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## Homework Statement

A dynamics cart 1 ahs a mass of 1.8 kg and is moving with a velocity of 4.0 m/s

along a frictionless track. Dynamics cart 2 has a mass of 2.2 kg and is moving at 6.0 m/s

. The carts collide in a head-on elastic collision cushioned by a spring with spring constant k = 8.0 x 104 N/m.

Determine the compression of the spring in cm, during the collision when cart 2 is moving at 4.0m/s

and

Calculate the maximum compression of the spring in cm

so the givens are these:

m1 = 1.8 kg

m2 = 2.2 kg

v1=4 m/s

v2 = 6 m/s

K = 80000N/m

a)

Ek = 1/2m2v2`

Ek = 1/2(2.2kg)(4m/s

Determine the compression of the spring in cm, during the collision when cart 2 is moving at 4.0m/s

and

Calculate the maximum compression of the spring in cm

## The Attempt at a Solution

so the givens are these:

m1 = 1.8 kg

m2 = 2.2 kg

v1=4 m/s

v2 = 6 m/s

K = 80000N/m

a)

Ek = 1/2m2v2`

Ek = 1/2(2.2kg)(4m/s

)^2

Ek = 17.6 J

17.6 J = 1/2kx^2

17.6 J = 1/2(80000N/m)x^2

0.020976176 m = x

b)

I am not sure what to do for this particular part?

v1`=(m1-m2)/(m1+m2)v1 + (m1xm2)/(m1+m2)v2

v1`=0.4 m/s

Ek = 17.6 J

17.6 J = 1/2kx^2

17.6 J = 1/2(80000N/m)x^2

0.020976176 m = x

b)

I am not sure what to do for this particular part?

v1`=(m1-m2)/(m1+m2)v1 + (m1xm2)/(m1+m2)v2

v1`=0.4 m/s

+5.94 m/s

v1`= 6.34 m/s

v2` = (2m1)/(m1+m2)v1 + (m2-m1)/(m1+m2)v2

v2` = 3.6 m/s

v1`= 6.34 m/s

v2` = (2m1)/(m1+m2)v1 + (m2-m1)/(m1+m2)v2

v2` = 3.6 m/s

+ 0.6 m/s

v2` = 3 m/s

Ektot = 1/2m1v1^2 + 1/2m2v2^2

Ektot = 14.4 J +39.6 J

Ektot = 54 J

Ektot` = 1/2m1v1`^2 + 1/2m2v2`^2

Ektot` = 36.17604 J + 9.9 J

Ektot` = 46.07604 - but they are not the same since its elastic they are supposed to be the same

v2` = 3 m/s

Ektot = 1/2m1v1^2 + 1/2m2v2^2

Ektot = 14.4 J +39.6 J

Ektot = 54 J

Ektot` = 1/2m1v1`^2 + 1/2m2v2`^2

Ektot` = 36.17604 J + 9.9 J

Ektot` = 46.07604 - but they are not the same since its elastic they are supposed to be the same

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