Use the exact values you enter to make later calculations. Relaxed length Push down, release from rest A spring has a relaxed length of 34 cm (0.34 m) and its spring stiffness is 14 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 15 cm. You make sure the block is at rest, then at time r=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 0.06-second interval after you release the block, by applying the Momentum Principle in three steps each of 0.02-second duration. We will only consider the y components in the following calculations, because there is no change in x orz

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Chapter6: Energy Of A System
Section: Chapter Questions
Problem 29P
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Use the exact values you enter to make later calculations.
Relaxed
length
Push down,
release from
rest
A spring has a relaxed length of 34 cm (0.34 m) and its spring stiffness is 14 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 15 cm. You make sure the block is at rest, then at time
r=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 0.06-second interval after you
release the block, by applying the Momentum Principle in three steps each of 0.02-second duration.
We will only consider the y components in the following calculations, because there is no change in x orz
Transcribed Image Text:Use the exact values you enter to make later calculations. Relaxed length Push down, release from rest A spring has a relaxed length of 34 cm (0.34 m) and its spring stiffness is 14 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 15 cm. You make sure the block is at rest, then at time r=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 0.06-second interval after you release the block, by applying the Momentum Principle in three steps each of 0.02-second duration. We will only consider the y components in the following calculations, because there is no change in x orz
Part 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 (remember near the Earth's surface, the gravitational force due to the Earth is very nearly constant):
N
Fspring-
FEarthy =
Forty =
Your answer is partially correct.
Vy=
ym
Part 3
Momentum update: Calculate the average net force during the next time interval by the force you just calculated. At time = 2 x
0.02 0.04 seconds, what will the new momentum and velocity of the block be?
Py = i 0.03492
kg-m/s
Farthy
Fact, y =
2.53
-0.784
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 timer = 2 x0.02-0.04 seconds?
ym
1.746
i
i
i 0.4365
0.16746
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 (remember near the Earth's surface, the gravitational force due to the Earth is very nearly constant):
N
Fspring-
N
N
m
m/s
Momentum update: Calculate the average net force during the next time interval by the force you just calculated. At timer = 3 x
0.02 0.06 seconds, what will the new momentum and velocity of the block be?
Py =
kg-m/s
m
m/s
N
N
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 timer 3 x0.02-0.06 seconds?
Transcribed Image Text:Part 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 (remember near the Earth's surface, the gravitational force due to the Earth is very nearly constant): N Fspring- FEarthy = Forty = Your answer is partially correct. Vy= ym Part 3 Momentum update: Calculate the average net force during the next time interval by the force you just calculated. At time = 2 x 0.02 0.04 seconds, what will the new momentum and velocity of the block be? Py = i 0.03492 kg-m/s Farthy Fact, y = 2.53 -0.784 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 timer = 2 x0.02-0.04 seconds? ym 1.746 i i i 0.4365 0.16746 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 (remember near the Earth's surface, the gravitational force due to the Earth is very nearly constant): N Fspring- N N m m/s Momentum update: Calculate the average net force during the next time interval by the force you just calculated. At timer = 3 x 0.02 0.06 seconds, what will the new momentum and velocity of the block be? Py = kg-m/s m m/s N N 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 timer 3 x0.02-0.06 seconds?
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