PY 205 Ch2 HW4

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A 0.55 kg block of ice is sliding by you on a very slippery floor at 3.5 m/s. As it goes by, you give it a kick perpendicular to its path. Your foot is in contact with the ice block for 0.003 seconds. The block eventually slides at an angle of 23 degrees from its original direction (labeled # in the diagram). The overhead view shown in the diagram is approximately to scale. The arrow represents the average force your toe applies briefly to the block of ice. Which of the possible paths shown in the diagram corresponds to the correct overhead view of the block's path? B Which components of the block's momentum are changed by the impulse applied by your foot? (Check all that apply. The diagram shows a top view, looking down on the xz plane.) z component y component * component What is the unit vector in the direction of the block's momentum after the kick? p = What is the x-component of the block's momentum after the kick? Pfx = 2.8 x kg . m/s Remember that p = Iplp. What is the magnitude of the block's momentum after the kick? Ipl = 3.12 x kg . m/'s Use your answers to the preceding questions to find the z-component of the block's momentum after the kick (drawing a diagram is helpful): Pfz = -1.37 x kg . m/'s What was the magnitude of the average force you applied to the block? IFavgl = 455 * N Additional Materials WeBookA spring of stiffness 108 N/m, and with relaxed length 0.25 m, stands vertically on a table, as shown in the figure. Instead of compressing the spring with a heavy block, with your hand you push straight down on the spring until your hand is only 0.2 m above the table. (Assume that the positive y-axis points upward and is normal to the table.) Relaxed Push down (a) What is now the vector _, with the spring compressed? m (b) What is the magnitude of E? m (c) What is the unit vector ? (d) What is the stretch, s, including the correct sign? m (e) What is the force F exerted on your hand by the spring? F = Additional Materials WeBookNear the surface of the Earth, what is the magnitude of the gravitational force acting on a 7 kg mass? Fgrav = N Acting on a 70 kg mass? Fgray = NPush down, release from length A spring has a relaxed length of 23 cm (0.23 m) and its spring stiffness is 12 N/m. You glue a 71 gram block (0.071 kg) to the top of the spring, and push the block down, compressing the spring so its total length is 16 cm. You make sure the block is at rest, then at time t = 0 you quickly move your hand away. The block begins to move upward, because the upward force on the block by the spring is greater than the downward force on the block by the Earth. Calculate approximately y vs. time for the block during a 0.24-second interval after you release the block, by applying the Momentum Principle in three steps each of 0.08-second duration. To avoid buildup of small errors causing you to lose credit, in Step 2 we use your answers to Step 1 even if they are not correct, and in Step 3 we use your answers to Step 2 even if they are not correct. We will only consider the y components in the following calculations, because there is no change in x or z. STEP 1 Force: Just after releasing the block, calculate the force exerted on the block by the spring, the force exerted on the block by the Earth, and the net force: Fspring,y FEarth,y = Fnet,y = Momentum update: Just after releasing the block, the momentum of the block is zero. Approximate the average net force during the next time interval by the force you just calculated. At t = 0.08 seconds, what will the new momentum and velocity of the block be? Py kg . m/'s m/s Position update: Initially the bottom of the block is at y = 0.16 m. Approximationg the average velocity in the first time interval by the final velocity, what will be the new position of the bottom of the block at time t = 0.08 seconds? m STEP 2 Force: At the new position, calculate the force exerted on the block by the spring, the force exerted on the block by the Earth, and the net force: Fspring,y = FEarth,y = Fnet,y= Momentum update: Approximate the average net force during the next time interval by the force you just calculated. At time t = 2 x 0.08 = 0.16 seconds, what will the new momentum and velocity of the block be? Py kg . m/'s Vy= m/s Position update: Approximationg the average velocity in the second time interval by the final velocity, what will be the new position of the bottom of the block at time t = 2 x 0.08 = 0.16 seconds? IT STEP 3 Force: At the new position, calculate the force exerted on the block by the spring, the force exerted on the block by the Earth, and the net force: Fspring,y= FEarth, y= Fnet,y = Momentum update: Approximate the average net force during the next time interval by the force you just calculated. At time t = 3 x 0.08 = 0.24 seconds, what will the new momentum and velocity of the block be? Py kg . m/'s m/s Position update: Approximationg the average velocity in the third time interval by the final velocity, what will be the new position of the bottom of the block at time t = 3 x 0.08 = 0.24 seconds? m Applying the Momentum Principle in this way to predict motion is a "numerical integration" -- adding up the cumulative effects of many impulses in a succession of time intervals. As you can see, this can be very tedious if done by hand, and this task is much more easily carried out by programming a computer to do all the repetitive operations. However, it is important to do some calculations by hand to understand in detail the procedure that you would program a computer to carry out