Force: At the new position, calculate the force exerted on the block by the spri

Question

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 = N FEarth,y = N Fnety = N Momentum update: Approximate the average net force during the next time interval by the force you just calculated. At time t = 2 times 0.09 = 0.18 seconds, what will the new momentum and velocity of the block be? py = kg . m/s vy = m/s Position update: Approximating 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 times 0.09 = 0.18 seconds? y = m 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 = N FEarth,y = N Fnet,y = N Momentum update: Approximate the average net force during the next time interval by the force you just calculated. At time t = 3 times 0.09 = 0.27 seconds, what will the new momentum and velocity of the block be? Py = kg . m/s vy = m/s Position update: Approximating 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 times 0.09 = 0.27 seconds? y = 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.

Explanation / Answer

STEP 3 : Fspring = K*(0.33-0.33412) = 9*(0.33-0.33412) = -0.03708 N Fearth = -9.8*0.075 = -0.735 N Fnet = -0.77208 N py - 0.07355 = -0.77208 * 0.09 py = 0.0040628 kgm/s vy = py/m = 0.05417 m/s y = 0.33412 m +0.09*0.05417 = 0.33899 m

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