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PHSX 220 Homework 8 D2L - Due Thursday March 22nd - 5:00 pm Momentum and Impulse Problem 1 (2 pts): A 8 kg box, initially at rest is placed on a frictionless horizontal surface. At t=0 a horizontal force to the right is applied to the box. The magnitude of the force changes as a function of time as shown in the graph. Rank the impulse applied to the box by this force during each 2-second interval indicated below from greatest to least. A = 0 to 2 s, B = 2 to 4 s, C = 4 to 6 s, D = 6 to 8 s, E = 8 to 10 s Problem 2 (2 pts): Shown below are six cases in which two carts, traveling in opposite directions, are about to collide. The carts are all identical in size and shape, but they are loaded with different masses and are initially traveling with different velocities. The carts stick together after the collision with no friction between the carts and the ground. Rank the cases based on the speed of the two-cart system after the collision occurs from greatest to least. Problem 3 (2 pts): The eight situations below show before and after ”snapshots” of a car’s velocity. All cars have the same mass. Rank these situations, in terms of the impulse on these cars, from most positive to most negative, to create these changes in velocity. Problem 4 (2 pts): Boxes with varied masses are being pushed for 10 seconds across a floor by a net horizontal force as shown below. The mass of the boxes and the net horizontal force for each case is given in the indicated figures. All boxes have an initial velocity of 10 m/s to the right, considering motion to the right as positive. Rank the final momentum of each box from the greatest momentum to the least momentum. Suggestion - Don’t use kinematics as this is a HW assignment on momentum and impulse PHSX 220 Homework 8 Paper - Due Thursday March 22nd - 5:00 pm Momentum Problem 1: The power available in wave energy can be determined from the rate of change in the center of mass of a crest of a wave to a trough of a wave. This is traditionally done with a sine wave, but can also be estimated from three boxes set on top of each other. The figure below shows initial and final configurations for three boxes. The largest box has a height of 0.5 m, width of 3 m and a total mass of 1500 kg. The medium box has a height of 0.5 m, width of 2 m and a total mass of 1000 kg. The smallest box has a height of 0.5 m, width of 1 m and a total mass of 500 kg. a) Calculate the vertical center of mass of the initial configuration. b) Calculate the change in potential energy of the system from the initial to final configuration. c) If this occurs once every 2 seconds, calculate the power available for this model of wave power. Problem 2: Block A (5 kg) initially moves to the right with a speed of 6 m/s, while block B (2 kg) moves to the left with a speed of 3 m/s. The blocks collide and both move off to the right. Block A has a final velocity of 1.6 m/s to the right. Answer the following questions in regards to this collision. a) Calculate the magnitude and direction of the final velocity of block B b) Calculate the magnitude and direction of the impulse by block B on block A c) Calculate the change in kinetic energy of the system (block A and B) from the initial to final states Problem 3: A 9 kg sledge hammer head is initially moving downward at 5 m/s and eventually comes to a rest after hitting a concrete cinder block. a) Calculate the magnitude of the impulse to the hammer head while coming to a stop b) If the block does not break, the hammer head comes to a stop in only 0.02 seconds. What is the magnitude of the average net force acting on the block while it comes to a stop in this case? c) If the block does break, the hammer head comes to a stop in over a longer time of 0.22 seconds. What is the magnitude of the average net force acting on the block while it comes to a stop in this case? Problem 4: An ion propulsion system uses ejected ions to change the momentum of a spacecraft (https://www.nasa.gov/multimedia/imagegallery/image_feature_2416.html). If 1x1020 protons are ejected per second at 3x105 m/s relative to to a 100 kg spacecraft that starts at zero velocity, how many days will it take for the spacecraft to reach 9x103 m/s? You may look up the mass of a proton in the back of your textbook and neglect any change in mass of the space craft due to the loss of the protons. Hint: Do the problem for 1 proton first and build from there. Problem 5: A 5 g bullet enters and passes through a grapefruit of mass 0.25 kg hanging from a length of string forming a pendulum with a length of 0.5 meters. The bullet emerges from the grapefruit at a velocity equal to 1/3 of it’s initial velocity before entering the delicious piece of fruit. At what minimum initial velocity for the bullet does the grapefruit maintain circular motion through it’s highest point in the pendulum’s rotation 1 meter above the starting point? Hint: Remember there is a minimum speed at the top of the pendulum’s path to maintain circular motion Problem 6: A mass, m1 , moves with an initial constant velocity, ~v1 , at an angle θ below the x-axis. A mass,m2 , collides with the m1 moving with its initial constant velocity, ~v2 , at an angle of θ above the x axis. After the collision between the two masses they stick together and moves off along the -x axis with a constant velocity of ~vf This is an old exam problem, a 2d momentum problem will be one of the three written problems on exam 3. a) In terms of variables given develop an expression for the initial momenum in the x direction, p~ix . b) In terms of variables given develop an expression for the initial momenum in the y direction, p~iy . c) With values of m1 = 1kg, m2 = 3 kg, | ~v1 |= 10 m/s, θ=30 degrees - calculate | ~v2 | and | ~vf |. d) Calculate the impulse by m2 on m1 in unit vector notation. e) Calculate the impulse by m1 on m2 in unit vector notation. f) Calculate the percent change in kinetic energy from initial to final. Use a negative percentage for a loss and a positive percentage for a gain. Problem 7: You are investigating the scene of an accident involving a 2000 kg truck originally traveling south and a 1200 kg car orignially traveling west. The two vehicles became attached when the collision occured and came to rest 9.18 meters away from the point of collision at an angle of 51.34 degrees south of west. The coefficient of friction between the vehicles and the road is µk = 0.8 Calculate the initial speeds of the truck and the car. Hints: Use the work done by friction between the collision point to the final location to find the kinetic energy, and thus velocity of both masses just after their collision. Then it becomes a 2-d momentum problem. Problems 8: Chapter 9 - Problems 38 Additional Suggested Problems: Chapter 9 - Problems 33, 53, 60, 71
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