- #1
ucentralf15
Homework Statement
A spring has a relaxed length of 20 cm (0.20 m) and its spring stiffness is 9 N/m. You glue a 80 gram block (0.08 kg) to the top of the spring, and push the block down, compressing the spring so its total length is 10 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 y vs. time for the block during a 0.21-second interval after you release the block, by applying the Momentum Principle in three steps each of 0.07-second duration.
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 = 0.9
FEarth,y = -0.784
Fnet,y = 0.116
Momentum update: Just after releasing the block, the momentum of the block is zero. Calculate the average net force during the next time interval by the force you just calculated. At t = 0.07 seconds, what will the new momentum and velocity of the block be?
py = .00812
vy = 0.1015
Position update: Initially the bottom of the block is at y = 0.10 m. Calculating 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 = 0.07 seconds?
y = .107105
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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 = 0.836055
FEarth,y = -0.784
Fnet,y = .052055
Momentum update: Calculate the average net force during the next time interval by the force you just calculated. At time t = 2 × 0.07 = 0.14 seconds, what will the new momentum and velocity of the block be?
py = 0.01176385
vy = 0.147048125
Position update: Calculating 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 × 0.07 = 0.14 seconds?
y = .119357
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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 = 0.72579
FEarth,y = -0.784
Fnet,y =
Momentum update: Calculate the average net force during the next time interval by the force you just calculated. At time t = 3 × 0.07 = 0.21 seconds, what will the new momentum and velocity of the block be?
py =
vy =
Position update: Calculating 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 × 0.07 = 0.21 seconds?
y =
Homework Equations
The Attempt at a Solution
For step three I am having problems with the net force. I tried adding both the force of the spring and the force of the Earth but it keeps telling me it is incorrect.