- #1

## 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.