Question

A bumper, consisting of a nest of three springs, is used to arrest the horizontal motion of a large mass which is traveling at 27 ft/sec as it contacts the bumper. The two outer springs cause a deceleration proportional to the spring deformation. The center spring increases the deceleration rate when the compression exceeds 3 in. as shown on the graph. Determine the maximum compression x of the outer springs.

Answer 1

Can this problem be addressed using energy or are you required to solve looking only at force and acceleration.

Answer 2

it's based on the graph

Answer 3

Boi you bumped ahead of meh

Answer 4

of well the initial velocity is 27 and the change in velocity is going to be the area under the graph. So you need to find at what position is the area equal to 27.

Answer 5

*I think

Answer 6

ok well I guess not, since time is not your axis,

Answer 7

I think energy is the way to go here, since I see you are using a physics question I guess from the name

Answer 8

it's a sort of combination of engineering mechanics and physics

Answer 9

So if we solve for k/m we can use conservation of energy without mass.

Answer 10

So for springs the magnitude of F=kx or a=kx/m so for your graph for the first period when the two springs are working we have kx/m=1000/3 x so k /m of two spring is 1000/3, once all 3 springs are working, the third spring contributes also a coefficient of 1000/3

Answer 11

so in total I would go with

1/2 m v^2=1/2k(x^2) for two springs + 1/2 k (x-3)^2) for third spring where x is that max compress

Answer 12

so dividing the m out and substituting, .5*27^2=.5*1000/3* x^2 + .5*1000/3*(x-3)^2

Answer 13

Finally solve the quadratic

Answer 14

Thank you :)

Answer 15

the unit is ft right?

Answer 16

uh no, inches in this case