision. Visualize: Solve: Using the impulse-momentum theorem p f x p i x = Fdt , 0.6 kg () 3 m /s 0.6 kg 3 m / s = area under force curve = 1 2 36 N ( ) Δ t ( )⇒Δ t = 0.20 s 9.13. Model: Choose car + gravel to be the system. Visualize: Solve: There are no external forces on the car + gravel system, so the horizontal momentum is conserved. This means p f x = p i x . Hence, 10,000 kg + 4, 000 kg v f x = 10, 000 kg 2.0 m /s ( ) + 4, 000 kg ( ) 0.0 m /s ( ) v f x = 1.43 m /s
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9.17. Model: We will define our system to be Dan + skateboard. Visualize: The system has nonzero initial momentum p i x . As Dan (D) jumps backward off the gliding skateboard (S), the skateboard will move forward in such a way that the final total momentum of the system p f x is equal to p i x . This conservation of momentum occurs because r F ext = r 0 on the system. Solve: We have m S v f x () S + m D v f x D = m S + m D ( ) v i x . Hence, 5.0 kg 8.0 m /s + 50 kg v f x ( ) D = 5.0 kg + 50 kg ( ) 4.0 m /s ( ) v f x ( ) D = 3.6 m/s 9.19. Model: The two cars are not an isolated system because of external frictional forces. But during the collision friction is not going to be significant. Within the impulse approximation, the momentum of the Cadillac + Volkswagen system will be conserved in the collision. Visualize: Solve: The momentum conservation equation p f x = p i x is m C + m VW v f x = m C v i x ( ) C + m VW v i x ( ) VW 0 kg mph = 2000 kg 1.0 mph ( ) + 1000 kg ( ) v i x ( ) VW v i x ( ) VW =− 2.0 mph You need a speed of 2.0 mph. 9.21. Model: This problem deals with the conservation of momentum in two dimensions in an inelastic collision. Visualize:
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Solve: The conservation of momentum equation r p before = r p after is m 1 v i x () 1 + m 2 v i x 2 = m 1 + m 2 ( v f x ) m 1 v i y ( ) 1 + m 2 v i y ( ) 2 = m 1 + m 2 ( ) v f y Substituting in the given values, .02 kg 3.0 m /s + 0 kg m /s = .02 kg + .03 kg ( ) v f cos θ 0 kg m / s + .03 kg 2.0 m /s ( ) = .02 kg + .03 kg ( ) v f sin v f cos = 1.2 m / s v f sin = 1.2 m / s v f = 1.2 m /s 2 + 1.2 m / s 2 = 1.7 m /s = tan 1 v y v x = tan 1 1 () = 45 ° The ball of clay moves 45 ± north of east at 1.7 m/s.
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HW5 - PHYS125 Homework Assignment #5 Grading Rubric Stage 1...

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