Question

One hazard of space travel is debris left by previous missions. there are several thousand objects orbiting earth that are large enough to be detected by radar, but there are far greater numbers of very small objects, such as flakes of paint. calculate the force exerted in newtons by a 0.160 mg chip of paint that strikes a spacecraft window at a relative speed of 3.00 ✕ 103 m/s and sticks, given the collision lasts 6.00 ✕ 10−8 s. (enter the magnitude.)

Answer 1

The chip, during the collision, has a change in momentum:
Δp = m · (v₂ - v₁)

The final speed is equal to zero, since it sticks to the spacecraft, therefore:
Δp = m · v
      = 1.6×10⁻⁷ · 3×10³
      = 4.8×10⁻⁴ kg·m/s
where we transformed the mass into the proper units of measurement (kg).

This change in momentum is equal to the impulse J:
Δp = J = F · t

We can solve for F
F = J / t = Δp / t
   = 4.8×10⁻⁴ / 6×10⁻⁸
   = 8.0×10³ N

Hence, the force exerted by the chip on the spacecraft is F = 8000N.