Question

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The 210-kg capsule hit the ground at 311 km/h and penetrated the soil to a depth of 81.0

Assuming it to be constant, what was its acceleration (in m/s2) during the crash?
cm

Answer 1

There are a couple ways to answer this, the first would be to use a kinematic equation to solve for how long it took the capsule to slow down and then use the change in momentum over the change in time to solve for the force. The shorter way will be to use the kinematic equation to solve for the acceleration and then multiply by the mass to get force as follows. To express as a multiple of the capsules weight we then simply need to divide the force by the weight of the capsule (weight, not mass).

1) vf^2 = vi^2 + 2a(xf-xi)
0^2 = (-86.39m/s)^2 + 2a(-0.81m-0m) * Convert km/hr to m/s and keep your signs consistent
a= 4607 m/s^2
2) F=ma= (210kg)*(4607m/s^2)= 967456 N = ~967 kN
3) Fg= (210 kg)*(9.81 m/s^2) = 2060 N
4) 967456 N / 2060 N = 470 times the capsules weight

Answer 2

311km/h = 86.389 m/s
Initial KE
= 0.5 * 210 * 86.389^2 J

work done by force of ground
= F * 0.81 J

0.5 * 210 * 86.389^2 = 0.81 F

F = 967433.58 N

capsule's weight W= 210 * 9.81 = 2060.1 N

F = 469.6 times capsule weight ---answer

Answer 3

u = 311*5/18 = 86.39 m/s

v = 0

v^2-u^2 = 2*a*s

==> a = v^2-u^2 / 2*s

= 0 - 86.39^2 / (2*0.81)

= -53.32 m/s^2

Answer 4