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A 2.00kg package is released on a 53.1 degree inclide 4.00m from a long spring which is attached at the bottom of the incline (so to picture this there is a ramp with a spring and 4m above the end of the spring there sits this package), the force constant of the spring is 120 N/m. The coefficents of friction are us = 0.40 and uk = 0.20, the mass of the spring is negligable.

a) what is the speed of the package before it hits the spring?

h = 4.00m sin (53.1)

Sum Forces in Y Direction = N - mg cos 53.1 = 0; N = mg cos 53.1

Frictional Force = .20(mg cos 53.1)

W = Frictional Force * 4m = 9.41 J

K1 + U1 + W = K2 + U2

U1 + W = K2 + U2

mgh + w = 1/2m(v2)^2

2gh + 2w/m = (v2)^2

v2 = 7.3m/s

Not sure about that answer.

b) what is the maximum compression of the spring?

1/k(m(v1)^2 + 2w = (x2)^2

x2 = -1.02 m

Again not sure.

c) when the package rebounds back up the ramp how close does it get to its original position.

U1 + W = U2

1/2k(x1)^2 + w = 1/2k(x2)^2

(x2)^2 = x1^2 - 2w/k

x2 = .94m, so its 3.06m away from its starting point.

I am not sure about any of these answers, if incorrect please advise what i'm doign wrong.

Brian

a) what is the speed of the package before it hits the spring?

h = 4.00m sin (53.1)

Sum Forces in Y Direction = N - mg cos 53.1 = 0; N = mg cos 53.1

Frictional Force = .20(mg cos 53.1)

W = Frictional Force * 4m = 9.41 J

K1 + U1 + W = K2 + U2

U1 + W = K2 + U2

mgh + w = 1/2m(v2)^2

2gh + 2w/m = (v2)^2

v2 = 7.3m/s

Not sure about that answer.

b) what is the maximum compression of the spring?

1/k(m(v1)^2 + 2w = (x2)^2

x2 = -1.02 m

Again not sure.

c) when the package rebounds back up the ramp how close does it get to its original position.

U1 + W = U2

1/2k(x1)^2 + w = 1/2k(x2)^2

(x2)^2 = x1^2 - 2w/k

x2 = .94m, so its 3.06m away from its starting point.

I am not sure about any of these answers, if incorrect please advise what i'm doign wrong.

Brian

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To give you a visualization of the situation. Think of an elevator shaft with a spring at the bottom, rotated from 90 degrees straight up to n degrees above the horizontal. Thats what it looks like. The spring is parallel with the ramp and the box slides on the ramp....

Yes, i think they want friction to still be acting as it compresses the spring.

Brian

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Brian

For parts (b) & (c) did you set the origin at the point where the spring is in equilibrium? Because the sum of (b) & (c) should equal (4.0m) if the origin is at the point of equilibrium, is this correct?

Brian

If "original position" was the end of the relaxed spring, then

"how close does it get" would seem to suggest that it does not quite reach it, but since I thought it went beyond there, I would have expected "how far does it get"

Math / Science

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