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The force net of a spring system

  • Thread starter ucentralf15
  • Start date
  • #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



-----------------------------------------------------------

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



-----------------------------------------------------------

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.
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,848
1,645
Don't forget to put the units on your numbers.
Also please show your working - otherwise it looks like you are pulling numbers out of the air.

You last position looks like 0.119357m from the base
... the force from the spring is given by (0.9N/m)(0.119357m)=0.10742N ... not what you got.
 
Last edited:

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