A student proposes a design for an automobile crash barrier in which a 1850-kg s

Question

A student proposes a design for an automobile crash barrier in which a 1850-kg sport utility vehicle moving at 24.0 m/s crashes into a spring of negligible mass that slows it to a stop. So that the passengers are not injured, the acceleration of the vehicle as it slows can be no greater than 5.00g .

Part A

Find the required spring constant k . In your calculation, disregard any deformation or crumpling of the vehicle and the friction between the vehicle and the ground.

Part B

Find the distance the spring will compress in slowing the vehicle to a stop.

Part C

What disadvantages are there to this design?

Explanation / Answer

Wtot = K2 - K1 to the vehicle

Call the bumper compression x and the initial speed vo. The work done by the spring is 1/2*kx^2 and K2 = 0.

part a)

1/2kx^2 = 1/2mv^2

kx < 5mg

k < 25mg^2/v^2

k < 25 * (1850 ) ( 9.8 ) ^2 / (24)^2 = 7711.5 N/m

part b )

x > v^2/5g

x = (24)^2/5*9.8

x = 11.755 m

part c )

the car stops only momentarily and then returns to its original speed when the spring returns to its original length

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